Abstract
This paper examined and discussed a Meshless Wavelet Galerkin Method (MWGM) formulation for a first-order shear deformable beam, the properties of the MWGM, the differences between the MWGM and EFG, and programming methods for the MWGM. The first-order shear deformable beam (FSDB) consists of a pair of second-order elliptic differential equations. The weak forms of two differential equations are deduced using Hat wavelet series. The exact integration and reduced integration were used to analyze the problems. Some indeterminate beam problems are considered. Condition numbers of the stiffness matrix were analyzed with exact integration and reduced integration for two cases of these problems. Consequently, the results were converged on the analytic solutions. The shear-locking phenomenon also occurred in the MWGM as it occurs in the conventional FEM. The stiffness matrix calculated from the reduced integration causes a similar numerical error to the stiffness matrix calculated from the exact integration in the MWGM. The MWGM showed desirable results in the examples.
Highlights
The aim of this study was to formulate a Meshless Wavelet Galerkin Method (MWGM) to solve a pair of 2nd-order elliptic differential equations, in other words, the Timoshenko beam differential equation using Hat wavelets
Most of the studies in the literature have been about spline wavelet and Daubechies wavelet
This paper examined and discussed the MWGM formulation for a first-order shear deformable beam, the properties of the MWGM, the differences between the MWGM and EFG, and programming methods for the MWGM
Summary
The aim of this study was to formulate a Meshless Wavelet Galerkin Method (MWGM) to solve a pair of 2nd-order elliptic differential equations, in other words, the Timoshenko beam differential equation using Hat wavelets. The B-spline wavelet finite element method was developed to analyze vibrations in structures [1]. A study that used Daubechies wavelets as the shape functions was performed to solve the Euler beam bending problem [3]. A study using B-spline wavelet as the shape functions was conducted [4]. Basu et al did a study comparing the FEM, BEM, Meshless Method, and Wavelet Methods [5, 6]. Thin plate problems were analyzed with Daubechies wavelets [7]. Daubechies wavelets and DeslauriersDubuc interpolating functions were used to analyze the Euler beam on elastic foundation and thin plate problem [8]. Most of the studies in the literature have been about spline wavelet and Daubechies wavelet
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
