Unimechanics Fundamental Sciences Systems as a System of Revolutions in Solid Mechanics

by

© Ph. D. & Dr. Sc. Lev Gelimson

Academic Institute for Creating Fundamental Sciences (Munich, Germany)

Physical Monograph

The “Collegium” All World Academy of Sciences Publishers

Munich (Germany)

12th Edition (2012)

11th Edition (2010)

10th Edition (2004)

9th Edition (2003)

8th Edition (2001)

7th Edition (2000)

6th Edition (1995)

5th Edition (1994)

4th Edition (1993)

3nd Edition (1992)

2nd Edition (1987)

1st Edition (1977)

Abstract

The usual mechanics of deformable solids is based on considering usual dimensional mechanical stresses which depend on the choice of the system of measurement units and, therefore, are neither invariant nor universal. In addition, usual stresses themselves are not related to their limits and hence are unable to directly express their degrees of risk (danger). There are no known simple namely analytical solutions to nontrivial truly three-dimensional problems without often inappropriate assumptions on the relative smallness of some characteristic solids sizes such as thickness even in thick plate theory. Moreover, there are no known general power-law solutions to the homogeneous harmonic and biharmonic equations which play key roles not only in elasticity theory. The finite element method and many other standard numerical methods themselves give uncheckable "black box" results and do not provide their error, reliability, and risk estimation. These methods create the illusion of allegedly harmful solutions (actually, pseudosolutions) to problems without understanding the nature and characteristics of solids deformation and give huge nonobservable data sets often hiding very important qualitative regularities and laws. Therefore, testing the numerical methods results by means of namely analytical methods is necessary. And if the results of numerical and analytical methods are consistent, then their complementary harmony is extremely useful both scientifically and practically.

Universal stresses, or unistresses, which can be defined and determined via the natural transformations of conventional dimensional stresses give the name to universal mechanics of deformable solids, or unimechanics which can be also representable in conventional dimensional mechanical stresses.

Uniphilosophy (Exclusively Constructive Creative Philosophy) Principles as a System of Revolutions in Philosophy

Fundamental principles of uniphilosophy (exclusively constructive creative philosophy) build a fundamental system of revolutions in philosophy, in particular, the following subsystems.

1. Fundamental Principles of Uniphilosophy as a Fundamental Subsystem of Revolutions in Philosophy

The fundamental subsystem of revolutions in philosophy includes the following fundamental principles of uniphilosophy:

1. Exceptional natural constructivism (with the complete absence of artificial destructiveness).

2. Free efficient creativity (exclusively practically purposeful, verified, and efficient unlimitedly free creativity, intuition, and phantasy flight).

3. Scientific optimism and duty (each urgent problem can and must be solved adequately and efficiently enough).

4. Complication utilization (creating, considering, and efficiently utilizing only necessary and useful also contradictory objects and models, as well as difficulties, problems, and other complications).

5. Symbolic feasibility (at least symbolic existence of all the necessary and useful even contradictory objects and models).

2. Advanced Principles of Uniphilosophy as an Advanced Subsystem of Revolutions in Philosophy

The advanced subsystem of revolutions in philosophy includes the following advanced principles of uniphilosophy:

1. Exclusively efficient intuitive evidence and provability (reasonable fuzziness, intuitive ideas without axiomatic rigor if necessary and useful).

2. Unrestrictedly flexible constructivism (if necessary even creating new knowledge (concepts, approaches, methods, theories, doctrines, and even sciences) to adequately set, consider, and solve urgent problems).

3. Tolerable simplicity (choosing the best in the not evidently unacceptable simplest).

4. Perfect sensitivity, or conservation laws universality (no uncompensated change in a general object conserves its universal measures).

5. Exact discrimination of noncoinciding objects and models (possibly infinitely or overinfinitely large with infinitesimal or overinfinitesimal distinctions and differences).

6. Separate similar (proportional) limiting universalizability (the reduction of objects, systems, and their models to their own similar (proportional) limits as units).

7. Collective coherent reflectivity, definability, modelablity, expressibility, evaluability, determinability, estimability, approximability, comparability, solvability, and decisionability (in particular, in truly multidimensional and multicriterial systems of the expert definition, modeling, expression, evaluation, determination, estimation, approximation, and comparison of objects, systems, and models qualities which are disproportionate and hence incommensurable and not directly comparable, as well as in truly multidimensional and multicriterial decision-making systems).

3. Some Other Principles of Uniphilosophy

Among other principles of uniphilosophy are the following:

1. Truth priority (primacy of practically verified purely scientific truths and criteria prior to commonly accepted dogmas, views, agreements, and authority, with all due respect to them).

2. Peaceful pluralism (with peaceful development of scientific and life diversity).

3. Efficient creative inheritance (efficiently using, analyzing, estimating, and developing already available knowledge and information).

4. Efficient constructive freedom (unrestrictedly free exclusively constructive and useful self-determination and activity, in particular, in knowledge and information research, creation, and development).

5. Fundamentality priority (primacy of conceptual and methodological fundamentals).

6. Knowledge efficiency (only useful quality (acceptability, adequacy, depth, accuracy, etc.) and amount (volume, completeness, etc.) of knowledge, information, data, as well as creation, analysis, synthesis, verification, testing, structuring, systematization, hierarchization, generalization, universalization, modeling, measurement, evaluation, estimation, utilization, improvement, and development of objects, models, knowledge, information, and data along with intelligent management and self-management of activity).

7. Mutual definability and generalizability (relating successive generalization of concepts in definitions with optional linear sequence in knowledge construction).

8. Efficient unificability of opposites only conditionally distinguished (such as real/potential, real/ideal, specific/abstract, exact/inexact, definitively/possibly, pure/applied, theory/experiment/practice, nature/life/science, for example, the generally inaccurate includes the accurate as the limiting particular case with the zero error).

9. Partial laws sufficiency (if there are no known more general laws).

10. Focus on discoveries and inventions (dualistic unity and harmony of academic quality and originality, discovering phenomena of essence, inventive climbing, helpful knowledge bridges, creative multilingualism, scientific art, anti-envy, learnability, teachability, and terminology development).

The Principles of Uniphysics as the System of Revolutions in the Principles of Physics

The principles of uniphysics constitute the system of scientific revolutions in the principles of physics including the following subsystems.

The Fundamental Principles of Uniphysics as the Fundamental Subsystem of Revolutions in the Principles of Physics

The fundamental subsystem of revolutions in the principles of physics includes the following fundamental principles of uniphysics:

1. Urgent problems priority, exclusiveness, and typificability (adequately setting, exhaustively solving, and efficiently using urgent problems types only (with completely avoiding unnecessary considerations) as the unique criterion of the necessity and usefulness of creating and developing new knowledge).

2. Intuitive conceptual and methodological fundamentality priority (creating and efficiently using unified knowledge foundation due to fundamental general systems including objects, models, and intuitive fuzzy principles, concepts, and methodology).

3. Philosophical, mathematical, physical, and engineering meaningfulness, synergy, and intelligence primacy (with intuitive clarity, learnability, teachability, and efficient beauty as the united duality and harmony of quality and quantity, as well as of applicability and acceptability).

4. Controllability (the step-by-step testability, verifiability, estimability, invariance, immutability, strength, stability, and reliability of data, intermediate and final results, information, and general knowledge including concepts, approaches, methods, theories, doctrines, and sciences with the possibility of their correction, comprehensive improvement, generalization, universalization, structuring, systematization, and hierarchization).

5. Creating, inventing, and discovering directionality (the focus on creating and inventing new knowledge and the know-how, as well as on reasonably discovering new phenomena and laws of nature, along with the possibility of the generalization, universalization, systematization, and hierarchization of discoveries and inventions and with the united duality of scientific and technical architecture).

The Universalizability Principles of Uniphysics as the Universalizability Subsystem of Revolutions in the Principles of Physics

The universalizability subsystem of revolutions in the principles of physics includes the following universality principles of uniphysics:

1. Free efficient physical controlability (the expressibility, universalizability, invariance, measurability, estimability, and improvability of physical quantities, models, transformations, criteria, and knowledge).

2. Free efficient quality controlability (modelability, expressibility, universalizability, invariance, measurability, estimability, and improvability including providing and efficiently using the unity of variety and diversity, multicriteriality, polymethodicity, and multivariability in universally invariantly modeling, expressing, evaluating, measuring, and estimating data processing and approximation quality (via unierrors) along with accuracy and/or acceptability certainty via unireserves, unireliabilities, and unirisks without artificial randomization in deterministic problems).

3. Conservation laws universalizability (in the overinfinitesimal, the infinitesimal, the finite, the infinite, and the overinfinite).

4. The universalizability of laws of nature.

The General Noncriticality Principles of Uniphysics as the General Noncriticality Subsystem of Revolutions in the Principles of Physics

The general noncriticality subsystem of revolutions in the principles of physics includes the following general noncriticality principles of uniphysics:

1. Critical and limiting relations efficiency (the efficiency of the critical and limiting relations between the determining initial parameters of a problem).

2. General noncriticality (the joint definability and determinacy of subcritical, critical, and supercritical states, processes, and phenomena in a general structured system via joint generally noncritical relations).

3. General nonlimitability (the joint definability and determinacy of underlimiting, limiting, and overlimiting states, processes, and phenomena in a general structured system via joint generally nonlimiting relations).

4. Parameters reserves separability (the separability of the proper own reserves of the independent determining initial parameters in a problem).

The Unimathematical Principles of Uniphysics as the Unimathematical Subsystem of Revolutions in the Principles of Physics

The unimathematical subsystem of revolutions in the principles of physics includes the following unimathematical principles of uniphysics:

1. Tolerable simplicity (including the necessity and possibility of the tolerably simplest acceptable analytical solutions).

2. Unimodelability, uniexpressibility, unievaluability, and unimeasurability (using the unimathematical uninumbers, perfectly sensitive uniquantities as universal measures without any absorption and violations of conservation laws in the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal, as well as unioperations, unisets, uniaggregates (unicontents), and unisystems).

3. Uniestimability, uniapproximability, and uniproblem unisolvability (using the unimathematical unierrors, unireserves, unireliabilities, and unirisks, as well as uniproblem unisolving methods, theories, doctrines, and sciences).

4. Unicomputability (using the computer fundamental sciences system, the overcoming complication fundamental sciences system, and the unimathematical data processing fundamental sciences system).

The Other Principles of Uniphysics

Among the other principles of uniphysics are the following:

1. The efficiency of transparency and ergonomicity (the analytical, numerical, and graphical unity, clarity, visibility, observability, and reviewability of knowledge, information, data, conditions, and results).

2. Creative inheritance efficiency (refining, correcting, improving, generalizing, and universalizing classical results, establishing the limits of their applicability, acceptability, adequacy, and efficiency).

3. Comprehensive self-responsibility concentration (the unity and indivisibility of research, expressing, interpreting, explaning, and presenting the results with the creative and efficient utilization of routine).

Unimechanics Principles

Unimechanics principles build a system of revolutions in mechanics which consists of the following subsystems.

The Problem Setting Subsystem of Unimechanics Principles

The problem setting subsystem of revolutions including such unimechanics principles:

1. Urgent problems priority and exclusiveness (adequately setting, exhaustively solving, and efficiently using urgent problems types only (with completely avoiding unnecessary considerations) as the unique criterion of the necessity and usefulness of creating and developing new knowledge).

2. Typificability (of real objects and design schemes for load distribution with determining the basic types whose homogeneous linear combinations exhaustively express the general types).

3. Tolerable analytical simplicity (the necessity and possibility of the tolerably simplest acceptable analytical solutions, in particular, the general power-law solutions to the homogeneous harmonic and biharmonic equations).

4. True three-dimensionality (excluding any assumptions on the relative smallness of some characteristic solids sizes such as thickness even in thick plate theory).

The Unimathematical Subsystem of Unimechanics Principles

The unimathematical subsystem of revolutions including such unimechanics principles:

1. Uniproblem uniparametrizability.

2. Uniproblem unilinearizability.

3. The infinite and overinfinite generalizability of generally inhomogeneous linear combinations.

4. The infinite and overinfinite generalizability of linear dependence and linear independence.

5. Correspondences classes system properizability.

6. Uniproblem operators required functions classes system properizability.

7. Unequicomplicated uniproblem unirestructurability.

8. The unipartitionability an unequicomplicated system of equations into a solvable and an estimable subsystems.

The Problem Solving Subsystem of Unimechanics Principles

The problem solving subsystem of revolutions including such unimechanics principles:

1. Mechanical stress universalizability.

2. The discretizability of a solid into a few macroelements if necessary and useful only.

3. Approximate quasisolution error concentrability in explicit macroelement surface residuals.

4. Stress analysis unierror minimizability.

5. Minimized residual correction distributivity.

6. Complex unioptimizability.

Unimechanics Fundamental Sciences System

Unimechanics includes the following fundamental mathematical and mechanical sciences:

1. Analytical Uniparametrization Science

Analytical uniparametrization science includes general analytical theories and methods useful for solving uniproblems, in particular, unisystems of functional (often differential and/or integral) equations with initial and/or boundary conditions in many typical urgent scientific and life problems. (In them, there are often no known appropriate analytical methods of their solving whereas the finite element method gives huge numeric arrays inconvenient for improving objects and systems.) General uniparametrization theory searches for a general solution to a uniproblem in its general pseudosolutions as the uniparametrized unisystem of unisystems differing by the unisystems of the univalues of some uniparameters, e.g. point methods for solving uniproblems whose all unknowns are constants only. General (possibly infinite or overinfinite) linear-combination theory provides explicitly determining the general solution to a uniproblem as a unisystem of equations in such a system of classes of the unknown functions which is proper for the unisystem of the uniproblem operators each of which takes values ​​in its own (separate) class of finite, infinite, or overinfinite homogeneous linear combinations of generally linearly independent coordinate functions. That is, their even infinite or overinfinite homogeneous linear combination vanishes if and only if all its factors vanish. This naturally generalizes the classical definition of a finite linear independence to infinities and overinfinities. A further natural generalization gives such a unisystem of the proper classes of the unisystem of the unicorrespondences as the unisystem of their common unisistem of the domains of definition that each uniimage in any unicorrespondence is a general homogeneous linear combination of some generally linearly independent unisystem which may be own (separate) for each unicorrespondence. In this case, each of the equations of the unisystem is reduced to its unisubsystem of the conditions of vanishing the homogeneous linear combination which is the value of the operator of the equation. If the proper class of each of the unknown functions is parameterized, then this unisystem of equations is reduced to a unisystem of equations whose unknowns are numerical values of the parameters. If the proper parametric class of each of the desired functions is the set of homogeneous linear combinations of their generally linearly independent coordinate functions and all the operators in the uniproblem are linear with respect to the homogeneous linear combinations to be transformed, then the resulting algebraic unisystem is linear. If the system of the coordinate functions of each of these classes is a basic one, then the resulting solution is exhaustive (comprehensive). And if this system is full, then an approximate quasisolution (with any desired accuracy) can be obtained in the form of a set of finite homogeneous linear combinations of the coordinate functions of the corresponding classes. In the particular single-element case of the unisistem and of the values of the operator of a single equation in its domain of definition with unit quantities, the system of the classes of the unknown functions which is proper for the unisystem of the operators is reduced to a class of unknown functions which is proper for the sole operator transforming each of these functions into some function of the same class, in this case, into a homogeneous linear combination of the coordinate functions of the class. But this homogeneous linear combination is not necessarily proportional to the preimage with a very flexible generalization of the concept of an eigenfunction. Above all, unlike known eigenfunctions, orthonormal bases, and nonorthogonal fundamental solutions, some sufficiently general proper functions classes for many linear operators are obvious. This provides explicitly solving uniproblems due to the principle of tolerable simplicity.

2. Analytical Unirestructuring Science

Analytical unirestructuring science includes general analytical theories and methods efficient by solving unequicomplicated uniproblems, in particular, unisystems of functional (often differential and/or integral) equations with initial and/or boundary conditions in many typical urgent scientific and life problems. The created theory of preliminarily unirestructuring an unequicomplicated uniproblem most reasonably changes its overall structure on the basis of the principle of tolerable simplicity with the smallest possible redistribution of the roles of individual unisubsystems of such a uniproblem as a unisystem. For example, general unipartition theory divides an original system of unequicomplicated equations into two subsystems, namely a solvable subsystem (with the greatest possible number of the simplest equations of the system) and an estimable subsystem (with the smallest possible number of the most complicated equations of the system). The solvable subsystem of equations allows us to explicitly find an exact solution or an approximate quasisolution to this subsystem (by the principle of tolerable simplicity) as a general pseudosolution to the original system of unequicomplicated equations so that this pseudosolution optionally contains some uncertain parameters. The estimable subsystem of equations is used simplistically only, namely for estimating this general pseudosolution to the initial system of unequicomplicated equations via unimathematical unierrors, unireserves, unireliabilities, and unirisks. Their improvement by the principle of tolerable simplicity provides determining the best values ​​of these uncertain parameters. It can be useful to additionally include some consequences (e.g. by averaging or pointwise satisfying) ​​of the equations of the estimable subsystem into the solvable subsystem, provided that such equations in their original forms remain in the estimable subsystem. The ambiguity of unipartitioning causes the natural nonuniqueness of approximate quasisolutions with the possibility of self-verifiability and mutual verifiability. This general unipartition theory develops and generalizes known approaches with preliminarily exactly satisfying either determining equations or boundary conditions. It is also possible to combine this theory with linear-combination theory used for analytically solving the solvable subsystem.

3. Power Analytic Macroelement Science

Power analytic macroelement science which general analytical theories and methods efficient by solving uniproblems, in particular, unisystems of functional (often differential and/or integral) equations with initial and/or boundary conditions in many typical urgent scientific and life problems. In contrast to the finite element method, this science provides namely analytical exact solutions (if they exist) or the simplest approximate quasisolutions. Power analytic macroelement science applies analytical uniparametrization science (e.g. linear-combination theory) to a uniproblem. In particular, for the first time, it became possible to obtain the general power-law solutions to the harmonic and biharmonic homogeneous equations in three-dimensional and axisymmetric problems of mathematical theory of elasticity, respectively, with their obvious proper classes of arbitrary power series as stress functions with variable coefficients as parameters. All displacements and stresses are uniquely expressed via these functions by the Love linear differential operators. Formerly known particular power solutions to these equations are not exhaustive and separately (altogether) provide very restricted (doubtful, respectively) possibilities to satisfy the boundary conditions. The advantages of the comprehensive general power-law solutions are similar to those due to introducing series in addition to finite sums. In the three-dimensional axisymmetric problem for an elastic cylindrical body (solid), it has been proven that there exists such an explicit fundamental type of loading schemes with one free edge that the homogeneous linear combinations of the schemes of this type exhaustively build the general type of the schemes. If in the problem for the fundamental types, all the nonzero boundary conditions are expandable in power series, then the generally linear independence of the power functions leads to the four subsystems of infinite linear algebraic equations for a single sequence of the numerical values ​​of variable parameters. General solutions to the homogeneous analogs of these subsystems are some homogeneous linear combinations of the successive powers of the zeros of the two Bessel functions and their two new analogs. This allows us not only to establish the presence or absence of an exact power-law solution to the problem, but also to explicitly and immediately find such a solution if it exists. Otherwise, we have to be satisfied with an approximate quasisolution using a finite sum instead of a series. For the first time, it was shown that the Love stress function biharmonicity is not only sufficient but also necessary for accurately satisfying all the equations of equilibrium and strain compatibility, so this approach is exhaustive. This is the general power-law solution that provides discovering the phenomenon that the boundary conditions can limit the exponent of the stress function not only from below but also from above, which could not be achieved in the principle via the welll-known particulal solutions. Hence it is clear the reason for the narrowness of the range available at the exact elastic solutions. The ultimate role of the well-known linear generalization of the Lame solution has been also proven. If the exact solution is impossible, then the residuals of coupling a simple approximate quasisolution explicitly derived with the boundary conditions on the lateral surfaces of the adjacent macroelement or of the cylinder are the only violations. These residuals can be improved, e.g. via minimizing the maximum or the power mean of the residual modulus or via pointwise vanishing the residual. This leads to generalizations of plate theory and thick plate theory. Power analytic macroelement science is essentially exact and provides determining the exact power-law solution (if it exists) to the given problem or to another problem with similar boundary conditions on the lateral surface so that the loading schemes of these problems differ by the improved residuals. The ratios of the greatest moduli of the residual stresses and displacements to the greatest moduli of the actual stresses and displacements themselves, respectively, gives simply and exactly estimating quasisolution admissibility and adequacy. Tolerably simplest distributing the residuals (discrepancies) corrections in the cylinder volume makes errors in the equations of equilibrium and strain compatibility it reduces the errors of the quasisolution namely to the given problem due exactly satisfying its all boundary conditions.

4. Integral Analytic Macroelement Science

4. Integral analytic macroelement science includes general analytical theories and methods useful for solving uniproblems, in particular, unisystems of functional (often differential and/or integral) equations with initial and/or boundary conditions in many typical urgent scientific and life problems. In contrast to the finite element method, this science leads to the tolerably simplest namely analytical exact solutions or approximate quasisolutions. To dramatically simplify determing them, integral analytic macroelement science applies analytical unirestructuring science, in particular, general unipartition theory, to a uniproblem. It becomes possible to avoid expansions into series and solving the problems of coupling with improving the residuals with the further tolerably simplest distribution of the already improved residuals corrections, to make no own explicit errors, and even to consider the whole body as a single macroelement. Integral analytic macroelement science can determine an exact solution (if it exists, e.g. in the Lame problem also linearly generalized) or a sufficiently close approximation to it. In the same three-dimensional axisymmetric problem of the mathematical theory of elasticity, all the boundary conditions are satisfied exactly. The solvable subsystem includes the both relatively simple equations of equilibrium and the simpler equations of strain compatibility. The estimable subsystem includes the only remaining certainly much more complicated equation of strain compatibility. The solvable subsystem of equations provides explicitly and exactly expressing all the normal stresses via the shear stress due to the determined integro-differential operators. Exactly solving the estimable system with the very complicated integro-differential equation for the distribution of the shear stress is unrealistic. According to the principle of tolerable simplicity, determine the simplest statically possible distribution of the shear stress with exactly satisfying all the boundary conditions. Then the solvable subsystem of equations provides explicitly and exactly expressing all the normal stresses via this shear stress distribution due to the determined integro-differential operators. Moreover, all the normal stresses are determined much mor accurately than the shear stress due to exactly satisfying not only all the boundary conditions, but also the both equilibrium equations and the simplest of the two equations of compatibility. The estimable subsystem of equations is used only simplistically, namely only for estimating the accuracy of the resulting exact solution or approximate quasisolution to the complete original system of unequicomplicated equations of equilibrium and strain compatibility via unimathematical unierrors, unireserves, unireliabilities, and unirisks. It can be useful to additionally include some consequences (e.g. by averaging or pointwise satisfying) ​​of the equations of the estimable subsystem into the solvable subsystem, provided that such equations in their original forms remain in the estimable subsystem. The ambiguity of unipartitioning causes the natural nonuniqueness of approximate quasisolutions with the possibility of self-verifiability and mutual verifiability. This general unipartition theory develops and generalizes known approaches with preliminarily exactly satisfying either determining equations or boundary conditions. It is also possible to combine this theory with linear-combination theory used for analytically solving the solvable subsystem.

The System of Revolutions in Deformable Solid Mechanics

The system of revolutions in the mechanics of deformable solids includes the following subsystems.

1. The Universal Stress Subsystem of Revolutions in Deformable Solid Mechanics

The universal stress subsystem of revolutions includes, in particular:

1. Scalar universal stress definition and determination by constantly loading via dividing each usual dimensional principal stress by the modulus of the individual strength limit of this principal stress so that this limit holds in uniaxial stress state and has the same direction and the same sign as this principal stress.

2. Vectorial universal stress definition and determination by variably loading via the definition and determination of the universal stress cycle equidangerous to the complete program (process) of each separate usual dimensional principal stress whose unordered number remains constant during the whole time variably loading so that the mean and the amplitude universal stresses of this cycle are the abscissa and the ordinate of the desired universal stress vector, respectively.

3. Solid mechanics equations presentation in the universal stresses.

2. The Unimathematical Subsystem of Revolutions in Deformable Solid Mechanics

The unimathematical subsystem of revolutions, in particular:

1. Uniproblem uniparametrization.

2. Uniproblem unilinearization.

3. Generally inhomogeneous inear combination infinitization.

4. Generally inhomogeneous inear combination overinfinitization.

5. General linear dependence and independence.

6. A proper system of classes for a system of mappings or correspondences.

7. A system of classes of required functions which is proper for a system of uniproblem operators.

8. Unirestructuring unequicomplicated uniproblems.

9. Unipartitioning an unequicomplicated system of equations into a solvable and an estimable subsystems.

10. The general power-law solutions to the harmonic and biharmonic equations.

3. The Stress Analysis Subsystem of Revolutions in Deformable Solid Mechanics

The stress analysis subsystem of principal innovations, in particular:

1. Considering the whole body as a single macroelement.

2. Power and integral analytic macroelement sciences.

3. Setting and solving nontrivial truly three-dimensional problems of elasticity theory.

4. Setting and solving nontrivial truly three-dimensional optical-mechanical problems.

4. The Error Tolerance Subsystem of Revolutions in Deformable Solid Mechanics

The error tolerance subsystem of principal innovations, in particular:

1. Approximate quasisolution error concentration in explicit macroelement surface residuals.

2. Minimized residual correction (compensation) distribution.

3. Stress analysis unierrors.

5. The Phenomenon Discovery Subsystem of Revolutions in Deformable Solid Mechanics

The phenomenon discovery subsystem of principal innovations, in particular:

1. The necessity of Love stress function biharmonicity for satisfying all the equations of axisymmetric equilibrium and strain compatibility.

2. The existence of the basic types of loading schemes whose homogeneous linear combinations exhaustively express the general types.

3. Bilateraly limiting power-law stress function degree via boundary conditions.

4. The limiting role of the linear generalization of the Lame solution.

5. The possibility of the multiple overdetermination of a type of problems.

6. The possibility of multiple differences in the bases curvatures of a deformable three-dimensional cylindrical body.

7. The significant influence of the stress and strain state of the cylindrical glass element of a porthole on the longitudinal defocusing only of a submarine optical system.

8. The significant influence of the internal base curvature only of the cylindrical glass element of a porthole on the longitudinal defocusing of a submarine optical system.

9. Multiply reducing the longitudinal defocusing of a submarine optical system with a deformable illuminator (deep-sea porthole) and especially its glass element via the optical system initial longitudinal defocusing opposite to the average working defocusing.

10. The existence of the critical values ​​of the tightening (compressing) axial force in the groupwise (multiple-solid) axisymmetric contact thermoelasticity with friction, namely of the two principal critical values corresponding to transitions from the total mutual slippage through combining the local zones either of mutual slippage or of mutual linkage (coupling, adhesion) to the total mutual linkage, as well as of the intermediate critical values (between the two principal critical values) corresponding to appearing or disappearing separate local zones either of mutual slippage or of mutual linkage.

11. The existence of the two symmetrical end zones of the length of a heat-collected combined cylinder with the mutual axial slippage of the cylinder layers and with the exponential growth both of the moduli of the axial stresses in the layers and of the contact pressure between the layers from the classical values ​​at the cylinder ends toward the cylinder length midpoint.

12. The existence of the heat-collected combined cylinder critical length whose exceeding leads to appearing the intermediate middle cylinder length zone of the mutual axial linkage (coupling) of the cylinder layers with the uniform axial stresses in the layers and with the uniform contact pressure between them which is greater than the classical value (by 40 per cent for a steel cylinder).

13. The existence of the two asymmetric end zones of mutual axial slippage which are separated by the intermediate middle zone of the mutual axial linkage (coupling) of the layers of a press-fit assembled combined cylinder so that this intermediate middle zone has half the length of the cylinder by the equal Poisson ratios of the cylinder layers materials, as well as the uniform axial stresses in the cylinder layers and the uniform contact pressure between them, whereas the end zones have the exponential growth of the moduli of the axial stresses in the cylinder layers and of the contact pressure from the classical values ​​at the ends toward the cylinder length midpoint.

Basic Results and Conclusions

References

[1] Encyclopaedia of Mathematics / Managing editor M. Hazewinkel. Volumes 1 to 10. Kluwer Academic Publ., Dordrecht, 1988-1994

[2] Lev Gelimson. Generalization of Analytic Methods for Solving Strength Problems [In Russian]. Drukar Publishers, Sumy, 1992

[3] Lev Gelimson. General Strength Theory. Drukar Publishers, Sumy, 1993

[4] Lev Gelimson. The method of least normalized powers and the method of equalizing errors to solve functional equations. Transactions of the Ukraine Glass Institute, 1 (1994), 209-213

[5] Lev Gelimson. General estimation theory. Transactions of the Ukraine Glass Institute, 1 (1994), 214-221

[6] Lev Gelimson. Basic New Mathematics. Drukar Publishers, Sumy, 1995

[7] Lev Gelimson. Quantianalysis: Uninumbers, Quantioperations, Quantisets, and Multiquantities (now Uniquantities). Abhandlungen der WIGB (Wissenschaftlichen Gesellschaft zu Berlin), 3 (2003), Berlin, 15-21

[8] Lev Gelimson. General Problem Theory. Abhandlungen der WIGB (Wissenschaftlichen Gesellschaft zu Berlin), 3 (2003), Berlin, 26-32

[9] Lev Gelimson. Quantisets Algebra. Abhandlungen der WIGB (Wissenschaftlichen Gesellschaft zu Berlin), 3 (2003), Berlin, 262-263

[10] Lev Gelimson. Elastic Mathematics. Abhandlungen der WIGB (Wissenschaftlichen Gesellschaft zu Berlin), 3 (2003), Berlin, 264-265

[11] Lev Gelimson. Elastic Mathematics. General Strength Theory. The "Collegium" All World Academy of Sciences Publishers, Munich (Germany), 2004, 496 pp.

[12] Lev Gelimson. Providing helicopter fatigue strength: Flight conditions [Megamathematics]. Structural Integrity of Advanced Aircraft and Life Extension for Current Fleets, Proc. of the 23rd ICAF Symposium, 2005, Hamburg, Vol. II, pp. 405-416

[13] Lev Gelimson. Science Unimathematical Test Fundamental Metasciences Systems. Mathematical Journal of the “Collegium” All World Academy of Sciences, Munich (Germany), 12 (2012), 1

[14] Bridgman, P. W. Collected Experimental Papers, Vols. 1 to 7, Harvard University Press, Cambridge, Massachusetts, 1964

[15] Goldenblatt, I. I. and Kopnov, V. A. Strength and Plasticity Criteria for Structural Materials [In Russian]. Mashinostroenie Publishers, Moscow, 1968

[16] Hosford, W. F. A generalized isotropic yield criterion. Trans. A. S. M. E., 1972, Ser. E 2, p. 290-292

[17] Pisarenko, G. S. and Lebedev, A. A. Deformation and Strength of Materials with a Complex Stress State [In Russian]. Naukova Dumka Publishers, Kiev, 1976

[18] Goldenblatt I. I., Bazhanov V. L., Kopnov V. A. Long-Term Strength in Engineering [In Russian]. Mashinostroenie, Moscow, 1977

[19] Lebedev, A. A., Kovalchuk, B. I., Giginyak, F. F., and Lamashevskii, V. P. Mechanical Properties of Structural Materials with a Complex Stress State [In Russian]. Naukova Dumka Publishers, Kiev, 1983

[20] Handbuch Struktur-Berechnung (1998), Industrie-Ausschuss-Struktur-Berechnungsunterlagen, Prof. Dr.-Ing. Schwarmann, L. (Ed.), Bremen.

[21] Encyclopedia of Materials - Science and Technology. Edited by Buschow, K.H. Jürgen; Cahn, Robert W.; Flemings, Merton C.; Ilschner, Bernhard; Kramer, Edward J.; Mahajan, Subhash. Volumes 1-11. Elsevier, 2001

[22] Yu M. H. Advances in strength theories for materials under complex stress state in the 20th Century. Appl. Mech. Rev., 2002, 55, No. 3, 169–218.

[23] Yu M. H. Unified Strength Theory and Its Applications. Springer-Verlag, Berlin-Heidelberg-New York, 2004

[24] Lev Gelimson. The generalized structure for critical state criteria. Transactions of the Ukraine Glass Institute, 1 (1994), 204-209

[25] Lev Gelimson. General strength theory. Dedicated to Academician G. S. Pisarenko. Abhandlungen der WIGB (Wissenschaftlichen Gesellschaft zu Berlin), 3 (2003), Berlin, 56-62

[26] Lev Gelimson. Critical State Theory. In: Review of Aeronautical Fatigue Investigations in Germany During the Period March 2003 to May 2005, Ed. Dr. Claudio Dalle Donne, SC/IRT/LG-MT-2005-039 Technical Report, Aeronautical fatigue, ICAF2007, EADS Corporate Research Center Germany, 2005, 67-68

[27] Lev Gelimson. Providing helicopter fatigue strength: Unit loads [Fundamental strength sciences]. Structural Integrity of Advanced Aircraft and Life Extension for Current Fleets, Proc. of the 23rd ICAF Symposium, 2005, Hamburg, Vol. II, pp. 589-600

[28] Lev Gelimson. Fatigue of Metallic Materials and Structures vs. Composites in General Strength Theory. Mechanical Monograph. The “Collegium” All World Academy of Sciences Publishers, Munich (Germany), 2006

[29] Lev Gelimson. Fundamental Material Strength Sciences: Theories and Applications. Strength Monograph. The “Collegium” All World Academy of Sciences Publishers, Munich (Germany), 2006

[30] Lev Gelimson. Regarding the Ratio of Tensile Strength to Shear Strength in General Strength Theory. In: Review of Aeronautical Fatigue Investigations in Germany During the Period May 2005 to April 2007, Ed. Dr. Claudio Dalle Donne, Pascal Vermeer, CTO/IW/MS-2007-042 Technical Report, Aeronautical fatigue, ICAF2007, EADS Innovation Works Germany, 2007, 44-46

[31] Lev Gelimson. Correcting and Further Generalizing Critical State Criteria in General Strength Theory. In: Review of Aeronautical Fatigue Investigations in Germany During the Period May 2005 to April 2007, Ed. Dr. Claudio Dalle Donne, Pascal Vermeer, CTO/IW/MS-2007-042 Technical Report, Aeronautical fatigue, ICAF2007, EADS Innovation Works Germany, 2007, 47-48

[32] Lev Gelimson. General Linear Strength Science. Strength Monograph. The “Collegium” All World Academy of Sciences Publishers, Munich (Germany), 2008

[33] Lev Gelimson. Generalization of the Tresca Criterion in General Strength Theory. In: Review of Aeronautical Fatigue Investigations in Germany during the Period May 2007 to April 2009, Ed. Dr. Claudio Dalle Donne, Pascal Vermeer, CTO/IW/MS-2009-076 Technical Report, International Committee on Aeronautical Fatigue, ICAF 2009, EADS Innovation Works Germany, 2009, 52-53

[34] Lev Gelimson. Generalization of the Huber-von-Mises-Henky Criterion in General Strength Theory. In: Review of Aeronautical Fatigue Investigations in Germany during the Period May 2007 to April 2009, Ed. Dr. Claudio Dalle Donne, Pascal Vermeer, CTO/IW/MS-2009-076 Technical Report, International Committee on Aeronautical Fatigue, ICAF 2009, EADS Innovation Works Germany, 2009, 54-55

[35] Lev Gelimson. Uniform Stress Fundamental Science (on Strength Criteria Generally Considering Influence of Pressure and the Intermediate Principal Stress). Strength Monograph. The “Collegium” All World Academy of Sciences Publishers, Munich (Germany), 2009

[36] Lev Gelimson. Shear to Normal Stress Fundamental Science (on Strength Criteria Generally Considering Relations between the Shear and Normal Limiting Stresses). Strength Monograph. The “Collegium” All World Academy of Sciences Publishers, Munich (Germany), 2009

[37] Lev Gelimson. Strength criteria generally considering influence of pressure and the intermediate principal stress. Strength of Materials and Structure Elemernts, Abstracts of the International Conference Dedicated to the 100th Birthday of the Founder of the Institute for Problems of Strength of the National Academy of Sciences of Ukraine Georgy Stepanovich Pisarenko, 28-30 September 2010, Kyiv (Kiev), Ukraine, Vol. 2, pp. 229-231

[38] Lev Gelimson. General linear strength theory. Strength of Materials and Structure Elements, Abstracts of the International Conference Dedicated to the 100th Birthday of the Founder of the Institute for Problems of Strength of the National Academy of Sciences of Ukraine Georgy Stepanovich Pisarenko, 28-30 September 2010, Kyiv (Kiev), Ukraine, Vol. 2, pp. 232-234

[39] Lev Gelimson. Strength criteria generally considering relations between the shear and normal limiting stresses. Strength of Materials and Structure Elemernts, Abstracts of the International Conference Dedicated to the 100th Birthday of the Founder of the Institute for Problems of Strength of the National Academy of Sciences of Ukraine Georgy Stepanovich Pisarenko, 28-30 September 2010, Kyiv (Kiev), Ukraine, Vol. 2, pp. 235-237

[40] Lev Gelimson. General Power Strength Theory in Fundamental Material Strength Sciences. In: Review of Aeronautical Fatigue Investigations in Germany during the Period 2009 to 2011, Ed. Dr. Claudio Dalle Donne, Katja Schmidtke, EADS Innovation Works, CTO/IW/MS-2011-055 Technical Report, International Committee on Aeronautical Fatigue, ICAF 2011, 2011, 49-50

[41] Lev Gelimson. Fundamental Science of Strength Data Unification, Modeling, Analysis, Processing, Approximation, and Estimation. In: Review of Aeronautical Fatigue Investigations in Germany during the Period 2009 to 2011, Ed. Dr. Claudio Dalle Donne, Katja Schmidtke, EADS Innovation Works, CTO/IW/MS-2011-055 Technical Report, International Committee on Aeronautical Fatigue, ICAF 2011, 2011, 61-62

[42] Filonenko-Borodich M. M. Mechanical Strength Theories [In Russian]. Moscow University Publishers, Moscow, 1961, 92 pp.

[43] Ishlinsky A. Yu. Hypothesis of strength of shape change [In Russian]. Uchebnye Zapiski Moskovskogo Universiteta, Mekhanika, 1940, 46

[44] Drucker D. C. A more foundational approach to stress-strain relations. Proc. of 1st US-Natl. Congress Appl. Mech., ASME, 1951, P. 487-491

[45] Malinin N. N. Applied Theory of Plasticity and Creep [In Russian]. Mashinostroenie, Moscow, 1975, 400 pp.

[46] Guest J. J. On the strength of ductile materials under combined stress. Philos. Mag., 1900, 50, 69-133

[47] Scoble W. A. The strength and behavior of ductile materials under combined stress. Philos. Mag., 1906, 12, 533-547

[48] Scoble W. A. Ductile materials under combined stress. Philos. Mag., 1910, 16, 116-128

[49] Hancock E. L. Williams W. B. Experiments on Combined Stress. Part 1. Philos. Mag., 1906, 12

[50] Hancock E. L. Williams W. B. Experiments on Combined Stress. Part 2. Philos. Mag., 1908, 15

[51] Pashkov P. O. Plasticity and Fracture of Metals [In Russian]. Sudpromgiz, Saint Petersburg, 1950

[52] Ratner S. I. Strength and Plasticity of Metals [In Russian]. Gosoborongiz, Moscow, 1949

[53] Daunis M. A. Investigation of Cyclic Deformation Diagrams in Tension-Compression and Shear [In Russian]. Thesis. Kaunas Polytechnic Institute, Kaunas, 1964

[54] Pisarenko G. S., Troshchenko V. T., Krasovsky A. Ya. Investigation of mechanical properties of porous iron in tension and torsion. Report 2 [In Russian]. Poroshkovaya Metallurgiya, 1965, 7, 88-96

[55] Mogi K. Fracture and flow of rocks under high triaxial compression. J. Geophys., 1971, Res. 76, 1255-1269

[56] Michelis P. True triaxial cyclic behavior of concrete and rock in compression. International Journal of Plasticity, 1987, 3, Issue 3, 249-270

[57] Michelis P. Polyaxial Yielding of Granular Rock. J. Engrg. Mech., 1985, 111, Issue 8, 1049-1066

[58] Takahashi M., Koide H. Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000m. Rock at Great Depth. V. Maury, D. Fourmaintraux (eds). Rotterdam, Balkema, 1989, 19-26

[59] Chang C., Haimson B. True triaxial strength and deformability of the KTB deep hole amphibolite. J. Geophys., 2000, Res. 105, 18999-19013

[60] Haimson B., Chang C. A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly Granite. Int. J. Rock Mech. and Mining Sci., 2000, 36, 285-296

[61] Kwaśniewski M., Takahashi M. Behavior of a sandstone under axi- and asymmetric compressive stress conditions. The 4th Asian Rock Mechanics Symposium Rock Mechanics in Underground Construction, Singapore, November 8, 2006

[62] Descamps F., Tshibangu J. P. Modelling the limiting envelopes of rocks in the octahedral plane. Oil & Gas Science and Technology. Rev. IFP, 2007, 62, No. 5, 683-694

[63] Lev Gelimson. Unimathematical Modeling Fundamental Sciences System. Monograph. The “Collegium” All World Academy of Sciences, Munich (Germany), 2011

[64] Lev Gelimson. Unimathematical Data Processing Fundamental Sciences System. Monograph. The “Collegium” All World Academy of Sciences, Munich (Germany), 2011

[65] Lev Gelimson. Unimathematical Approximation Fundamental Sciences System. Monograph. The “Collegium” All World Academy of Sciences, Munich (Germany), 2011

[66] Lev Gelimson. Unimathematical Estimation Fundamental Sciences System. Monograph. The “Collegium” All World Academy of Sciences, Munich (Germany), 2011

[67] Lev Gelimson. General Problem Fundamental Sciences System. Monograph. The “Collegium” All World Academy of Sciences, Munich (Germany), 2011

[23] Timoshenko S.: Strength of Materials. 3rd edition. Krieger Publishing Company, 1976

[24] Pisarenko, G. S. y otros : Manual de Resistencia de Materiales. Editorial MIR, Moscú, 1989

Military Handbook. Metallic Materials and Elements for Aerospace Vehicle Structures. MIL-HDBK-5H, 1998

[9] Marin, J. (1957), Theories of strength for combined stresses and nonisotropic materials, J. Aeronaut. Sci., 4.

[10] Nadai, A. L. (1950), Theory of Flow and Fracture of Solids, McGraw-Hill, N. Y.

[11] Forrest, P. G. (1962), Fatigue or Metals, Pergamon Press, Oxford.

[12] Haigh (1920), The strain energy function and the elastic limit, Engineering, 109, p. 158.

[13] Timoshenko, S. P. (1956), Strength of Materials, Van Nostrand Co., Inc., Princeton, N. J.

[1] Galilei G., Discorsi e dimostrazioni matematiche intorno a due nuove scienze. Leiden, 1638

[2] Mariotto E., Traite du mouvement des eaux, (posthumously),de la Hire M. ed., 1686; Œuvres de Mariotte. Leiden, 1717; English transl. by Desvaguliers J. T. London, 1718

[3] Coulomb C. A., Essai sur une application des regles demaximis et minimis a quelques problemes de statique, relatifs al’architecture, Memoires de Mathematique et de Physique, presentesa l’ Academie, Royale des Sciences par divers Savans, et lus dansses Assemblees, 7, 343–382, Paris, 1773, 1776; English translation: Note on anapplication of the rules of maximum and minimum to some staticalproblems, relevant to architecture, Heyman J., 1997, 41–74

[4] Rankine W. J. M., Manual of Applied Mechanics, 1st edition, 1861; 21st edition, 1921

[5] Tresca H., Sur I’ecoulement des corps solids soumis a defortes pression, Comptes Rendus hebdomadaires des Seances del’Academie des Sciences, Paris, 59 (1864), 754-758

[6] de Saint-Venant, Memoire sur l’establissement des equationsdifferentielles des mouvements interieurs operes dans les corpssolides ductiles au dela des limites ou l’e´lasticite´ pourrait les ramenera leur premier e´tat, Comptes Rendus hebdomadaires des Seancesde l’Academie des Sciences, 70 (1870), 473–480

[7] Mohr O., Welche Umstande bedingen die Elastizitatsgrenzeund den Bruch eines Materials? Zeitschrift des Vereins DeutscherIngenieure Band, 44 (1900), 1524–1530

[8] Guest J. J., On the strength of ductile materials under combinedstress. Philos. Mag., 50 (1900), 69–133

[9] Huber M. T., Die spezifische Formänderungsarbeit als Maß der Anstrengung eines Materials. Czasopismo Techniczne, Lemberg (Lwow), 1904

[10] Hancock E. L. and Williams W. B., Experiments on Combined Stress. Phil. Mag., 12(1906) and 15(1908)

[11] Scoble W. A., The strength and behavior of ductile materialsunder combined stress. Philos. Mag., 12 (1906), 533–547

[12] Scoble W. A., Ductile materials under combined stress. Philos.Mag., 16 (1910), 116–128

[13] Mises R. von, Mechanik der festen Körper im plastisch-deformablen Zustand. Nachrichten der Gesellschaft der Wissenschaften, Göttingen, 1913

[14] Hencky H., Zur Theorie plastischer Deformationen. Zeitschrift angewandter Mathematik und Mechanik, 1924

[15] Ishlinsky A. Yu., Hypothesis of strength of shape change. Uchebnye Zapiski Moskovskogo Universiteta, Mekhanika,46 (1940) (in Russian)

[16] Davidenkov N. N., In favour and against a uniform theory of strength. Bulletin Engineering and Technology, 4 (1947), 121–129 (in Russian)

[17] Ratner S. I. Strength and Plasticity of Metals. Gosoborongiz Publishers, Moscow, 1949

[18] Pashkov P. O., Plasticity and Fracture of Metals. Sudpromgiz Publishers, Saint Petersburg, 1950

[19] Drucker D. C., A more foundational approach to stress-strainrelations, Proc. of 1st US-Natl. Congress Appl. Mech., ASME, 1951, 487–491

[20] Timoshenko S. P., History of Strength of Materials. McGraw-Hill, New York, 1953

[21] Marin J., Theories of strength for combined stresses and nonisotropic materials. J. Aeronaut. Sci. 4 (1957)

[22] Bridgman P. W., Collected Experimental Papers, Vols. 1 to 7. Harvard University Press Publ., Cambridge (Massachusetts), 1964

[23] Daunis M. A., Investigation of Cyclic Deformation Diagrams in Tension-Compression and Shear: Thesis. Kaunas Polytechnic Institute, 1964

[24] Pisarenko G. S., Troshchenko V. T., and Krasovsky A. Ya., Investigation of mechanical properties of porous iron in tension and torsion. Report 2. Poroshkovaya Metallurgiya, 7 (1965), 88-96

[25] Pisarenko G. S. and Lebedev A. A., Resistance of Materials to Deformation and Fracture at a Complex Stress State. Naukova Dumka Publishers, Kiev, 1969 (in Russian)

[26] Tsai S. W., A General Theory of Strength for Anisotropic Materials. Journal of Composite Materials, 5 (1971), No. 1, p. 58-80

[27] Malinin N. N., Applied Theory of Plasticity and Creep. Mashinostroenie Publishers, Moscow, 1975 (in Russian)

[28] Lebedev A. A., Methods of Mechanical Testing at a Complex Stress State. Naukova Dumka Publishers, Kiev, 1976 (in Russian)

[29] Pisarenko G. S. and Lebedev A. A., Deformation and Strength of Materials in Complex Stress State. Naukova Dumka Publishers, Kiev, 1976 (in Russian)

[30] Strength of Materials and Structural Elements in Extreme Conditions, Ed. G. S. Pisarenko. Vols. 1, 2. Naukova Dumka Publishers, Kiev, 1980 (in Russian)

2. Troshchenko V. T. Deformation and Fracture of Metals under High-Cycle Loading. – Kiev, Naukova Dumka, 1981. – 344 pp. – In Russian.

3. Lebedev A. A., Koval'chuk B. I., Giginyak F. F., Lamashevsky V. P. Mechanical Properties of Structural Materials at a Complex Stress State. Handbook. – Kiev, Naukova Dumka, 1983. – 366 pp. – In Russian.

4. Troshchenko V. T., Sosnovsky L. A. Strength of Metals and Alloys. Handbook in 2 parts. – Kiev, Naukova Dumka, 1987. – Part 1. – 509 pp. – Part 2. – 1304 pp. – In Russian.

20. Pisarenko G. S., Troshchenko V. T., Krasovsky A. Ya. Investigation of mechanical properties of porous iron in tension and torsion. Report 2 // Poroshkovaya Metallurgiya. – 1965. – 7. – P 88 – 96.

2. Pisarenko G.S., Yakovlev A.P., Matveev V.V. Handbook on Strength of Materials. – Kiev, Naukova Dumka, 1975. – 704 pp. – In Russian. – The same: in Spanish, – Moscow, 1979, – 696 pp. – The same in Spanish, 1985. – 696 pp. – The same in Spanish. – Moscow, 1989. – 694 pp. – The same in Portugese. – Moscow, 1985. – 682 pp. – The same in French. – Moscow, 1979. – 874 pp. – The same in French. – Moscow, 1985. – 874 pp.

[1] Tresca H. E. Memoire sur l'ecoulement des corps solides soumis a de fortes pressions. Comptes Rendus de l’Academie des Sciences, Paris, 1864, 59, 754-758

[2] Mohr O. Abhandlungen aus dem Gebiete der Technischen Mechanik. W. Ernst und Sohn, Berlin, 1914

[1] Huber M. T. Die spezifische Formänderungsarbeit als Maß der Anstrengung eines Materials. Czasopismo Techniczne, Lemberg (Lwow), 1904

[2] von Mises R. Mechanik der festen Körper im plastisch-deformablen Zustand. Nachrichten der Gesellschaft der Wissenschaften, Göttingen, 1913

[3] Henky H. Zur Theorie plastischer Deformationen. Zeitschrift angewandter Mathematik und Mechanik, 192

Tresca, H., Compt. Rend. Acad. Sci. (Paris), 1864, 59, 754

2. Huber, M. T., Czas. Techn. (Lwow), 1904, 22, 38

3. Mises, R. von, Göttingen Nachr. Math. Phys. K., 1913, 1, 582

4. Hencky, H., Z. Angew. Math. Mech., 1924, 4, 323

5. Galilei, G., Discorsi e dimonstrazioni matematiche intorno a due nuove scienze. Leiden, 1638

6. Coulomb, C. A., Mém. Math. Phys. Acad. Sci. (Paris), 1773, 7, 343

7. Pisarenko, G. S. and Lebedev, A. A., Deformation and Strength of Materials in Complex Stress State (in Russian). Naukova Dumka, Kiev, 1976

8. Marin, J., J. Aeronaut. Sci., 1957, 4

9. Hill, R., The Mathematical Theory of Plasticity. Clarendon Press, Oxford, 1950

10. Tsai, S. W., J. Composite Mater., 1971, 5, 58

11. Goldenblatt, I. I. and Kopnov, V. A., Strength and Plasticity Criteria for Structural Materials (in Russian). Mashinostroenie, Moscow, 1968

12. Lebedev, A. A., Kovalchuk, B. I., Giginyak, F. F., and Lamashevskii, V. P., Mechanical Properties of Structural Materials in Complex Stress State (in Russian). Naukova Dumka, Kiev, 1983

13. Kaliszky, S., Plasticity Theory and Engineering Applications. Elsevier, Amsterdam, 1989

14. Sobotka, Z., Theory of Plasticity and Limit Design of Plates. Elsevier, Amsterdam, 1989

15. Lemaitre, J. and Chaboche, J.-L., Mechanics of Solid Materials. Cambridge University Press, Cambridge, 1990

16. Lubliner, J., Plasticity Theory. Macmillan, New York, 1990

17. Maugin, G. A., The Thermomechanics of Plasticity and Fracture. Cambridge University Press, Cambridge, 1992

18. Ol'khovik, O. E., Kaminskii, A. A., Gelimson, L. G., et al., Strength Mater. (USA), 1984, 15, 8, 1127

19. Kaminskii, A. A., Gelimson, L. G., et al., Strength Mater. (USA), 1986, 17, 12, 1691

20. Lev Gelimson, Ph. D. thesis. Institute for Strength Problems, Acad. Sci., Kiev, 1987

21. Lev Gelimson, Generalization of Analytic Methods for Solving Strength Problems (in Russian). Drukar Publishers, Sumy, 1992

22. Lev Gelimson, General Strength Theory. Drukar Publishers, Sumy, 1993

23. Amel'yanovich, K. K., Gelimson, L. G., and Karintsev, I. B., Sov. J. Opt. Technol. (USA), 1993, 59, 11, 664

24. Amel'yanovich, K. K., Gelimson, L. G., and Karintsev, I. B., Strength Mater. (USA), 1994, 25, 10, 772

25. Lev Gelimson, Dr. Sc. thesis. Institute for Strength Problems, Nat. Acad. Sci., Kiev, 1994

26. Lev Gelimson, Transactions of the Ukraine Glass Institute, 1994, 1, 209 and 214

27. Lev Gelimson, Basic New Mathematics. Drukar Publishers, Sumy, 1995

28. Bridgman, P. W., Studies in Large Plastic Flow and Fracture. Harvard University Press, Cambridge, Mass., 1952

29. Lev Gelimson, Transactions of the Ukraine Glass Institute, 1994, 1, 204

30. Lev Gelimson, International Scientific and Technical Conference “Glass Technology and Quality”, 1993, 98

31. Timoshenko, S. P., History of Strength of Materials. McGraw-Hill, New York, 1953

32. Drucker, D. C., Proc. 1st US Nat. Congr. Appl. Mech. Edward Brothers Inc., Chicago, 1951, 487

33. Okhrimenko, G. M., Problemy Prochnosti (USSR) (in Russian), 1984, 5, 70

34. Lode, W., Z. Phys., 1926, 36, 913

[5] Hosford W. F. A generalized isotropic yield criterion. Trans. A. S. M. E., Ser. E 2 (1972), 290-292

Okhrimenko G. M. The strength of porcelain in biaxial compression. Problemy Prochnosti (1984), no. 5, 70-75

5. J. Marin (1962) Mechanical Behavior of Engineering Materials. Prentice-Hall

17. C. A. Coulomb (1773) Sur une application des regles de maximis et minimis a quelques problemes de statique relatifs a l'archltecture. Memoires Mathematique et de Physique. Acad. Sci. Paris 7, 343-382

18. W. J. M. Rankine (1858) A Manual of Applied Mechanics. 8 vols. London

19. H. E. Tresca (1864) Memoire sur l'ecoulement des corps solides soumis a de fortes pressions. Comptes Rendus de l’Academie des Sciences, Paris 59, 754-758

20. M. T. Huber (1904) Die spezifische Formänderungsarbeit als Maß der Anstrengung eines Materials. Czasopismo Techniczne, Lemberg (Lwow)

21. R. von Mises (1913) Mechanik der festen Körper im plastisch-deformablen Zustand. Nachrichten der Gesellschaft der Wissenschaften, Göttingen

22. H. Henky (1924) Zur Theorie plastischer Deformationen. Zeitschrift angewandter Mathematik und Mechanik

23. O. Mohr (1914) Abhandlungen aus dem Gebiete der Technischen Mechanik. W. Ernst und Sohn, Berlin

25. F. A. McClintock and A. S. Argon (1966) Mechanical Behaviour of Materials. Addison-Wesley, London

27. V. V. Fyodorov (1969) Analysis and development of theories of strength of materials [In Russian]. Transactions of the Tashkent Institute for Railway Engineering 40, 3-41

28. A. K. Malmeister, V. P. Tamuzh, and T. A. Teters (1972) Strength of Rigid Polymeric Materials [In Russian]. Zinatne, Riga

30. Encyclopedia of Physics. Chief Editor S. Flügge. Vol. 6a/1. Mechanics of Solids 1. Editor C. Truesdell (1973) Springer Verlag, Berlin, Heidelberg, N. Y.

31. L. M. Sedokov (1975) Mechanical Strength Theories [In Russian]. Tomsk Polytechnic Institute Publishers, Tomsk

36. Encyclopedia of Composite Materials and Components. Ed. M. Grayson (1983) N. Y.

37. Encyclopedia of Materials Science and Engineering. Ed. M. B. Bever (1986) Pergamon Press, N. Y.

38. V. T. Troshchenko and L. A. Sosnovskii (1987) Strength of Metals and Alloys in Fatigue [In Russian]. Naukova Dumka, Kiev

39. Yu. G. Vazhentsev (1978) Strength and Plasticity of Materials under External Pressure [In Russian]. Tomsk Polytechnic Institute Publishers, Tomsk

40. Yu. G. Vazhentsev (1978) Study of the strength of some brittle materials in triaxial stress state. Problemy Prochnosti 8, 65-67

43. V. A. Man'kovskii (1987) Strength and Reliability of Composites in Nonuniaxial Deformation. Znanie, Kiev

44. D. C. Drucker (1950) Some implication of work hardening and ideal plasticity. Quart. Appl. Math. 7, No. 4, 414-418

45. G. M. Okhrimenko (1984) Strength or porcelain in biaxial compression. Problemy Prochnosti 5, 70-75

46. R. von Mises (1928) Mechanik der plastischen Formänderungen von Kristallen. Zeitschrift für angewandte Mathematik und Mechanik 8, H. 3

47. J. Marin (1957) Theories of strength for combined stresses and nonisotropic materials. J. Aeronaut. Sci. 4

48. Haigh (1920) The strain energy function and the elastic limit. Engineering 109, 158

49. P. G. Forrest (1962) Fatigue or Metals. Pergamon Press, Oxford

L. B. Tsvik. Finite Element Method Application to Static Deformation [In Russian]. Irkutsk State University Publishers, Irkutsk, 1995

L. B. Tsvik. Triaxial Stress and Strength of Single-Layered and Multilayered High Pressure Vessels with Branch Pipes [In Russian]. Dr. Sc. Dissertation, Irkutsk, 2001

L. B. Tsvik. Computational Mechanics of Structural Elements Deformation and the Finite Element Method [In Russian]. GUPS Publishers, Irkutsk, 2005

L. B. Tsvik. Computer Technology, Stress and Strain Fields Modeling [In Russian]. Irkutsk State Technical University Publishing House, Irkutsk, 2005

In this paper the problem. Dry to handle. for 1978 is a fact - the destruction, where a rigid scheme of stress ..

L. B. Tsvik, P. G. Pimshteyn, E. G. Borsuk. Experimental studies of the stress-strain state of a multilayered cylinder with a monolithic input [In Russian]. Strength Problems, 1978, 4, 74-77

In the work 67 - tity of rooms specimen for mechanical testing in conditions of mild stress.

L. B. Tsvik. Specimen for mechanical testing of structural steel under cyclic loading [In Russian]. Track Facilities Problems in Eastern Siberia. Scientific papers of IrGUPS, 2005, 3, 200-203