A specialized nonlinear thin plate inextensional bending theory

Abstract

The present paper describes a fundamentally different approach to the nonlinear plate theory. Based upon an analogy between linear elasticity theory and linear thin plate theory, the development herein presented introduces a “moment tensor,” a nonlinear “curvature tensor,” boundary conditions on moment, torque and loadings, a nonlinear relation between moment and curvature tensors and nonlinear curvature compatibility conditions. It must be emphasized that the theory and relations presented herein are postulated; there is no assurance that solutions of physical interest exist.