Open Access

ABSTRACT

B-Spline Wavelet Galerkin Method for the Problems of Elastostatics

S. Tanaka¹, H. Okada¹

1 Department of Nano-Structure and Advanced Materials, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan

The International Conference on Computational & Experimental Engineering and Sciences 2007, 3(4), 217-224. https://doi.org/10.3970/icces.2007.003.217

Abstract

It has been recognized that the bottle-neck in solid/structural analyses using the finite element method is in their model generation phase. Methodologies that eliminate the needs for "elements" have been proposed by many researchers. They can be categorized into "meshless" and "virtually meshless" finite element methods. The "meshless" method may be represented by moving least square Ptrov-Galerkin (MLPG) method [1] and element free Galerkin Method (EFGM) [2]. The free-mesh method [3] and voxel finite element method [4], etc. are classified to be the "virtually meshless" approaches. The "meshless" methods eliminated needs for element connectivity information in their input data and interpolation functions are based on nodal points only. The "virtually meshless" methods do not require element connectivity data as input, but they do use elements in their computations. The free-mesh method generates triangular (2D) or tetrahedral (3D) elements when stiffness matrices are evaluated. The voxel approach is a kind of fixed grid approach. The authors have developed an advanced fixed grid finite element method that is based on B-spline scaling function/wavelet functions [5, 6]. Proposed method is considered to be a "virtually" meshless approach. In this paper, we present equation formulations and numerical implementations. Then, some numerical examples are presented.

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