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用有限元法对大型复杂结构进行形状优化设计,往往因计算量过大而无法实现,改用边界元法虽有不少优点,但这一困难尚不能从根本上克服。本文采用边界元法结合改进的复形优化方法——即将复杂的非线性隐式约束逐点展开为线性约束,简化了顶点应力约束检验过程,从而减少了计算量。文中就混凝土重力坝和空腹坝二种坝型给出了优化数学模型,并用本文提出的方法对一重力坝进行具体的形状优化计算,与初始形状相比优化结果说明可节省混凝土20%。
The use of finite element method for shape optimization design of large and complex structures is often impossible due to the large amount of calculations. There are many advantages to using the boundary element method, but this difficulty cannot be fundamentally overcome. In this paper, the boundary element method is used in conjunction with the improved complex optimization method—that is, the complicated nonlinear implicit constraint is expanded into a linear constraint point by point, which simplifies the verification process of the vertex stress constraint and reduces the computational complexity. In this paper, the optimal mathematical models for concrete dams and open-belly dams are given, and a concrete gravity dam is optimized by the method proposed in this paper. Compared with the initial shape, the optimization results show that 20% of the concrete can be saved.