Variable Shape Parameter RBF Interpolation And Applying In BEM For Elastic Analysis Of Thin-walled Structures

Thin-walled structure is one of the most common engineering structures.At present,the finite element method(FEM)is the main numerical analysis method for the mechanical problems of thin-walled structure.However,the shell element is often used to simplify the calculation when the FEM is used to analyze the thin-walled structure,which ignores the influence of the thickness dimension on the structural displacement and stress distribution.The boundary element method(BEM),which is based on the boundary integral equation,takes into account the influence of the thickness dimension on the thin-walled structures,and combines the dual reciprocity method(DRM)to transform the domain integral into the boundary integral,so as to avoid the use of the domain grid.Due to the incomplete research and application of the dual reciprocity BEM(DRBEM)in the analysis of the static elastic problem of thin-walled structures at home and abroad,especially the research on the radial basis function(RBF)interpolation of variable shape parameters is less.Therefore,in order to expand the application of the DRBEM in the analysis of thin-walled structures,the main work of this paper is as follows:(1)The basic theory of boundary element for statically elastic problems of thin-walled structures is reviewed.Combined with the DRM,the RBF is used to interpolate the inhomogeneous force function when the BEM is used to analyze the static-elastic problem of thin-walled structures,and the special solution of the static-elastic problem of multi-quadratic RBF is derived,and the boundary integral transformation of the domain integral term is realized.RBF interpolation does not need to introduce the domain grid and keeps the characteristic of boundary discretization of BEM.(2)In view of the indefinite choice of shape parameters in the RBF,a variable parameter multi-quadratic interpolation scheme is adopted in this paper,and a hybrid parameter variation scheme is used to effectively balance the interpolation accuracy and numerical stability of the RBF.Through the verification of different regions and various interpolation functions,the scheme can improve the condition number of interpolation matrix effectively while maintaining the calculation accuracy.In particular,by comparing with the constant parameter interpolation scheme,it is found that the variable parameter interpolation scheme can converge stably as the number of interpolation nodes increases.(3)The DRBEM is applied to the static analysis of four kinds of thin-walled structures.The calculation results show that the DRBEM with variable parameter interpolation scheme is effective.Compared with the constant parameter interpolation scheme,the DRBEM with variable parameter scheme has higher computational accuracy in thin-walled structure analysis.