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SUMMARYA comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

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A strategy is developed for designing structures that radiate sound inefficiently in light fluids. The problem is broken into two steps. First, given a frequency and overall geometry of the structure, a surface velocity distribution is found that produces a minimum radiation condition. This particular velocity distribution is referred to as the "weak radiator" velocity profile. Second, a distribution of Young's modulus and density distribution is found for the structure such that it exhibits the weak radiator velocity profile as one of its mode shapes. In the first step, a finite element adaptation of the integral wave equation is combined with the Lagrange multiplier theorem to obtain a surface velocity distribution that minimizes the radiated sound power. In the second step, extensive use of structural finite element modeling as well as linear programming techniques is made. The result is a weak radiator structure. When compared to a structure with uniform material properties, the weak radiator structural response is found to exhibit three important characteristics. First, the weak radiator structure shows lower vibration amplitude near its boundaries. Second, the weak radiator structure exhibits lower wave number content in the supersonic region. Third, the distribution of surface acoustic intensity on the weak radiator structure is very small at all the points along its surface. The effect of modal overlap on the performance of the weak radiator structures is found to be negligible. While the method employed here is general, the example of a simple beam radiating in a rigid baffle is used for the purpose of illustration.

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