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This study focuses on the shape optimization of concrete gravity dams considering dam–water–foundation interaction and nonlinear effects subject to earthquake. The concrete gravity dam is considered as a two–dimensional structure involving the geometry and material nonlinearity effects. For the description of the nonlinear behavior of concrete material under earthquake loads, the Drucker–Prager model based on the associated flow rule is adopted in this study. The optimum design of concrete gravity dams is achieved by the hybrid of an improved gravitational search algorithm (IGSA) and the orthogonal crossover (OC), called IGSA–OC. In order to reduce the computational cost of optimization process, the support vector machine approach is employed to approximate the dam response instead of directly evaluating it by a time–consuming finite element analysis. To demonstrate the nonlinear behavior of concrete material in the optimum design of concrete gravity dams, the shape optimization of a real dam is presented and compared with that of dam considering linear effect.

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