Making sense of the Quadrilateral Area Coordinate membrane elements
IR@C-MMACS: CSIR-Centre for Mathematical Modelling and Computer Simulation, Bangalore
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Title |
Making sense of the Quadrilateral Area Coordinate membrane elements
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Creator |
V, Senthilkumar
G, Prathap |
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Subject |
Mechanical Engineering
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Description |
The introduction of the Quadrilateral Area Coordinate (QAC) membrane elements has
generated more heat than light on the subject of why distorted membrane elements
perform very poorly. The canonical guidelines for construction of robust elements are
continuity and completeness. It is known that isoparametric (or parametric) quadrilateral
membrane elements satisfy the continuity requirements always. In rectangular form, they
perform extremely well, except in cases where parasitic shear is involved (plane stress
modeling of bending of thin beams). So their poor performance when the elements are
used in general (i.e. distorted) quadrilateral form is now attributed to the failure to
accommodate the completeness requirements. Completeness is understood to be
maintained in physical (i.e. Cartesian, or metric ) space and not in the natural (i.e.
parametric) space. The QAC approach is a compromise that tries to use shape functions
which are in physical space, but as these cannot ensure exact continuity, require a relaxed
generalized continuity to be imposed. However, here, the patch test cannot be ensured in
the strictest sense as a careful examination of the results from various QAC elements in
this paper will reveal. Even this is not enough to remove locking in the simpler 4 node
elements and additional displacements fields have to be introduced through internal
parameters to ensure what Prathap calls the consistency requirement. These issues are
carefully studied in this investigation.
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Publisher |
Elsevier
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Date |
2008-09-15
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Type |
Article
PeerReviewed |
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Format |
application/pdf
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Identifier |
http://cir.cmmacs.ernet.in/89/1/Making%20sense%20of%20the%20Quadrilateral%20Area%20Coordinate%20%20membran_.pdf
V, Senthilkumar and G, Prathap (2008) Making sense of the Quadrilateral Area Coordinate membrane elements. Computer Methods in Applied Mechanics and Engineering, 197 (49-50). pp. 4379-4382. |
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Relation |
http://www.sciencedirect.com/science/article/pii/S004578250800203X
http://cir.cmmacs.ernet.in/89/ |
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