A finite element based method for solution of large-deformation hyperelastic constitutive models is developed, which solves the Cauchy-stress balance equation using a single rotation of stress from principal directions to a fixed co-ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration-order incompressibility enforcement, and an iterative solution method that employs notional `small strain¿ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer `necking¿; the method is shown to give good agreement with published results from a well-established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved.

This thesis deals with developing a thermodynamically consistent model to simulate the electromechanical response of ionic polymer-metal composites based on Euler-Bernoulli beam theory. Constitutive assumptions are made for the Helmholtz free energy and the rate of dissipation. The governing equations involving small deformations are formulated using the conservation laws, the power theorem, and the maximum rate of dissipation hypothesis. The model is extended to solve large deformation cantilever beams involving pure bending which could be used in the characterization of the material parameters. A linear finite element solution along with a staggered time stepping algorithm is provided to numerically solve the governing equations of the small deformations problem under generalized electromechanical loading and boundary conditions. The results are in qualitative and quantitative agreement with the experiments performed on both Nafion and Flemion based Ionic Polymer-Metal Composite strips.

Elastic Buckling Simplified Methods for Structural Members with Edge-Stiffened Holes: Presently, the current design methods available to engineers to predict the strength of cold-formed steel members with edge-stiffened holes remains largely unaddressed in the North American Specification for the Design of Cold-Formed Steel Structural Members (NAS). Research was conducted to explore and develop a further understanding of the effects of stiffened edge holes on the elastic buckling parameters for local, distortional, and global buckling. Elastic buckling parameter studies have been conducted on a suite of cold-formed members including recently developed DeltaSTUDs manufactured by Steelform Building Products, Inc. and a series of common Steel Stud Manufacturers Association (SSMA) members. Furthermore, a suite of simplified methods for determining elastic buckling parameters used to predict capacity with the Direct Strength Method (DSM) for members with edge stiffened holes were developed and validated. The elastic buckling studies are used to validate the simplified methods presented in this thesis. All simplified methods are further validated with thin shell finite element eigen-buckling parameter studies where the edge-stiffened holes are explicitly modeled. Purlin Distortional Buckling Strength Under Gravity Loading: Laterally braced cold-formed steel beams generally fail due to local and/or distortional buckling in combination with yielding. For many members, distortional buckling is the dominant buckling mode and is addressed in the current North American Specification for the Design of Cold-formed Steel Structural Members. The current main code equation, AISI C3.1.4-10 for calculating the available distortional buckling stress was derived experimentally based on a series of four-point bending tests at John Hopkins University. Where this provides a good basis for determining capacity, in most loading conditions purlins are subjected to a downward uniform loading that provides additional resistance to distortional buckling in the top flange beyond the resistance of the steel roofing panel. This research describes an experimental study to explore and quantify the difference in distortional buckling flexural capacity of metal building Z-purlins treated as isolated components and Z-purlins loaded with a constant pressure applied to metal roof panels. A series of three different types of tests have been developed to quantify the system effect provided by the metal roof panels as well as downward pressure on distortional buckling. Results are also extended to validate the Direct Strength Method when predicting flexural capacity of purlins in a roof system. / Master of Science