Journal ArticleDOI
The extended free formulation of finite elements in linear elasticity
TLDR
In this paper, the free formulation of Bergan and Nygard has been recast within the framework of a mixed-hybrid functional that allows internal stresses, internal displacements, and boundary displacements to vary independently.Abstract:
The free formulation of Bergan and Nygard has been successfully used in the construction of high-performance finite elements for linear and nonlinear structural analysis. The present paper recasts the free formulation within the framework of a mixed-hybrid functional that allows internal stresses, internal displacements, and boundary displacements to vary independentlyread more
Citations
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A study of optimal membrane triangles with drilling freedoms
TL;DR: In this article, the authors compared derivation methods for constructing optimal membrane triangles with corner drilling freedoms, and showed that the optimal element that fits the ANDES template is unique if energy orthogonality constraints are enforced.
Journal ArticleDOI
Membrane triangles with corner drilling freedoms II: the ANDES element
TL;DR: In this article, a 3-node, 9-dof membrane elements with normal-to-its-plane rotational freedoms (drilling freedoms) using parametrized variational principles is derived.
Journal ArticleDOI
The first ANDES elements: 9-dof plate bending triangles
TL;DR: Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.
Journal ArticleDOI
A survey of parametrized variational principles and applications to computational mechanics
TL;DR: The paper describes the recent construction of multifield PVPs in several areas of elasticity and electromagnetics and discusses three applications to finite-element computational mechanics: the derivation of high-performance finite elements, the development of element-level error indicators, and the construction of finite element templates.
Journal ArticleDOI
Membrane triangles with corner drilling freedoms III: implementation and performance evaluation
TL;DR: The numerical studies indicate that the ALL, FF and EFF-ANDES elements are comparable in accuracy for elements of unitary aspect ratios and the ALL elements are found to stiffen rapidly in inplane bending for high aspect ratios, whereas the FF andEFF elements maintain accuracy.
References
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Journal ArticleDOI
Derivation of element stiffness matrices by assumed stress distributions
Journal ArticleDOI
Basis of finite element methods for solid continua
Theodore H. H. Pian,Pin Tong +1 more
TL;DR: In this article, a review and reinterpretation of the existing finite element methods and other alternative schemes are presented, and a comparison of the relative merits of the various methods is made.
Journal ArticleDOI
A triangular membrane element with rotational degrees of freedom
P. G. Bergan,Carlos A. Felippa +1 more
TL;DR: In this article, a new plane-stress triangular element is derived using the free formulation of Bergan and Nygard, which possesses nine degrees of freedom: six corner translations and three corner normal rotations.
Journal ArticleDOI
Finite elements with increased freedom in choosing shape functions
P. G. Bergan,M. K. Nygård +1 more
TL;DR: In this article, the authors discuss displacement shape functions that may be used in connection with the potential energy principle, but they need not be conforming (satisfy interelement compatibility) and the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes.
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A triangular membrane element with rotational degrees of freedom
P. G. Bergan,Carlos A. Felippa +1 more