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

  • Authors:

  • Satoyuki Tanaka;Hiroshi Okada;Shigenobu Okazawa

  • Affiliations:

  • Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 739-8527;Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, Noda, Japan 278-8510;Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 739-8527

  • Venue:
  • Computational Mechanics
  • Year:
  • 2012

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Abstract

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.