The Semi-analytic Algorithm Of Nearly Singular Integrals In High Order Boundary Element Analysis Of 2D Orthotropic Anisotropic Potential Problems

Many practical engineering problems,such as heat conduction,fluid flow,torsion problems etc.,can be all concluded as the governing equations of potential problems.In this thesis,the two-dimensional orthotropic anisotropic potential problem is solved by using the boundary element method(BEM)with higher order elements.Accurate calculations of the nearly singular integrals are one of the difficulties of boundary element method.In the thesis,a semi analytical formula is established to solve the nearly singular integrals on the high order elements in the boundary element analysis of two-dimensional orthogonal anisotropic potential problems.The semi analytical method can accurately calculate the nearly singular integrals on the quadratic element.By a series of derivations,the approximate singular kernel functions with the same nearly singularity as the integral kernels on 3-noded quadratic isoparametric elements are constructed for two-dimensional orthogonal anisotropic potential boundary element analysis.Then the approximate singular kernel functions are deducted from the integral kernels of the nearly singular integral elements of two-dimensional orthotropic potential.Thus the nearly singular integral terms are transformed into the sum of two parts: regular integrals and nearly singular integrals.The regular integrals are directly calculated by the conventional Gauss numerical integration.The nearly singular integrals are calculated by the derived analytical formulas.The semi analytic algorithm of the nearly strong singular and super singular integrals for 3-noded quadratic isoparametric elements of the two-dimensional orthotropic anisotropic potential problems is established.The three numerical examples of the boundary element analysis about the heat conduction problems in the orthotropic anisotropic media are given with the semi analytic algorithm.The computed results verify the efficiency and accuracy of the present semi-analytic algorithm in evaluating the potentials in the interior points near the boundary.