标题： 基于累积损伤准则的拓扑优化设计中荷载的概率组合 显示英文标题

标题： Probabilistic combination of loads in topology optimization designs via cumulative damage criteria

摘要： 拓扑优化（TO）是一种在用户定义约束下进行结构设计的成熟方法，例如最小体积和最大刚度。 然而，这些方法传统上仅应用于静态、确定性载荷，在这种情况下模量、位置和方向都是已知且不变的。 这与结构工程设计中使用的概率载荷组合相矛盾，并导致两个重要的缺点。 第一个与维护和可靠性有关：静态载荷未能考虑载荷过程、测量或常规服务中的自然出现的不确定性；同时定量地忽略了诸如振动等未预见现象，材料行为被假设为线性各向同性，忽略了功能梯度材料中的疲劳、塑性和各向异性。 第二个涉及最优性本身：通常，作为“最优”结构呈现的结构实际上高估了载荷，从而因超过其实际需求和/或在整个设计域中分布不当而浪费材料。 本文提出了一种概率框架：引入不确定和伪动态载荷，通过一种增强的SIMP方案并嵌入惩罚项，以解决疲劳损伤、层方向、力学响应（拉伸/压缩）和屈服极限（冯·米塞斯等效应力）。 这个计算高效的框架被应用于各种载荷场景，生成具有相同体积分数约束的多样化设计，性能得到改善且更加现实。 在所提出的方法下，如果载荷是永久性的且损伤各向同性，该方法将收敛到传统的（确定性）拓扑优化结果。 本文还探讨了这项工作的未来影响，特别是关于超材料设计。 显示英文摘要

摘要： Topology optimization (TO) is a well-established methodology for structural design under user-defined constraints, e.g. minimum volume and maximum stiffness. However, such methods have traditionally been applied to static, deterministic loading, in which modulus, position and direction are known and invariant. This is against the probabilistic load combination used in the structural engineering designs, and entails two important shortcomings. The first one is related to maintenance and reliability: static loading fails to consider naturally occurring uncertainties in the loading process, measurements or regular service; also ignoring (quantitatively) unforeseen phenomena such as vibrations, and the material's behavior is assumed linear isotropic, ignoring fatigue, plasticity and anisotropy in functionally-graded materials. The second one concerns optimality itself: often times, the structure presented as "optimal" in fact over-estimates loading and thus wastes material by exceeding its real needs and/or distributing it poorly throughout the design dominion. In this article, a probabilistic framework is presented: uncertain and pseudo-dynamic loading is introduced to create robust topologies via a reinforced SIMP scheme with embedded penalization addressing fatigue damage, layer direction, mechanical response (traction/compression) and yield limit (von Mises equivalent stress). This computationally efficient framework is applied to various loading scenarios, generating diverse designs for the same volume fraction constraint with improved and more realistic performances. Under the proposed method, if loads are permanent and damage isotropic, the methodology converges to the traditional (deterministic) topological optimization results. Future ramifications of this work are pondered, especially regarding metamaterial design.