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On first‐ and second‐order moderate rotation theories of laminated plates
Author(s) -
Sacco E.,
Reddy J. N.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330102
Subject(s) - finite element method , order theory , elasticity (physics) , displacement field , rotation (mathematics) , mathematics , anisotropy , plate theory , mathematical analysis , virtual work , geometry , physics , structural engineering , boundary value problem , engineering , optics , thermodynamics
The first‐ and second‐order, small strain and moderate rotation, theories of anisotropic laminated plates are developed and numerically evaluated. Beginning with an assumed displacement field and introducing various order‐of‐magnitude assumptions, the governing equilibrium equations of laminated plates are derived from the principle of virtual displacements. The finite‐element formulation for the second‐order moderate rotation theory is developed, and numerical results are presented to evaluate the new plate theories in comparison with the von Kàrmàn plate theory with shear deformation. For comparison purposes, the 2‐D elasticity theory with full non‐linearity is also analysed using the finite element method. It is found that the second‐order theory with moderate rotations is closest to the 2‐D finite elasticity theory.