Disjoint design spaces in the optimization of harmonically excited structures

Abstract

The paper deals with a method of optimizing harmonically or dynamically excited structures which removes the frequency constraint (that specifies that the structure's first natural frequency of vibration must be greater than the excitation frequency), replaces the displacement constraint by an inequality constraint on the allowable stress and applies finite element approximations to the continuous one-dimensional structures. When the problem is posed in this manner, the feasible design space is disconnected or 'disjoint'. An attempt is made to explain this disjointness by studying the optimal design of a thin-walled cantilevered rod subjected to steady, simple harmonic torsional excitation. The finite element method is applied to the optimization of a harmonically excited structure with an arbitrary number of design variables, with the disjointness of the design space, a complicating factor.