STRUCTURAL INVERSE DESIGN AND OPTIMIZATION

G. S. Dulikravich

The Pennsylvania Stale University, University Park. PA, USA

14.1 Introduction

Design of structural components for specified aerodynamic and dynamic loads can be achieved with an extensive use of a reliable and versatile stress-deformation prediction code and a con­strained optimization code. The finite element method (FEM) is the favorite method for structur­al analysis because of its adaptability to complex 3-D structural configurations and the ability to easily account for a point-by-point variation of physical properties of the material. With the re­cent improvements in the sparse matrix solver algorithms, the finite clement techniques arc also becoming competitive with the finite difference techniques in terms of the computer memory and computing time requirements. For relatively smaller problems in elasticity, it is even more ad­vantageous to use boundary clement method (BEM) because it is faster and more reliable since it is non-iterative and it requires only surface discretization.

14.2 Optimization in Elasticity

The field of structural optimization (269J-(273) has a considerably longer history than aerody­namic shape optimization. Almost every textbook on optimization involves examples from linear elastostatics since these types of problems usually result in smooth convex function spaces that have continuous and finite sensitivity derivatives, making them ideal for gradient search optimi­zation. As the geometric complexity and the diversity of materials involved in aerospace struc­tures has increased, so has the demand for a more robust non-gradient search optimization

algorithms. Consequently, the majority of the present-day Structural optimization is performed using different variations of genetic evolution search strategy and a hybrid gradicm/genetic ap­proach (274|, (275). This is quite evident when researching the literature dealing with structures made of composite materials, ceramically coated structures, and smart structures. In the case of smart structures, their “smart" attribute comes from the ability of such materials to respond with a desired degree of deformation to the applied pressure, thermal, electric or magnetic field. This automatic response can be very fast and can be used for active control of the structural shape in the regions exposed to the air flow. This influences the flow field, surface heat transfer and the aerodynamic forces acting on the structure.

Structural optimization is routinely used for the purpose of achieving aeroclastic tai­loring. Since this requires specifications of a large number of constraints in the form of desired local deformations, this application can also be qualified as a de facto inverse structural shape design. The objective is to find the appropriate shape and orientation of each layer of a compos­ite material to be formed so that the final object (for example, a helicopter rotor blade, an air­plane wing, etc.) will have (he most uniform stress distribution (thus minimum weight) and. when loaded, will deform into a desired form.