Multivariable wavelet finite element method for 1D structural analysis

Based on B-spline wavelet on the interval (BSWI) and multivariable generalized potential energy functional, the wavelet finite elements with two kinds of variables for 1D structural analysis are constructed. The formulations are derived from generalized potential energy functional based on potential variational principle and BSWI is selected as trial function to discrete the field functions. The advantage of the elements proposed in this paper is that it can improve the solving accuracy of generalized stress. Because there is only one kind of field function in traditional method, generalized stress should be calculated through differentiation of generalized displacement. However, to multivariable element, generalized displacement and stress are treated as independent variables, differentiation is avoided. Besides, BSWI has very good numerical approximation property among all existing wavelets, which can further guarantee the precision. The meaningless wavelet coefficients are translated to physical space by transformation matrix, which makes the solving process more convenient. In the end, several numerical examples of Euler beam and Plane frame are provided to verify the correctness and efficiency.