Numerical manifold method based on the method of weighted residuals

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • S. Li
  • Y. Cheng
  • Y. F. Wu

Detail(s)

Original languageEnglish
Pages (from-to)470-480
Journal / PublicationComputational Mechanics
Volume35
Issue number6
Publication statusPublished - May 2005

Abstract

Usually, the governing equations of the numerical manifold method (NMM) are derived from the minimum potential energy principle. For many applied problems it is difficult to derive in general outset the functional forms of the governing equations. This obviously strongly restricts the implementation of the minimum potential energy principle or other variational principles in NMM. In fact, the governing equations of NMM can be derived from a more general method of weighted residuals. By choosing suitable weight functions, the derivation of the governing equations of the NMM from the weighted residual method leads to the same result as that derived from the minimum potential energy principle. This is demonstrated in the paper by deriving the governing equations of the NMM for linear elasticity problems, and also for Laplace's equation for which the governing equations of the NMM cannot be derived from the minimum potential energy principle. The performance of the method is illustrated by three numerical examples. © Springer-Verlag 2005.

Research Area(s)

  • Finite covers, Galerkin method, Manifold element, Method of weighted residuals, Numerical manifold method

Citation Format(s)

Numerical manifold method based on the method of weighted residuals. / Li, S.; Cheng, Y.; Wu, Y. F.
In: Computational Mechanics, Vol. 35, No. 6, 05.2005, p. 470-480.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review