Selected optimization problems in structural mechanics.

Abstract

I. Geometric optimization of contact problems in the presence of singularities. Starting from the idea that the stress singularity of a sharp wedge in contact can be avoided by changing the wedge shape, shape optimization is accomplished with the geometric strain method (GSM), an optimality criterion method. Several numerical examples are provided for different materials in a wedge and half plane, and two bonded wedges. Optimum wedge shapes are obtained and the critical corner angle is compared with the critical wedge angle from classical contact mechanics. Numerical results are well matched to analytic and experimental results. It is shown that shape optimization by GSM is a useful tool to reshape the wedge and to avoid a stress singularity in wedge contact problems. The method applies to more general geometries where the singular behavior would be more difficult to avoid by classical means. II. Effect of interference on design sensitivities. The stiffness of interfering bodies affects the response and design sensitivities of a structure. Design sensitivity relations involving interference force due to the bodies are derived on the basis of thermoelasticity equations, and are modeled by thermal loads. As practical examples, a transfer press, which is commonly used in the automobile industry, is studied to investigate the effect of interference force due to die stiffness. Misalignment and out-of-parallelism, which cause manufacturing error in a slide in the transfer press, are defined. Design sensitivity analysis is done for two different finite element models (with/without die stiffness). In contrast to earlier studies, it is found that the stiffness of interfering bodies has an effect on design sensitivity and should be considered in structural design of a transfer press. For future redesign of the transfer press, a few recommendations are suggested.