General theorems and generalized variational principles for nonlinear elastodynamics

Abstract

Generalized variational principles with 11 - arguments, 9 - arguments, 5 - arguments, 3 - arguments and the variational principles of action of potential/complementary energy are developed to solve initial-value, final-value and two time boundary-value problems in nonlinear elastodynamic systems. The displacement gradient is decomposed into a symmentric part D subscript ij and a rotation part W subscript ij = -e subscript ijk W subscript k which are variables in functionals.

The theoretical approach is illustrated by examining one-dimensional elastostatic and elastodynamic problems. In the former, it is shown that by solving for the displacement gradient u subscript ij as a function of the stress tensor ? subscript ij from the constraint equations of the variational principle of complementary energy, the functional of the variational principle of complementary energy can be expressed in a form involving the single argument ? subscript ij only.

An application of the variational principles is illustrated in an elastodynamic final-value problem. Complementing these examples is a discussion indicating how other generalized variational principles may be deduced and how numerical schemes of study may be enhanced through a matrix decomposition of the displacement gradient u subscript ij.

More information

Identifiers

Catalogue record

Export record