MESHFREE METHODS FOR THERMO-MECHANICAL PROBLEM

Abstract

The Finite Element Method (FEM) is extensively used as an engineering analysis tool because of its versatility and flexibility. However, the method suffers from drawbacks such as discontinuous secondary variables across inter-element boundaries and the need for remeshing in large deformation problems. Therefore, researchers in recent years have begun to explore the possibility of developing new and innovative analysis tools that do not have these drawbacks, and yet have all the advantages of the FEM. Introducing new advanced materials into many fields of engineering it is increasingly growing the necessity to solve boundary value problems in continuous non-homogeneous solids. Conventional computational methods with domain (FEM) discretization have their own drawbacks to solve such kind of problems. Since new composite material are frequently used for structures under a thermal load, it is indispensable to analyze their thermal properties. In spite of the great success of the finite and boundary element methods as effective numerical tools for the solution of boundary value problems on complex domain, there is still a growing interest in development of new advanced methods A variety of meshless methods has been proposed so far. Many of them are derived from a weak form formulation on global domain or a set of local sub-domains. In the global formulation background cells are required for the integration of the weak form. In Meshfree methods based on local weak form formulations no cells are required and therefore they are often referred to call as truly meshless methods Recent literature shows extensive research work on meshless or element-free methods. One such method is the Meshless Local Petrov-Galerkin (MLPG) method. This method is based on a local weak form of the governing differential equation and allows for a choice of trial and test functions from different spaces. By a judicious choice of the test functions, the integrations involved in the weak form can be restricted to regular domains. In the persent work, Meshless Local Petrov-Galerkin method is used for solving thermal and thermo-mechanical problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. Here, MLPG method is applied to problems for which exact solutions are available to evaluate the effectiveness of the method. Additionally, a Petrov- VIII Galerkin implementation of the method is shown to greatly reduce computational time and effort, thus demonstrating that this Petrov-Galerkin approach is preferable over the previously developed Galerkin approach. IX