Development of meshless boundary element method for inhomogeneous materials and its application to material propertiy identification

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The meshless-type boundary element method is a novel boundary element method which can be applied to inhomogeneous media and nonlinear problems. In this method, the domain integral term originated from inhomogeneous term for body foroes, etc., is transformed to boundary integral terms by means of the dual reciprocity method(DRM). Therefore, no domain mesh is needed in the numerical analyses, only the boundary mesh and internal collocation points are required. Generating internal collocation points are much easier than discretizing the domain into mesh, hence the meshless-type boundary element method is more efficient than the conventional boundary element method in preparing the data.In this research project, we applied the meshless-type boundary element method to the inverse problems for inhomogeneous materials. First, we developed some new accurate numerical integration schemes when the source point of the fundamental solution is located at an internal collocation point near the boundary. Then, we formulated the boundary element method for transient thermal problems and thermoelasticity problems with temperature dependent material properties and arbitrary inhomogeneities. The effectiveness of the formulation has been demonstrated through numerical test examples obtained by using the developed boundary element code. The inhomogeneous term is treated as a equivalent source/body-force term. It is approximated with a linear combination of the radial basis functions. Therefore, identifying inhomogeneous material properties results in idenfications of the unknown coefficients of the linear combination. The inverse analysis algorithm to identify the inhomogeneous thermal conductivity distribution has been finally developed and its effectiveness has also been demonstrated through some numerical test examples.