Application of Daubechies wavelets approximation to plate bending
Tomasz Koźbiał · PAMM · 2006
Abstract In this paper a new wavelet‐based approach is presented for solving two‐dimensional boundary‐value mechanical problems on the example of plate bending. The deflection equation of a bending plate is approximated by two‐dimensional Daubechies wavelets using a least‐squares Galerkin method. Due to the order of the differential equation in mechanics of plate structures is four, a way to perform the calculations of high order connection coefficients (that is, integrals of products of basis functions with their high order derivatives) is suggested. The implementation of two‐dimensional Daubechies scaling functions approximation to plate bending is exhibited numerically in some examples. The results show that this method has good precision and reliability. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)