| The actual nonlinear constitutive character of most elastic materials is often approximated in engineering analysis by a linear relation-generalized Hooke's law. This approximation may introduce significant error into an analysis problem. This dissertation presents and demonstrates an approach for equilibrium analysis of a class of constitutively nonlinear systems within the context of small deformation (kinematically linear) elasticity.;The approach is given in the form of an extremum principle stated in terms of mixed stress and displacement field variables. Such fields represent a pointwise additive decomposition of the total stress field throughout the material domain. Nonlinear constitutive behavior is achieved through functional bounds on the individual stress component fields, in combination with a set of constraints which assure satisfaction of equilibrium and boundary conditions.;A finite-dimensional approximation of the extremum problem statement is obtained through the introduction of discrete representations of the problem fields. Numerical solutions for the resulting convex constrained minimization problem are obtained using an established minimization routine. Examples are presented which demonstrate the substantial flexibility available in specifying constitutive behavior within the model.;Applications of the described modelling approach within the context of non-conservative (inelastic) systems are also discussed. In addition, extensions of the established framework to problems of optimal design are presented. Specifically, a methodology for predicting the optimal distribution of nonlinear material properties, as defined for the additive representation, is described and demonstrated. |
