Structural mechanics is one of the most common engineering problems.At present,the most commonly used numerical method to analyze structural elasticity is the finite element method.The finite element method needs to discretize the whole structure area,which has a large amount of data and long calculation time;Secondly,it is difficult to accurately deal with the problems of infinite domain and stress concentration.The boundary type analysis method is represented by the boundary element method.Compared with the finite element method,the boundary element method is based on the boundary integral equation.It only needs to discretize the boundary and does not involve volume discretization.Therefore,it can reduce the dimension of the problem and has high calculation efficiency and accuracy.The boundary element method has limitations in the analysis of non-homogeneous elastic problems.There is a physical domain integral term in its boundary integral equation.If it is solved directly,it will lose the advantage that the boundary element only discretizes the boundary.Therefore,solving the domain integral problem is of great significance for the boundary element method to analyze elastic problems.This thesis is committed to analyzing the elastic problems of structures by using the dual reciprocity boundary element method,and mainly completes the following work:(1)Research on interpolation scheme of radial basis function.As a common method of interpolation for scattered data,radial basis function has the problem of unbalanced interpolation accuracy and stability,and the shape parameter interpolation scheme of radial basis function has an important impact on the interpolation accuracy and stability.In this thesis,the exponential radial basis function interpolation method is studied.Two interpolation schemes of constant parameter and variable parameter are adopted respectively.It is proved that the variable parameter scheme can gradually achieve the same accuracy as the constant parameter,and the interpolation stability is obviously better than the constant parameter scheme.The variable parameter scheme can meet the requirements in accuracy,greatly reduce the number of matrix conditions,and finally improve the interpolation stability.(2)Combined with the dual reciprocity technique,the boundary element method is used to solve the problems of non-homogeneous static elasticity.Based on the theory of boundary element method in elasticity,the dual reciprocity boundary element method is used to analyze the static elasticity of structures.In this method,the exponential radial basis function is used to interpolate and fit the physical force term,and its special solution in elasticity is deduced.The dual reciprocity technique is used to convert the volume sub item of the physical force term in the original boundary integral equation into boundary integral,and then the boundary element discretization technique is used,The linear equations are constructed by taking the displacement or surface force on the boundary nodes as unknowns.Numerical examples show that the exponential radial basis function has high interpolation accuracy and good stability under the variable parameter interpolation scheme.It is applied to the dual reciprocity boundary element method to solve non-homogeneous elastic problems.The results have high calculation accuracy and good numerical stability. |