Study On Thermoelastic Problems Of Homogeneous Materials By The Polygonal Manifold Method

Thermoelastic analysis is a very important issue in both scientific study and engineering practice.Numerical computations are widely used in this field due to their strong applicability,high efficiency and low cost.Recent years,the numerical manifold method(referred to as NMM,also known as the manifold element method)draws much attention due to its unique dual cover system.Besides,compared with the frequently used triangular and rectangular elements,the polygonal elements are more flexible in discretization and insensitive to volumetric locking.In this work,the polygonal NMM was developed to solve two-dimensional(2D)thermoelastic problems in homogeneous materials,and the feasibility and accuracy of the proposed method are verified by typical examples.The main work and associated achievements are summarized as follows:(1)The domestic and international research status of the thermoelastic problems,the NMM and polygonal element are briefly reviewed.(2)The basic theory of the NMM,including the basic concepts and the field approximation are described.The frequently used weight(shape)functions of the polygonal elements are presented.In addition,the comparisons among the NMM and some other represented numerical methods are made.(3)The polygonal NMM for 2D steady heat conduction problems in the homogeneous materials are proposed.The governing equations and associated boundary conditions are presented.The polygonal NMM temperature approximation is provided.With the variational principle,the polygonal NMM discrete equations for concerned problems are deduced and the corresponding integration schemes on polygonal elements are proposed.The computer codes are developed with C++ programming language.The approach is validated through typical numerical examples.(4)Upon the previous work,the polygonal NMM for 2D thermoelastic problems in the homogeneous materials are further developed.The governing equations and associated boundary conditions are presented.The polygonal NMM displacement approximation is provided.With the variational principle,the polygonal NMM discrete equations for concerned problems are deduced.The computer codes are developed with C++ programming language.The approach is validated through typical numerical examples.