Analysis of shallow hyperbolic shell by different kinds of wavelet elements based on B-spline wavelet on the interval

Abstract

Shallow hyperbolic shell is a typical structure widely used in mechanical engineering and architectural engineering. Accurate structural analysis is a very important procedure before it is used in practical engineering. Wavelet finite element method (WFEM) is a new numerical analysis method which takes wavelet functions to replace the polynomial functions in tradition FEM. Due to the excellent properties of wavelet, WFEM can improve the calculation efficiency and reduce the computational time. However, traditional WFEM mainly focuses on accurate analysis of generalized displacement, generalized stress and generalized strain should be calculated secondly through displacement. Multivariable WFEM, including WFEM with two kinds of variables and WFEM with three kinds of variables, can independently interpolate the generalized displacement, stress and strain in one time, thus the calculation time is greatly reduced and the calculation precision can be improved significantly. In this paper, taking B-spline wavelet on the interval (BSWI) as interpolating function, the traditional BSWI element, BSWI element with two kinds of variables and BSWI element with three kinds of variables for the typical shell structure-shallow hyperbolic shell are constructed. Through bending and vibration analysis of shallow hyperbolic shell, the superiority of these three constructed elements is proved.