Applications of a generalized complementary energy principle for the equilibrium analysis of softening structures

An interpretation for computational solution is given for a new global extremum principle that models a generalized form of elastic/softening structural behavior. The principle and its interpretation are expressed in a form that accommodates arbitrary heterogeneity and anisotropy in the structural material. Also the stress-strain properties that reflect evolution of local softening are represented in the model by a set of parameters defined over the field of the structure. Thus, the model may be used to predict the general behavior of solid structures having non-uniform stress/strain fields that evolve with change in external load. A discretized version of the principle used for computation is based on a consistent, mixed-form finite element interpretation of the principle as stated for the general softening continuum. Example computational solutions are provided covering the evolution of softening for a uniformly loaded homogeneous sheet with a hole, and simulations of a sheet with various configurations of softer or stiffer inclusions in an otherwise uniform structure.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31456/1/0000377.pd

Design of optimal material properties for structures composed of nonlinear material

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76247/1/AIAA-1994-4367-370.pd

An extremum principle for the analysis and design of constitutively nonlinear systems.

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.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104019/1/9423292.pdfDescription of 9423292.pdf : Restricted to UM users only