Abstract: A shape optimization method is presented for smoothing stress peaks that are caused by notch effects on unloaded edges of holes in plates or shell structures with linear-elastic, homogeneous, isotropic material under external forces. The optimization problem is first formulated as a functional whose integrand contains the difference between the stresses at the hole edge and the optimal stress. This mechanical problem is approximated by a sequence of purely geometric, substitute functionals. The substitute functional is discretized by means of splines and formulated as a nonlinear constrained optimization problem which is solved with a quasi-Newton method. The efficiency of the method is demonstrated on the basis of examples.

Abstract: Shape optimal design of an elastic solid of revolution under multiple constraints is treated. As a specific example, a device that seals a gun bore and transmits high in‐bore pressure to shear loading on the projectile, is considered. The design objective is minimum weight, with constraints on stress throughout the body, tractions on one surface of the boundary, and dimensions of the body. Methods of the calculus of variations and functional analysis are used to transform the variation of a functional over a variable region as a functional over a fixed region. An adjoint variable method of operator theory is then used to reduce this variation to an explicit function of only design variations. The resulting sensitivity coefficients are used in an iterative optimization algorithm. Numerical results are presented and show that the algorithm is stable and efficient.

Abstract: A numerical procedure for solving fluid flow and heat transfer equations by design optimization is presented. The procedure uses an optimization program based on an exterior penalty function method to solve the partial differential equations. The intent of the investigation is to show that the method is feasible so that the entire design process can be incorporated into an optimization algorithm. Three problems are chosen to examine this method: laminar flow through a rectangular duct; heat conduction on a flat plate; and viscous, incompressible flow over a sphere. Comparison of the optimization approach with the exact solution, when available, and approximate methods is made. The results of the investigation show that the method is feasible, but modifications in the optimization approach are necessary to improve the results.

Abstract: This paper presents a state of the art review of mathematical programming methods used in the design of skeletal elastic structures in which the possibility of altering the shape, position or layout of the members is considered. Virtually every type of optimization procedure including linear, nonlinear, and dynamic programming has been applied to this design problem. These methods have been implemented using three main approaches. The first, referred to as the ground structure approach, is one in which members are removed from a highly connect structure to derive an optimum subset of bars. In the second approach the co‐ordinates of the joints of the structure are treated as design variables and moved during the optimization procedure to enable an optimum layout to be designed. The third type of method includes those which allow for topological considerations at certain points during the design process and generally keeps the design variables in two separate groups. The paper discusses the way in which eac...