Object Strength Estimation Fundamental Sciences System (Essential)

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), 7

UDC 539.4:620.17

Keywords: object strength estimation fundamental sciences system, stress and strain states analysis, discretization error, critical structure stress analysis error, damage tolerance, reserve, reliability, risk, infringement, phenomenological approach, safety factor, complex nonproportional loading, worst combination, general problem, overestimating, artificial randomization, complex optimization.

This article is dedicated to the memory of my dear teacher, Academician Georgy Stepanovich Pisarenko (1910 - 2001) to the 101st anniversary of his birthday

The finite element method (FEM) is regarded standard in calculating the stress and strain states of objects. 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, obtains anyone "black box" result without any possibility and desire to check and test it but with beautiful graphic interpretation also impressing unqualified customers simply thinking 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 principal mistakes, 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. A computer is a blind powerful calculator 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.

The object strength estimation fundamental sciences system includes the following fundamental sciences.

Design Error Tolerance Fundamental Science

This fundamental science includes structure discretization error general theory, structure stress analysis error general theory, critical structure stress analysis error general theory, and structure reserve analysis error tolerance general theory.

Damage Tolerance Fundamental Science

This fundamental science includes infringement and damage admissibility general theory, infringement and damage measure general theory, critical infringement and damage general theory, infringement and damage reserve general theory, and infringement and damage tolerance general theory.

They provide comparing the influence of real objects macrodamages and infringements on objects stress and strain states and strengths with the influence on them due to the deviations of real materials from their hypothetical continua models by standard phenomenological approaches, as well as determining critical objects infringements and damages similar to real ones and the reserves of real damages and infringements with respect to these critical ones.

Object Reserve Fundamental Science

This fundamental science includes general theories of object safety factor (reserve) possibly by complex nonproportional loading including general theories and methods of considering separate parameters reserves expressed via a reserve common for them all. It is determined via the worst combination of the values of these parameters by their varying within the limits of the borders defined by the individual reserves of the separate parameters. This is further generalizing a reduced pure (dimensionless) stress. This universal science is applicable to any general problem with restrictions. Usual methods of safety factor determination can be adequate at simple (proportional) loading only and generally lead to systematically overestimating true safety factors (reserves).

Object Reliability Fundamental Science

This fundamental science includes general theories and methods of quantitatively measuring, evaluating, and estimating object reliability via object safety factors (reserves) without artificial randomization which unfairly complicates calculation formulae and hence the complex optimization of objects via their reliabilities possibly by complex nonproportional loading.

Object Risk Fundamental Science

This fundamental science includes general theories and methods of quantitatively measuring, evaluating, and estimating object risk via object safety factors (reserves) without artificial randomization which unfairly complicates calculation formulae and hence the complex optimization of objects via their risks possibly by complex nonproportional loading.

The object strength estimation fundamental sciences system leads to reliable results (the FEM can illustrate) and provides optimizing objects for extreme conditions.

References

[1] Encyclopaedia of Mathematics / Managing editor M. Hazewinkel. Dordrecht etc., 1988-1994.

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