A NEURAL DYNAMICS MODEL FOR STRUCTURAL OPTIMIZATION - THEORY

A neural dynamics model is presented for optimal design of structures. The Lyapunov function is used to develop the neural dynamics structur al optimization model and prove its stability. An exterior penalty fun ction method is adopted to formulate an objective function for the gen eral constrained structural optimization problem in the form of the Ly apunov function. A learning rule is developed by integrating the Kuhn- Tucker necessary condition for a local minimum with the formulated Lya punov function. The topology of the neural dynamics model consists of two distinct layers: variable layer and constraint layer. The numbers of nodes in the variable and constraint layers correspond to the numbe rs of design variables and constraints in the structural optimization problem. Both excitatory and inhibitory connection types are used for adjusting the states of the nodes. In addition to commonly-used inter- layer connections, recurrent connections are used to represent the gra dient information of the objective function. In a companion paper the neural dynamics model is applied to optimum plastic design of steel st ructures.