The paper presents a finite element method for minimum weight design of structures with lower‐bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn‐Tucker optimatility criterion. The three most important features of the algorithm are: (i) a‐small number of design iterations are needed to reach optimal or near‐optimal design, (ii) structural elements with a wide variety of size‐stiffness may be used. The only significant restriction is the exclusion of curved beam and shell elements, (iii) the algorithm will for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.
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Kiusalaas et al. (1978) studied this question.