2022 Volume 9 Issue 1 Pages 78-95
A wavelet Galerkin method (WGM) is presented to analyze mechanical behaviors of 3D elastic solids. A set of linear B-spline scaling/wavelet functions is employed as the basis functions. The wavelet bases have a nature of multiresolution analysis (MRA). The MRA property works well in the WGM to control spatial resolution of the model. Steep gradients of physical values in stress concentration region can be refined by superposing the higher resolution wavelet functions onto the low resolution bases. Since the linear B-spline wavelet function do not have so-called Kronecker delta property, a special treatment is required to handle the essential boundary conditions (BCs). In this study, applicability of the penalty method and multiple point constraint technique are studied for the BC enforcements in the 3D solid mechanics problems. Accuracy and effectiveness of the presented approach are examined through several numerical examples.
