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Multiple quadrature underintegrated finite elements
Author(s) -
Liu Wing Kam,
Hu YuKan,
Belytschko Ted
Publication year - 1994
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.1620371905
Subject(s) - quadrature (astronomy) , hourglass , numerical integration , clenshaw–curtis quadrature , tanh sinh quadrature , gauss–jacobi quadrature , finite element method , gauss–kronrod quadrature formula , mathematics , mathematical analysis , nyström method , structural engineering , gaussian quadrature , engineering , physics , boundary value problem , astronomy , electrical engineering
New multiple‐quadrature‐point underintegrated finite elements with hourglass control are developed. The elements are selectively underintegrated to avoid volumetric and shear locking and save computational time. An approach for hourglass control is proposed such that the stabilization operators are obtained simply by taking the partial derivatives of the generalized strain rate vector with respect to the natural co‐ordinates so that the elements require no stabilization parameter. To improve accuracy over the traditional one‐point‐quadrature elements, several quadrature points are used to integrate the internal forces, especially for tracing the plastic fronts in the mesh during loading and unloading in elastic–plastic analysis. Two‐ and four‐point‐quadrature elements are proposed for use in the two‐ and three‐dimensional elements, respectively. Other multiple‐quadrature points can also be employed. Several numerical examples such as thin beam, plate and shell problems are presented to demonstrate the applicability of the proposed elements.