Stress Analysis By Local Integral Equations
Free (open access)
V. Sladek, J. Sladek & Ch. Zhang
This paper is a comparative study for various numerical implementations of local integral equations developed for stress analysis in plane elasticity of solids with functionally graded material coefficients. Besides two meshless implementations by the point interpolation method and the moving least squares approximation, the element based approximation is also utilized. The numerical stability, accuracy, convergence of accuracy and cost efficiency (assessed by CPU-times) are investigated in numerous test examples with exact benchmark solutions. Keywords: elasticity, functionally graded materials, boundary value problems, force equilibrium, meshless implementations. 1 Introduction A rapid progress can be observed in the development of various meshless techniques especially in fluid problems. Simultaneously, a considerable expansion of such techniques can be found also in various applications to engineering and science problems. This can be explained by the fact that there are known certain limitations of standard discretization techniques especially when applied to some classes of problems (e.g. problems in separable media, problems with free or moving boundaries; crack problems; problems with large distortions, etc.). Although the standard discretization techniques are applicable to the numerical solution of boundary value problems in continuously nonhomogeneous elastic media, the formulations developed for homogeneous media are not applicable directly, since the governing equations are now given by partial differential equations with variable coefficients. There has not been a unique classification of meshless techniques up to now. Mostly they are classified according to the employed approximation. Some of
elasticity, functionally graded materials, boundary value problems, force equilibrium, meshless implementations.