This Small Business Innovation Research Phase I project is concerned with the development of a next generation Computer Aided Design (CAD) software package for three-dimensional (3-D) stress analysis and optimal shape design of solid structural components. Use of CAD software is commonplace throughout the industrial sector in the US and in other advanced countries. Typically, the main components of a CAD system are (a) geometric modeler and pre-processor, (b) computational engine for stress and sensitivity analysis, (c) optimizer, and (d) post-processor. The finite element method (FEM) is usually the computational engine. A serious shortcoming of such a system is the need to discretize (mesh) the entire domain of a 3-D body into (volume) finite elements. This task, which cannot be efficiently automated for bodies of complex shape, becomes particularly onerous during optimal shape design when the shape of a body changes during successive iterations. Also, volume discretization is not naturally compatible either with solid modeling or with shape design algorithms. This project proposes the development and use of an entirely new computational engine - the boundary contour method (BCM). This breakthrough approach only requires the modeling of the 1-D bounding contours of 2-D surface elements on a 3-D body, thus preserving a seamless geometry interface with a solid modeler. Automatic meshing, initially and between design iterations, now becomes straightforward. Also, the approach is extremely efficient since only line integrals (on the bounding contours of surface elements) need to be numerically evaluated in the BCM for 3-D problems. Development of the BCM, for stress and sensitivity analysis, is the main research goal for Phase I. Optimization, adaptive meshing and development of a data parallel version of the software package for parallel operation on networked workstations, are planned for Phase II.
