Abstract

The problem of structural optimization under variable loading conditions is discussed here. We assume a linearly-elastic structure subject to one single load of constant magnitude but of arbitrary orientation. Moreover, we assume that the structure is discretized by finite elements. The result of this study is an optimality criterion: the eigenvalues of the stiffness matrix of the optimum structure observe a minimum variance. In other words, the optimum structure under variable load must have a stiffness matrix that is as close as possible to isotropy. Furthermore, in order to implement the foregoing criterion, we introduce a novel method of automatic mesh generation, that is based on the concept of penalty functions of nonlinear programming. Finally, we illustrate these concepts by means of the optimization of a triangular lamina of given side lengths, with an elliptical hole centered at its centroid, of a prescribed area, the design parameters being the semiaxes of the ellipse and the orientation of these axes with respect to the edges of the lamina.

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