Some structural theorems for inelastic solids : an internal variable approach.

• Main Author: Carter, Peter
• Other Authors: Martin, JB
• Format: Doctoral Thesis
• Language: English
• Published: University of Cape Town 2015
• Subjects: Engineering
• Online Access: http://hdl.handle.net/11427/12455

Includes bibliographical references. === The theory of inelastic solids involving thermodynamic potential functions with internal variables is reviewed. Use is made of the condition for stable thermodynamic equilibrium in order to obtain dual minimum principles for the equilibrium state of a solid inelastic body. This leads to dual forms of the incremental (or rate) theorems and their respective extended forms. The extended static incremental theorem is applied to a pin-jointed truss and an algorithm suggested for solution of the ensuing programming problem. Numerical examples are given. A class of bounding theorems is also studied from the point of view of the potential functions. Bounds on the work and complementary work are obtained and properties of the bounding functions examined. Finally, the bound on a functional, which has been used to obtain general work and displacement bounds for dynamically loaded structures, is discussed.