The Complementary Potential Energy Principle in Finite Elastic Deformations

Abstract

<p> This thesis establishes the general Principle of Complementary Potential Energy for the finite deformations of an elastic continuum, in which the Lagrange stress tensor is employed as the stress variable. It is demonstrated that constitutive relations, formulated in terms of the Lagrange stress tensor and the deformation gradient, will admit inversion. Consequently, the present theorem and the theorem proposed by LEVINSON are established as valid principles. The complementary strain energy density of the present theorem, however, is shown to be Independent of rigid displacements, in contrast to that of the LEVINSON formulation. The general Principle is reduced to the form appropriate to finite elastic systems, and it is established that the present theorem reduces to, and therefore contains as a special case, the LIBOVE Theorem.</p>