Multivariable finite elements based on B-spline wavelet on the interval for thin plate static and vibration analysis

Based on B-spline wavelet on the interval (BSWI) and the generalized variational principle, multivariable wavelet finite elements were proposed in this paper. Firstly, formulations were derived from multivariable generalized potential energy functional. Then the matrix equations of different structures were obtained by using BSWI as trial function. The elements presented can improve the accuracy of moment and bending strain efficiently, because displacement, moment and bending strain are all interpolated separately in multivariable generalized potential energy functional. However, the moment and bending strain are calculated by the differentiation of displacement in traditional method, which leads to calculation error because of the differentiation. Furthermore, the good approximation property of BSWI further guarantees the precision by using BSWI as trial function. In the end, several examples of thin plate and thin plate on elastic foundation are given, and they show that the efficiency of the element proposed is exemplified.