Smooth Function Method For Solving The Problem, Different Compressive And Tensile Modulus Of Elasticity

Bimodular problems can be found in many engineering materials/structures. Since analytical solutions are difficult to be obtained in general, it is theoretically and practically significant to develop efficient numerical algorithms.This paper presents a technique smoothing the constitutive discontinuity to solve elasticity problems with dual extension/compression modulus. Maximum/minimum functions are employed to describe the nonlinear relationship of stress and strain, and are approximated by a set of smooth functions. An initial stress technique is utilized in the FEM based numerical analysis, which may lead to a higher computing efficiency since the stiffness matrix needs to be triangularized only once in the whole computing, and avoid the inconvenience induced by choosing shear modulus in the conventional iterative algorithm. 8-node isoparameteric finite elements are used in the computing, and a number of numerical examples are given to validate the proposed algorithm with satisfactory agreement with other solutions. In addition, the thermal stress analysis is conducted.The above algorithm is expanded in solving bimodular axisymmetric problems, and applied to a mechanical and thermal analysis for a suspended insulator made in Dalian Porcelain Insulator Works with model XZP1-400.