Wavelet-based finite element method for multilevel local plate analysis

• An efficient method for multilevel local plate analysis is presented.
• The size of the problem (number of unknowns) is reduced with the providing of high accuracy results in considering regions.
• The method is applicable to the plates with the arbitrary shapes and boundary conditions.
• The localization can be imposed to any arbitrary regains of the problem.
• The method is more efficient for local analysis of plates with the large dimensions.

In this paper, an efficient multilevel method is presented for local static analysis of plates based on the coupling of finite element method and discrete wavelet transform (FEM–DWT). The problem is discretized using finite element method and the corresponding governing equation is transformed into a localized one by applying the discrete Haar wavelet. Then the obtained governing equation is reduced using special averaging and reduction algorithms. Two types of the localization approach are used, the first is localization with respect to nodes and it is rather efficient for plates with localized parameters (such as concentrated loads or stress concentration). Another approach is the localization with respect to the degrees of freedom of each node and it is rather efficient for the evaluation of the effect of the degrees of freedom on the plate. The numerical results indicate that the proposed method provides accurate results for the selected regions, with respect to corresponding FEM solution, with a considerable reduction in the size of the problem. Moreover, in problems which itself have a localized properties, the efficiency of the method is considerably increased.