Shape Determination of Structures Based on the Inverse Variational Principle/the Finite Element Approach,
KOBE UNIV (JAPAN)
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In this paper, the numerical shape determination technique of structures is proposed by combining with the finite element method as an application of the principle. First of all, the optimal shapes of bodies which are subjected to statistical loads are determined on the basis of the potential energy principle. The triangular finite element model is employed, and coordinates of the nodal points on the periphery of the body are adopted as shape variables to obtain the optimal shapes independent of preconception. To solve the derived system of nonlinear equations, a new successive reforming procedure referred as Energy Ratio Method is proposed. The several numerical examples show that the shape of the body is stably reformed into the optimal one by the method. In the second place, the principle is extended to the eigenvalue problems to search the shape of the maximum buckling load and that of the maximum fundamental frequency. Several examples using one-dimensional finite element model are presented and the validity of the Energy Ratio Method is also shown.