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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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Finite Element Formulations of Solid Continua

Finite Element Formulations of Solid Continua

Chapter:
(p.327) 9 Finite Element Formulations of Solid Continua
Source:
An Introduction to Nonlinear Finite Element Analysis
Author(s):

J. N. REDDY

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525295.003.0009

In the linear description of the motion of solid bodies, the displacements and strains are assumed to be very small and the material is linearly elastic. In addition, the equilibrium equations are derived using the undeformed configuration of the body. In geometrically nonlinear analysis of beams and plates considered earlier, the assumption of small strains made it possible to ignore the changes in the geometry of the body and the distinction between various measures of stress and strain. This chapter examines geometrically nonlinear behavior in which changes in geometry, however large or small, have a significant effect on the load displacement characteristics of solid continua. Descriptions of motion are discussed, along with polar decomposition, stress tensors, strain tensors, energetically conjugate stresses and strains, conservation of mass, and finite element models of two-dimensional continua.

Keywords:   solid continua, stress, strain, motion, conservation of mass, strain tensors, stress tensors, virtual displacements, finite element models

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