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Tensor‐based matrices in geometrically non‐linear FEM
Author(s) -
Chekhov V. V.
Publication year - 2005
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.1343
Subject(s) - finite element method , tensor (intrinsic definition) , mathematics , geometry , mathematical analysis , structural engineering , engineering
In the framework of the object‐oriented paradigm, advantages of using the index‐free tensor notation in combination with the concept of generalized tensor‐based matrix are considered as being the most corresponding to the paradigm. The advantages reveal itself in the disappearance of a semantic gap between various stages of creation of FEM applications (theoretical inferences, use of the numerical methods, object‐oriented software implementation) and, as a result, use of the unified object model in all the stages, as well as simplification of theoretical transformations. Based on the considered approach, a new FEM equation for large strain analysis is developed and its solution technique is outlined. Copyright © 2005 John Wiley & Sons, Ltd.