Fundamental Defects of Classical Object Strength Sciences
by
© Ph. D. & Dr. Sc. Lev Gelimson
Academic Institute for Creating Fundamental Sciences (Munich, Germany)
Physical Journal
of the "Collegium" All World Academy of Sciences
Munich (Germany)
12 (2012), 4
Keywords: Object strength science, megascience, revolution, megastrength, megamathematics, overmathematics, unimathematical test fundamental metasciences system, knowledge, philosophy, strategy, tactic, analysis, synthesis, object, operation, relation, criterion, conclusion, evaluation, measurement, estimation, expression, modeling, processing, symmetry, invariance, bound, level, worst case, defect, mistake, error, reserve, reliability, risk, supplement, improvement, modernization, variation, modification, correction, transformation, generalization, replacement.
Introduction
There are many separate scientific achievements of mankind but they often bring rather unsolvable problems than really improving himan life quality. One of the reasons is that the general level of earth science is clearly insufficient to adequately solve and even consider many urgent himan problems. To provide creating and developing applicable and, moreover, adequate methods, theories, and sciences, we need their testing via universal if possible, at least applicable and, moreover, adequate test metamethods, metatheories, and metasciences whose general level has to be high enough. Mathematics as universal quantitative scientific language naturally has to play here a key role.
But classical mathematics [1] with hardened systems of axioms, intentional search for contradictions and even their purposeful creation cannot (and does not want to) regard very many problems in science, engineering, and life. This generally holds when solving valuation, estimation, discrimination, control, and optimization problems as well as in particular by measuring very inhomogeneous objects and rapidly changeable processes. It is discovered [2] that classical fundamental mathematical theories, methods, and concepts [1] are insufficient for adequately solving and even considering many typical urgent problems.
Megamathematics including overmathematics [2] based on its uninumbers, quantielements, quantisets, and uniquantities with quantioperations and quantirelations provides universally and adequately modeling, expressing, measuring, evaluating, and estimating general objects. This all creates the basis for many further megamathematics fundamental sciences systems developing, extending, and applying overmathematics. Among them are, in particular, science unimathematical test fundamental metasciences systems [3] which are universal.
Object Strength Science Unimathematical Test Fundamental Metasciences System
Object strength science unimathematical test fundamental metasciences system in megastrength [2] is one of such systems and can efficiently, universally and adequately strategically unimathematically test any object strength science. This system includes:
fundamental metascience of object strength science test philosophy, strategy, and tactic including object strength science test philosophy metatheory, object strength science test strategy metatheory, and object strength science test tactic metatheory;
fundamental metascience of object strength science consideration including object strength science fundamentals determination metatheory, object strength science approaches determination metatheory, object strength science methods determination metatheory, and object strength science conclusions determination metatheory;
fundamental metascience of object strength science analysis including object strength subscience analysis metatheory, object strength science fundamentals analysis metatheory, object strength science approaches analysis metatheory, object strength science methods analysis metatheory, and object strength science conclusions analysis metatheory;
fundamental metascience of object strength science synthesis including object strength science fundamentals synthesis metatheory, object strength science approaches synthesis metatheory, object strength science methods synthesis metatheory, and object strength science conclusions synthesis metatheory;
fundamental metascience of object strength science objects, operations, relations, and criteria including object strength science object metatheory, object strength science operation metatheory, object strength science relation metatheory, and object strength science criterion metatheory;
fundamental metascience of object strength science evaluation, measurement, and estimation including object strength science evaluation metatheory, object strength science measurement metatheory, and object strength science estimation metatheory;
fundamental metascience of object strength science expression, modeling, and processing including object strength science expression metatheory, object strength science modeling metatheory, and object strength science processing metatheory;
fundamental metascience of object strength science symmetry and invariance including object strength science symmetry metatheory and object strength science invariance metatheory;
fundamental metascience of object strength science bounds and levels including object strength science bound metatheory and object strength science level metatheory;
fundamental metascience of object strength science directed test systems including object strength science test direction metatheory and object strength science test step metatheory;
fundamental metascience of object strength science tolerably simplest limiting, critical, and worst cases analysis and synthesis including object strength science tolerably simplest limiting cases analysis and synthesis metatheories, object strength science tolerably simplest critical cases analysis and synthesis metatheories, object strength science tolerably simplest worst cases analysis and synthesis metatheories, and object strength science tolerably simplest limiting, critical, and worst cases counterexamples building metatheories;
fundamental metascience of object strength science defects, mistakes, errors, reserves, reliability, and risk including object strength science defect metatheory, object strength science mistake metatheory, object strength science error metatheory, object strength science reserve metatheory, object strength science reliability metatheory, and object strength science risk metatheory;
fundamental metascience of object strength science test result evaluation, measurement, estimation, and conclusion including object strength science test result evaluation metatheory, object strength science test result measurement metatheory, object strength science test result estimation metatheory, and object strength science test result conclusion metatheory;
fundamental metascience of object strength science supplement, improvement, modernization, variation, modification, correction, transformation, generalization, and replacement including object strength science supplement metatheory, object strength science improvement metatheory, object strength science modernization metatheory, object strength science variation metatheory, object strength science modification metatheory, object strength science correction metatheory, object strength science transformation metatheory, object strength science generalization metatheory, and object strength science replacement metatheory.
The object strength science unimathematical test fundamental metasciences system in megastrength [2] is universal and very efficient.
In particular, apply the object strength science unimathematical test fundamental metasciences system to classical object strength sciences.
Nota bene: Naturally, all the fundamental defects of classical material strength sciences discovered due to the material strength science unimathematical test fundamental metasciences system in megastrength [2] also hold in classical object strength sciences.
Fundamental Defects of Classical Material Strength Sciences
Even the very fundamentals of classical material strength sciences have evident cardinal defects of principle.
Modern engineering (astronautics, aircraft-building, ship-building, deep-sea industry, power engineering, electronics, chemical industry, building, etc.) requires optimal design of structural elements. It is based on a rational control of the necessary and sufficient strength of such elements and corresponding materials. Their types are diverse: ductile materials like metals; brittle alloys and nonmetals (glass, crystalline glass, concrete, and stone); anisotropic materials (fiber-reinforced ones and other composites). They are intended for extreme exploiting conditions (variable loading, high pressure, high or low temperature, radiation, etc.).
It is universally recognized that the most effective approach to solving strength problems in modern engineering is phenomenological. It provides considering more or less adequate mathematical, mechanical, physical, etc. models of materials and structural elements instead of real ones and uses mathematical (analytic and numeric) methods in theories of differential equations, elasticity, plasticity, creep, fracture, etc. to determine the usually triaxial stress state (in the stationary case) or process (in nonstationary loading) at each point of a structural element. It remains to compare the diverse triaxial stress states at all points of a solid (structural element) with one another by the degree of danger to reach the closest critical state (initiation of yielding, fracture etc.). Therefore, it is necessary to use so-called critical (limiting, ultimate) state (process) criteria (elasticity criteria, yield criteria, failure criteria, etc.) that reduce the problems to the simplest ones dealing with uniaxial stress states only investigated enough. To measure the proximity of a real stress state (process) to the closest critical one, safety factors might be used.
The well-known critical state and process criteria are separate for diverse materials types, have nothing in common with simple and universal fundamental laws of nature, and possess evident defects. Even if a ductile material is isotropic and has equal strength in tension and compression, the criteria ignore increasing strength in uniform triaxial compression. If a material has unequal strength in tension and compression, the criteria possess obviously restricted ranges of applicability and do not allow to compare arbitrary stress states with one another. No critical process criterion for anisotropic materials under variable loading, when the directions of the principal stresses at a solid's point under consideration can arbitrarily turn, is known at all.
Notata bene:
1. Modern engineering requires optimal design and rational control of resistant structural elements of ductile and brittle, isotropic and anisotropic materials under extreme stationary and variable loading. This needs adequately determining the danger of the real spatial stress process at any point of a solid with respect to the closest critical (limiting, ultimate) stress process. Critical (limiting, ultimate) spatial stress processes should be obtained from critical process criteria by using strength data available in simple experiments. The dangers of real spatial stress processes should be given by measures of the proximity of a real stress process to the closest critical one.
2. A usual stress is not a pure number, depends on the choice of physical dimensions (units) for a force and a length, is not numerically invariant by unit transformations, and alone represents no degree of the danger of itself even in stationary loading. If a solid’s material is not isotropic with equal strength in tension and compression, it is not reasonable even in stationary loading to compose functions of different stresses without their adequate weighing because of mixing their values having distinct limits and hence diverse degrees of danger. If loading is variable, the same holds even for different values of the process of a stress alone.
3. The known critical state criteria separate for diverse materials types, unlike simple and universal fundamental laws of nature, have contradictions, restricted and vague ranges of adequacy, sometimes lose physical sense, not always bring a suitable equivalent stress, and are applicable in the stationary case only. For an isotropic ductile material with equal strength in tension and compression even under stationary loading, the criteria ignore considerable strength increase in uniform triaxial compression. The only known attempts to propose a critical process criterion are reduced to very special cases of uniaxial stress cycles and of combined cyclic bending and twisting a bar. For anisotropic materials under variable loading, when the directions of the principal stresses at a solid's point under consideration can arbitrarily turn, there has been no attempt to propose a critical process criterion at all.
4. The only known measure of the proximity of a real stress process to the closest critical one is a safety factor as the ratio of a limiting stress to an equivalent stress. This could suffice only if all the principal stresses are directly proportional to a common variable parameter. Otherwise, a usual safety factor does not determine the permissible combinations of the initial data in a strength problem, can overestimate actual reserves by an order of magnitude, and is manifestly insufficient.
5. There were no fundamental mechanical and strength sciences satisfying the complex of modern requirements for inherent unity, consistency, sufficient completeness, universality, naturalness, simplicity, and convenience for practical application.
Therefore, the very fundamentals of classical material strength sciences have a lot of obviously deep and even cardinal defects of principle.
Fundamental Defects of Classical Object Strength Sciences
Additionally, even the very fundamentals of classical object strength sciences have own evident lacks and shortcomings:
6. The finite element method (FEM) is regarded standard in computer aided solving problems. To be commercial, its software cannot consider nonstandard features of studied objects. There are no trials of exactly satisfying the fundamental equations of balance and deformation compatibility in the volume of each finite element. Moreover, there are no attempts even to approximately estimate pseudosolution errors of these equations in this volume. Such errors are simply distributed in it without any known law. Some chosen elementary test problems of elasticity theory with exact solutions show that FEM pseudosolutions can theoretically converge to those exact solutions to those problems only namely by suitable (a priori fully unclear) object discretization with infinitely many finite elements. To provide engineer precision only, we usually need very many sufficiently small finite elements. It is possible to hope (without any guarantee) for comprehensible results only by a huge number of finite elements and huge information amount which cannot be captured and analyzed. And even such unconvincing arguments hold for those simplest fully untypical cases only but NOT for real much more complicated problems. In practically solving them, to save human work amount, one usually provides anyone accidental object discretization with too small number of finite elements and obtains anyone "black box" result without any possibility and desire to check and test it. But it has beautiful graphic interpretation also impressing unqualified customers. They simply think that nicely presented results cannot be inadequate. Adding even one new node demands full recalculation once again that is accompanied by enormous volume of handwork which cannot be assigned by programming to the computer. Experience shows that by unsuccessful (and good luck cannot be expected in advance!) object discretization into finite elements, even skilled researchers come to absolutely unusable results inconsiderately declared as the ultimate truth actually demanding blind belief. The same also holds for the FEM fundamentals such as the absolute error, the relative error, and the least square method (LSM) [1] by Legendre and Gauss ("the king of mathematics") with producing own errors and even dozens of cardinal defects of principle, and, moreover, for the very fundamentals of classical mathematics [1]. Long-term experience also shows that a computer cannot work at all how a human thinks of it, and operationwise control with calculation check is necessary but practically impossible. It is especially dangerous that the FEM creates harmful illusion as if thanks to it, almost each mathematician or engineer is capable to successfully calculate the stress and strain states of any very complicated objects even without understanding their deformation under loadings, as well as knowledge in mathematics, strength of materials, and deformable solid mechanics. Spatial imagination only seems to suffice to break an object into finite elements. Full error! To carry out responsible strength calculation even by known norms, engineers should possess analytical mentality, big and profound knowledge, the ability to creatively and actively use them, intuition, long-term experience, even a talent. The same also holds in any computer aided solving problems, e.g., in hydrodynamics. A computer is a blind powerful calculator only and cannot think and provide human understanding but quickly gives voluminously impressive and beautifully issued illusory "soluions" to any problems with a lot of failures and catastrophes. Hence the FEM alone is unreliable but can be very useful as a supplement of analytic theories and methods if they provide testing the FEM and there is result correlation. Then the FEM adds both details and beautiful graphic interpretation.
Therefore, the very fundamentals of classical object strength sciences have a lot of obviously deep and even cardinal defects of principle.
References
[1] Encyclopaedia of Mathematics / Managing editor M. Hazewinkel. Volumes 1 to 10. Kluwer Academic Publ., Dordrecht, 1988-1994.
[2] Lev Gelimson. Elastic Mathematics. General Strength Theory. The "Collegium" All World Academy of Sciences Publishers, Munich (Germany), 2004, 496 pp.
[3] Lev Gelimson. Science Unimathematical Test Fundamental Metasciences Systems. Mathematical Journal of the “Collegium” All World Academy of Sciences, Munich (Germany), 12 (2012), 1.