TY - JOUR
T1 - Numerical manifold method based on the method of weighted residuals
AU - Li, S.
AU - Cheng, Y.
AU - Wu, Y. F.
PY - 2005/5
Y1 - 2005/5
N2 - 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.
AB - 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.
KW - Finite covers
KW - Galerkin method
KW - Manifold element
KW - Method of weighted residuals
KW - Numerical manifold method
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U2 - 10.1007/s00466-004-0636-3
DO - 10.1007/s00466-004-0636-3
M3 - RGC 21 - Publication in refereed journal
VL - 35
SP - 470
EP - 480
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 6
ER -