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An Introduction to Nonlinear Finite Element Analysis$
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J. N. Reddy

Print publication date: 2004

Print ISBN-13: 9780198525295

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198525295.001.0001

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Nonlinear Bending of Elastic Plates and Shells

Nonlinear Bending of Elastic Plates and Shells

(p.141) 6 Nonlinear Bending of Elastic Plates and Shells
An Introduction to Nonlinear Finite Element Analysis


Oxford University Press

Simple two-dimensional plate and shell theories can be developed to study the deformation and stresses in plate structures undergoing small strains, small to moderate rotations, and large displacements. In this chapter, governing equations of the classical and first-order theories of elastic plates and shells with the von Kármán strains are derived, and their displacement finite element models are developed. The principle of virtual displacements is used to derive the weak forms, and the displacement finite element models are developed using the weak forms. The classical plate theory is discussed along with the assumptions of the underlying kinematics, variational formulation of the classical plate theory, equilibrium equations, boundary conditions, and computer implementation of the process.

Keywords:   kinematics, elastic plates, virtual displacements, finite element models, weak forms, von Kármán strains, classical plate theory, boundary conditions, computer implementation

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