A QUADRATIC MINDLIN ELEMENT USING SHEAR CONSTRAINTS
"Shear constraints" are used to derive a displacement-based bending element for the analysis of thin and moderately thick plates of general plan form. As a starting point, the eight serendipity modes are adopted for the normal rotations and the nine lagrangian modes for the transverse displacement, w. Subsequently, the shear constraints are used to eliminate the mid-side and central w variables so that the final element has three degrees-of-freedom at the corners and two at each mid-side. The bending energy is integrated using the standard formulation for the serendipity mindlin element (with two-point Gaussian integration) so that the only modifications to that element involve the shear strain-displacement matrix. The constraints, which are used to implement these modifications, involve explicit algebraic expressions rather than numerical integration or matrix manipulation. A FORTRAN subroutine is provided for implementing these changes in a general quadrilateral. Using hierarchical displacement functions, the mid-side displacement variables, that are missing from the standard serendipity element, may be simply constrained to zero as "boundary conditions". Numerical experiments are presented which show that the element does not "lock" and that it gives excellent results for both thin and moderately thick plates. It also passes the patch test for a general quadrilateral. (TRRL)
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Availability:
- Find a library where document is available. Order URL: http://worldcat.org/issn/00457949
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Corporate Authors:
Pergamon Press, Incorporated
Headington Hill Hall
Oxford OX30BW, -
Authors:
- Crisfield, M A
- Publication Date: 1984
Media Info
- Features: Figures; References; Tables;
- Pagination: p. 833-852
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Serial:
- Computers and Structures
- Volume: 18
- Issue Number: 5
- Publisher: Elsevier
- ISSN: 0045-7949
Subject/Index Terms
- TRT Terms: Bending; Bending moments; Computer programs; Constraints; Equations; Lagrangian functions; Mathematical analysis; Mathematical models; Mineral dislocations; Plate metal; Rotation; Shear strength; Strain (Mechanics); Stresses; Structural plates
- Uncontrolled Terms: Plate
- Old TRIS Terms: Strains
- ITRD Terms: 6471: Analysis (math); 5586: Deflection; 6473: Mathematical model; 5531: Shear; 3491: Slab; 8645: Software; 5575: Stress (in material)
- Subject Areas: Bridges and other structures; Design; Highways; I24: Design of Bridges and Retaining Walls;
Filing Info
- Accession Number: 00387242
- Record Type: Publication
- Source Agency: Transport Research Laboratory
- Files: ITRD, TRIS
- Created Date: Aug 30 1984 12:00AM