MODELING THE PROBLEM OF ELASTICITY THEORY IN TERMS OF STRESSES USING COMPUTER TOOLS

Abstract

The classical theory of elasticity has traditionally focused on solving problems
through displacements, whereas in recent years there has been a growing interest in
computer-based modeling of problems posed in terms of stresses. This approach
provides a more accurate analysis of the stress state of objects, particularly under
complex loads and boundary conditions. In this article, we first examine the
theoretical foundations and mathematical models of stress-based elasticity theory,
followed by the numerical methods applied to solve them using computer simulations.
Furthermore, the stages of the modeling process, the advantages of this approach, and
its fields of application are analyzed. In determining the strength and reliability of
structures and their elements—especially considering the effects of
thermoelectricity—traditional approaches may sometimes face limitations. For
instance, the classical Lamé (Navier) equations do not always precisely satisfy
boundary conditions. Stress-based problem formulations, however, aim to overcome
these issues, helping to reduce the risk of material failure and improve operational
properties