An optimization algorithm is proposed to assist in the design of extradosed concrete bridges under static and seismic loading. This procedure is composed of structural analysis, sensitivity analysis and optimization modules. The finite element method is used for the three-dimensional analysis considering static loading (dead load and road traffic live load), geometrical nonlinearities, time-dependent effects and seismic action by using a modal response spectrum analysis. The design is formulated as a multi-objective optimization problem with objectives of minimum cost, deflections and stresses including service and strength criteria. The solution of the minimax problem is obtained by minimizing a convex scalar function obtained through an entropy-based approach. The design variables are the extradosed cables and tendons forces, the extradosed cables and tendons cross-sectional areas, the deck, towers and piers sizes. The analytical discrete direct method is used to find the structural response to changes in the design variables. A convex optimization strategy with multiple starting points finds minimum cost solutions with an adequate stiffness and mass distribution that satisfy the design criteria under both, static loading and seismic action. Numerical examples concerning the optimization of a real-sized extradosed concrete bridge illustrate the features and capabilities of the proposed method.

提出了一种优化算法，在静载和地震荷载作用下辅助设计混凝土桥。该程序由结构分析，灵敏度分析和优化模块组成。通过模态响应谱分析，将有限元方法用于考虑静载荷（静载荷和道路交通活动载荷），几何非线性，时变效应和地震作用的三维分析。该设计被公式化为一个多目标优化问题，其目标是最小成本，变形和应力（包括服务和强度标准）。通过最小化通过基于熵的方法获得的凸标量函数来获得极大极小问题的解决方案。设计变量是电缆和钢索的作用力，电缆和钢筋束的横截面积，甲板，塔架和码头的尺寸。解析离散直接法用于找到对设计变量变化的结构响应。具有多个起点的凸优化策略可以找到具有足够刚度和质量分布的最小成本解决方案，这些刚度和质量分布在静载荷和地震作用下均满足设计标准。有关优化实际尺寸混凝土桥的数值实例说明了该方法的特点和功能。具有多个起点的凸优化策略可以找到具有足够刚度和质量分布的最小成本解决方案，这些刚度和质量分布在静载荷和地震作用下均满足设计标准。有关优化实际尺寸混凝土桥的数值实例说明了该方法的特点和功能。具有多个起点的凸优化策略可以找到具有足够刚度和质量分布的最小成本解决方案，这些刚度和质量分布在静载荷和地震作用下均满足设计标准。有关优化实际尺寸混凝土桥的数值实例说明了该方法的特点和功能。