A neural dynamics model for structural optimization—Theory

Abstract

A neural dynamics model is presented for optimal design of structures. The Lyapunov function is used to develop the neural dynamics structural optimization model and prove its stability. An exterior penalty function method is adopted to formulate an objective function for the general constrained structural optimization problem in the form of the Lyapunov function. A learning rule is developed by integrating the Kuhn-Tucker necessary condition for a local minimum with the formulated Lyapunov 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 numbers 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 gradient information of the objective function. In a companion paper the neural dynamics model is applied to optimum plastic design of steel structures.