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A high-precision sixth-order solution scheme based on wavelet theory is used to discretize the strongly coupled nonlinear Von Kármán equation for large deformations of the irregular plates. By establishing a series of integral relations about the original function in the equation and its partial derivatives and discretizing them using a high accuracy wavelet multiple integration approximation scheme, the approximation errors caused by the higher order derivatives in the equation can be avoided. Meanwhile, the unique boundary expansion and boundary node removal techniques are used to enable the approximation format to have better approximation accuracy and stability at the boundary. For various boundary conditions in irregular domains, they can be automatically and almost exactly included in the integration operation without any special treatment. The proposed wavelet approximation format combined with the traditional collocation point method is applied to large deformation problems of irregularly shaped plates. The obtained results of wavelet displacements and stresses are compared with analytical and finite element solutions, and it is found that in some cases the wavelet solution has better accuracy than the finite element solution and achieves the expected sixth-order accuracy. Moreover, the solutions under stress concentration around the holes can be obtained efficiently and accurately for irregular plates with multiple holes by the wavelet method using a uniform node distribution.

function approximation;numerical methods;error estimation