Open Access

ARTICLE

Construction of Operator-Orthogonal Wavelet-Based Elements for Adaptive Analysis of Thin Plate Bending Problems

by Y.M. Wang¹, Q. Wu¹

1 School of Automation, Xi’an University of Posts and Telecommunications,Xi’an 710121, People’s Republic of China.
2 State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China.

Computer Modeling in Engineering & Sciences 2013, 93(1), 17-45. https://doi.org/10.3970/cmes.2013.093.017

Abstract

A new kind of operator-orthogonal wavelet-based element is constructed based on the lifting scheme for adaptive analysis of thin plate bending problems. The operators of rectangular and skew thin plate bending problems and the sufficient condition for the operator-orthogonality of multilevel stiffness matrix are derived in the multiresolution finite element space. A new type of operator-orthogonal wavelets for thin plate bending problems is custom designed with high vanishing moments to be orthogonal with the scaling functions with respect to the operators of the problems, which ensures the independent solution of the problems in each scale. An adaptive operator-orthogonal wavelet method is proposed to approximate the exact solution of engineering problems by directly adding wavelets into the local domains until the relative error estimation satisfies the accuracy requirement. Numerical examples demonstrate that the operator-orthogonal method is an accurate and efficient method for bending analysis of thin plate.

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Keywords

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