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Mathematics and Mechanics of Solids
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Total-Lagrangian Formulation and Finite-Element Analysis of Highly Flexible Plates and Shells

P. Frank Pai

Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA

Presented here is a new total-Lagrangian displacement-based finite-element formulation for plates and shells undergoing large displacements and rotations. The theory fully accounts for geometric nonlinearities, general initial curvatures, and extensionality by using Jaumann stress and strain measures, an exact coordinate transformation, and orthogonal virtual rotations. Moreover, transverse shear deformations are accounted for by using a first-order shear deformation theory with shear correction factors obtained by matching the shear strain energy and stress resultants with those of a general layerwise higher-order shear deformation theory. Large static deformations of several different plates and shells under different loading and boundary conditions are obtained. Comparison with available results in the literature reveals that the finite-element model is accurate in predicting large deformations of highly flexible two-dimensional structures.

Key Words: highly flexible 2D structures • Jaumann strains • post-buckling finite element analysis

This version was published on April 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 2, 213-250 (2007)
DOI: 10.1177/1081286505055474
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