The Statement of Optimal Design Problem with the Cusp Catastrophe Theory Application

Abstract

The purpose of this paper is to present the catastrophe theory method for the optimal design of machine components. A brief description of the cusp catastrophe is presented in the introduction. The statement of optimal design problem is given in the second part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is devoted to probability approach. Manage variables are viewed as stochastic quantities, analytical and statistical linearization methods are used for the reliability function evaluation.