A study of optimal membrane triangles with drilling freedoms
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Editorial: CIMNE
Year of publication: 2002
Pages: 51
Index: Introduction; A gallery of triangles; the ANDES triangle with drilling freedoms; Finding the best; A methematica implementation; Retrofitting LST; The allman 1988 triangle; Numerical examples; discussion and conclusins; The higher order strain in field; Solving polynomial equations for template optimality
Editorial: CIMNE
Year of publication: 2002
Pages: 51
Index: Introduction; A gallery of triangles; the ANDES triangle with drilling freedoms; Finding the best; A methematica implementation; Retrofitting LST; The allman 1988 triangle; Numerical examples; discussion and conclusins; The higher order strain in field; Solving polynomial equations for template optimality
Description
This article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms. The term âoptimalâ is used in the same of exact inplane response of rectangular mesh units of arbitrary aspect ratio. Following a comparative summary of element formulation approaches, the construction of an optimal 3-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 a priori. Two other formulations are examined and compared with the optimal model. Retrofitting the conventional LST (Linear Strain Triangle) element by midpoint-migrating by congruential transformations is shown to be 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 exibit serious aspect ratio lock. These predictions are verified on benchmark examples.