Geometric Modeling for Structural and Material Shape Optimization

Abstract

A challenge many structural designers must soon face is shape optimization for components made from new, advanced materials. Designs reinforced with graphitic or ceramic materials offer mechanical and thermal performance gains that can give a competitive edge to an automotive product. Unfortunately, these advanced materials introduce material geometry into an already difficult problem as well as introducing new manufacturing constraints. In this paper, an interactive modeling system for both structural and material geometry is applied to the design of a connecting rod to explore modeling requirements for shape optimization of composites. These include new geometric and material data exchange requirements necessary for communication among design analysis and manufacturing activities for composite structures. Extensions to the current IGES system for material shape definition are recommended for components fabricated from these new materials.

Shape optimization is also explored for basic geometric design parameters such as the ratio of surface area to volume (which in large measure establish material processing requirements). Length, area volume, and point shape sensitivity derivatives are then presented for parametric cubic geometric design variables used to construct finite element analysis models by the PATRAN solid modeling system. In this way, a natural and significant reduction of the dimension of the mathematical programming problem for shape optimization results following the work of Fleury and his colleagues. Design sensitivity derivatives are also presented for global composite design variables used to define the construction of certain laminated composite shell structures. Unlike laminate point design variables based on local thickness, these variables directly define the global shape of the structural components.