A wavelet Galerkin method employing B-spline bases for solid mechanics problems without the use of a fictitious domain

Tanaka Satoyuki

Hiroshi Okada

Okazawa Shigenobu

Computational Mechanics

This study develops a wavelet Galerkin method (WGM) that uses B-spline wavelet bases for application to solid mechanics problems. A fictitious domain is often adopted to treat general boundaries in WGMs. In the analysis, the body is extended to its exterior but very low stiffness is applied to the exterior region. The stiffness matrix in the WGM becomes singular without the use of a fictitious domain. The problem arises from the lack of linear independence of the basis functions. A technique to remove basis functions that can be represented by the superposition of the other basis functions is proposed. The basis functions are automatically eliminated in the pre conditioning step. An adaptive strategy is developed using the proposed technique. The solution is refined by superposing finer wavelet functions. Numerical examples of solid mechanics problems are presented to demonstrate the multiresolution properties of the WGM.

Finite element method

Wavelet Galerkin method

B-spline scaling/wavelet functions

Adaptive analysis

Stress concentration problem

eng

Springer Nature

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00466-011-0671-9

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[DOI] http://dx.doi.org/10.1007/s00466-011-0671-9 isVersionOf