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On the enforcing energy conservation of time finite elements for discrete elasto‐dynamics problems
Author(s) -
Bui Q. V.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1875
Subject(s) - finite element method , scalar (mathematics) , midpoint , conservation of energy , energy conservation , integrator , numerical integration , mathematics , midpoint method , quadrature (astronomy) , context (archaeology) , conservation law , stability (learning theory) , scaling , simple (philosophy) , computer science , mathematical analysis , engineering , geometry , structural engineering , physics , computer network , paleontology , philosophy , electrical engineering , bandwidth (computing) , epistemology , thermodynamics , machine learning , biology
In the context of the time‐finite element method, algorithmic stresses, which enable the conservation of energy, are designed for temporal integrators derived from the midpoint and trapezoidal schemes. This is achieved through an appropriate modification of the standard midpoint and trapezoidal quadrature rules used for the numerical integration of time integrals. Either scalar scaling or vectorial adjustments can be employed for the modification, and well‐designed simple tests allow to investigate the quality of these different strategies of energy‐conserving enforcements. Numerical examples with semi‐discrete elasto‐dynamics problems are presented to show the superior stability of energy‐conserving schemes. Copyright © 2006 John Wiley & Sons, Ltd.