High Precision Solution Of Thermal-mechanical Analysis Under Complex Conditions Using Smoothed Finite Element Method

Thermal-mechanical problems play an important role in the engineering analysis of aerospace and energy metallurgy area,which components and structures work at severe environment with high temperature and strong load.The heat flux induced warps and cracks will degrade or even destroy the components and struct ures,which can be main reasons for the failure of structure.So an accurate solution of thermal-mechanical problems is significant to the design of structure.As an efficient numerical method,finite element method(FEM)has been applied to various problems in past decades,including thermal-mechanical problems.But FEM always figure out an inaccurate solution in displacement and stress for the stiffness matrix behaves“overly-stiff”.Recently,S-FEM has been proposed to overcome the shortcoming of FEM on the foundation of smoothed gradient,the results calculated by S-FEM can be more accurate than FEM.In this work,the ES-FEM and FS-FEM are applied to solve non-linear thermal-mechanical problems under complex conditions,which structure is composed by several materials and materials behave temperature-dependent.In addition,several mixed numerical schemes are proposed to deal with non-linear thermal-mechanical problems,the efficiency of mix numerical schemes are studied.The research can be described as follows:(1)The ES-FEM and FS-FEM are applied to solve non-linear thermal-mechanical problems based on MATAB programming,which the tetrahedron elements can be generated automatically by commercial software Hypermesh,and the thermal conductivity of material is assumed as a function of temperature.The accuracy and efficiency of ES-FEM and FS-FEM are studied through two numerical examples with a comparison to FEM.It can be found that ES-FEM can achieve higher accuracy and efficiency than FS-FEM and FEM.(2)Based on interfacial smoothed gradient technics,the ES-FEM and FS-FEM are extended to solve non-linear thermal-mechanical problems of composite structure which consist of several different materials,through two numerical examples to demonstrate the accuracy and efficiency of ES-FEM and FS-FEM.And it can be found that ES-FEM can still achieve higher accuracy and efficiency than FS-FEM and FEM.(3)In thermal-mechanical analysis,temperature and displacement are calculated separately,aiming such character several mixed numerical schemes are proposed to solve non-linear thermal-mechanical problems based on FEM,ES-FEM and FS-FEM.The efficiency of mixed numerical schemes is studied then.