Date of Award
Doctor of Engineering Science in Mechanical Engineering
Su Ling Cheng
Benedict C. Sun
The Sedov-Berdichevskii variational principle is extended, and this extended principle is employed in the construction of a shell theory.
The extension of the principle is accomplished by the use of Lagrangian multipliers, and a redefinition of terms in order to maintain the original generality of the principle. The Euler equations of the extended variational principle provide, in addition to those obtained in the original principle, elastic and plastic kinematic relations, and, elastic and plastic constitutive relations. Also, the Euler equations of the original principle are obtained in a physically more meaningful form. Examples are given which show how this principle can be applied to various classical models whose formulation is well known.
A shell theory is derived from the extended variational principle by integrating the three-dimensional equations across the thickness of the shell. Tensor notation and the theory of surfaces in curvalinear coordinates are used. The derived theory is "exact" within the assumption that the shifted displacements and velocities vary linearly across the thickness of the shell.
A complete set of shell equations is derived, including momentum equations, equations involving internal degrees of freedom, entropy balance, constitutive relations, and some typical boundary conditions. An application is also given which shows how the derived equations reduce to the classical equations for a special case of an elastic shell.
Prendergast, Francis X., "Extension and application of the Sedov-Berdichevskii variational principle" (1970). Dissertations. 1345.