| As the main numerical methods,finite element method and boundary element method are widely used in practical scientific and engineering problems.However,the finite element method needs to divide the entire area when solving and calculating,and it cannot get a good calculation result for the infinite domain problem and the crack problem.The boundary element method only needs to discretize the boundary of the study area when solving the problem,but it involves the calculation of singular integrals,and the calculation process is cumbersome.In order to avoid these problems caused by traditional methods,a new type of boundary meshless method-Average source boundary node method（ASBNM）was proposed.It only uses boundary nodes in the solution process,and does not involve any element or integral concept.It is a true meshless method and is easy to implement.This article is the first attempt of the average source boundary node method in elasticity problem.In elasticity problem,solving the boundary stress involves the calculation of singular integrals,which is difficult.The method proposed in this article is based on the average source technique and coupled with the fully regularized boundary integral equation[30].It has the advantage that it does not need to divide the grid in the traditional sense,nor does it need to be integrated,and it can solve the boundary stress and internal stress well.In addition,this paper extends the average source boundary node method to nonlinear and nonhomogeneous heat conduction problem.In general,it is difficult to solve nonlinear and nonhomogeneous heat conduction problem with traditional methods.This paper improves the average source boundary node method and combines with the radial basis function on the original basis,which can solve such problems well.A large number of numerical experiments prove that the method proposed in this paper is a simple,efficient,accurate and stable numerical algorithm with good convergence. |
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