PENALTY FUNCTION METHOD FOR OPTIMAL DESIGN OF MULTIPURPOSE VIBRATING BEAMS

A computational design algorithm is formulated to determine the optimal area distribution of a beam which undegoes free and forced harmonic vibrations during its service life. The structural element has to serve more than one function, and this necessitates a design which meets various requirements. Hence, the constraints on the multipurpose beam involve simultaneously its dynamic response under single or multiple loads and its fundamental frequency. These problems are formulated in a mathematical programming format by expressing the area function in terms of linear splines. The resulting optimization problems are solved using suitable penalty functions. The proposed design method is illustrated by several numerical examples which show the complex tradeoffs involved in the design of multipurpose structures.