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Improved strain interpolation for curved C ° elements
Author(s) -
Park K. C.
Publication year - 1986
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.1620220121
Subject(s) - invariant (physics) , interpolation (computer graphics) , quadratic equation , mathematics , strain energy , geometry , bending , beam (structure) , mathematical analysis , finite element method , physics , structural engineering , optics , engineering , classical mechanics , motion (physics) , mathematical physics
The strain energy of straight beam members derived from the isoparametric shape functions is known to be invariant with respect to the number of integration points as long as they exceed a minimum number. However, this invariant property is generally lost for curved members. For example, the two‐point integrated, membrane strain energy of curved beams by employing the quadratic shape functions is different from the three‐point integrated one. This paper presents an invariant strain interpolation scheme for quadratic curved beam elements, which can lead to improved membrane representations in curved shell elements, thus resolving the perplexing membrane‐bending coupling difficulties in thin shell analysis.