A study of optimal membrane triangles with drilling freedoms

By C. Felippa. 2003

226 citations recorded by the source corpus.

Abstract This article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms. The term “optimal” is used in the sense of exact inplane pure-bending response of rectangular mesh units of arbitrary aspect ratio. Following a comparative summary of element formulation approaches, the construction of an optimal three-node triangle using the ANDES formulation is presented. The construction is based upon techniques developed by 1991 in student term projects, but taking advantage of the more general framework of templates developed since. The optimal element that fits the ANDES template is shown to be unique if energy orthogonality constraints are enforced. Two other formulations are examined and compared with the optimal model. Retrofitting the conventional linear strain triangle element by midpoint-migrating and congruential transformations is shown unable to produce an optimal element, while rank deficiency is inevitable. Use of the quadratic strain field of the 1988 Allman triangle, or linear filtered versions thereof, is also unable to reproduce the optimal element. Moreover these elements exhibit serious aspect ratio lock. These predictions are verified on benchmark examples.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3bb24e4412df212dabb5183f0a8e9890143b9d7d

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In Biomedical Engineering

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

A unified formulation of small-strain corotational finite elements: I. Theory (2005, methodology): “Fit according to CST rotation The infinitesimal drilling rotation of a plane stress CST element (Turner triangle, linear triangle), is given by [27,32]”
Dynamic Nonlinear Aeroelastic Model of a Kite for Power Generation (2014, unknown): “The canopy is discretized by nonlinear three-node triangular flat shell elements combining a membrane element for the in-plane forces as proposed by [30, 31], and a bending element for the out-of-plane forces as proposed by [32], amounting in a total of 18 DOF.”
Design of Piezoelectric Energy Harvesting Systems: A Topology Optimization Approach Based on Multilayer Plates and Shells (2009, background): “The structural layers are built from four overlapping composite triangular elements (Hemez, 1994) composed of coupled 9-dof assumed natural deviatoric strain membrane (Felippa, 2003) and 9-dof bending (Militello and Felippa, 1991) triangular elements, resulting in 24 structural degrees of freedom pe”