Topology optimization of continuum structures with local and global stress constraints
Topology optimization of continuum structures with local and global stress constraints
复制标题
DOI：
10.1007/s00158-008-0336-2
复制
发表时间：
2009-10
影响因子：
3.9
通讯作者：
J. París;F. Navarrina;I. Colominas;M. Casteleiro
中科院分区：
文献类型：
--
作者：
J. París;F. Navarrina;I. Colominas;M. Casteleiro
拓扑结构优化问题通常用最大刚度（最小柔度）方法来描述。这种类型的方法的目的是将给定量的材料分布在某个区域中，使得对于给定的载荷情况，所得结构的刚度最大化（即，柔度或变形能量最小化）。因此，材料质量被限制为最大可能质量的预定义百分比，而不考虑应力或位移约束。本文提出了一种不同的拓扑优化策略：一种具有应力约束的最小重量连续体结构拓扑优化有限元列式。我们提出了两种不同的方法，以考虑应力约束的优化配方。应力约束的局部方法在域的预定义点（每个元素的中心点）处施加应力约束。i.e.at相反，全局方法仅施加一个全局约束，该全局约束通过某个所谓的聚合函数来聚集所有局部约束的效果。最后，一些应用实例解决了这两个配方，以比较所获得的解决方案。
Topology structural optimization problems have been usually stated in terms of a maximum stiffness (minimum compliance) approach. The objective of this type of approach is to distribute a given amount of material in a certain domain, so that the stiffness of the resulting structure is maximized (that is, the compliance, or energy of deformation, is minimized) for a given load case. Thus, the material mass is restricted to a predefined percentage of the maximum possible mass, while no stress or displacement constraints are taken into account. This paper presents a different strategy to deal with topology optimization: a minimum weight with stress constraints Finite Element formulation for the topology optimization of continuum structures. We propose two different approaches in order to take into account stress constraints in the optimization formulation. The local approach of the stress constraints imposes stress constraints at predefined points of the domain (i.e.at the central point of each element). On the contrary, the global approach only imposes one global constraint that gathers the effect of all the local constraints by means of a certain so-called aggregation function. Finally, some application examples are solved with both formulations in order to compare the obtained solutions.