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Multiresolution method for bending of plates with complex shapes

Applied Mathematics and Mechanics(English Edition) 2023年第4期44卷 561-582页

作者： Jizeng WANG Yonggu FENG Cong XU Xiaojing LIU Youhe ZHOU Key Laboratory of Mechanics on Disaster and Environment in Western China(Lanzhou University) the Ministry of EducationLanzhou 730000China College of Civil Engineering and Mechanics Lanzhou UniversityLanzhou 730000China

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular *** realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex *** the solution of differential equations,various derivatives of the unknown function are denoted as new ***,the integral relations between these functions are applied in terms of wavelet approximation of multiple ***,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order *** the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse *** examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various *** comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth *** solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of *** addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

关键词： multiresolution generalized coiflet wavelet integral collocation method irregular domain complex shape high accuracy plate bending

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