Optimal design of flexible mechanisms with frequency constraints

Abstract The paper presents a finite element method for minimum weight design of flexible mechanisms with multiple frequency constraints and upper and lower bound constraints on the design variables. The design algorithm developed in this paper is formulated in terms of the Kuhn-Tucker optimality criterion, in which two damping factors are introduced to guarantee the algorithm possesses good stability and convergence. The first and second order design sensitivity analyses of eigenvalues are presented and the values of the damping factors α and β are recommended. Results of three numerical examples show that the algorithm is stable and the optimal design can be obtained in less than 15 iterations.