Stiffened plates are widely used in high-performance structures, especially when a high stiffness/weight ratio is a relevant factor. In this work, the main objective relies on determining the optimum geometry of a simply supported stiffened thin plate which minimizes the maximum out-of-plane displacement, while complying with maximum von Mises stress constraints. The structure is subject to a pressure uniform load and has a constraint of constant total material volume. This work investigated the influence in the objective function of variations in several geometric parameters, such as volume, number, angle, position, and cross-sectional area of the stiffeners in the maximum displacement and the maximum von Mises stress. A new topology optimization algorithm denominated Modified Adaptive Morphogenesis Algorithm was proposed using a pattern of leaf vein formation to define the topology of the stiffeners in the plates. A Hybrid Genetic Algorithm was performed to initiate the optimization procedure called germination. Also, a Robust Optimization Algorithm has used multiple objectives to decrease the variability of the maximum displacement field. The results showed that near the Pareto Front, the maximum displacement is not very sensitive to changes in the project decision variables, thus being a robust optimum point. Moreover, the results obtained were compared with data available in the literature, which showed the relevance and validation of the proposed methodology. Finally, under equivalent conditions of the number of stiffeners, the Morphogenesis Algorithm showed better results (displacement or stress) than those obtained with perpendicular stiffeners.

加筋板广泛用于高性能结构，尤其是当高刚度/重量比是一个相关因素时。在这项工作中，主要目标依赖于确定简支加筋薄板的最佳几何形状，以最大限度地减少最大平面外位移，同时遵守最大 von Mises 应力约束。该结构承受压力均布载荷，并具有总材料体积不变的约束。这项工作研究了在最大位移和最大 von Mises 应力下加强筋的体积、数量、角度、位置和横截面积等几何参数变化对目标函数的影响。提出了一种新的拓扑优化算法，称为修改自适应形态发生算法，使用叶脉形成模式来定义板中加强筋的拓扑。执行混合遗传算法以启动称为萌发的优化过程。此外，稳健优化算法使用多个目标来降低最大位移场的可变性。结果表明，在帕累托前沿附近，最大位移对项目决策变量的变化不是很敏感，因此是一个稳健的最佳点。此外，获得的结果与文献中可用的数据进行了比较，这表明了所提出的方法的相关性和有效性。最后，在加强筋数量相等的条件下，