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首页> 外文会议>International Conference on Computer Aided Optimum Design in Engineering; 2007; Myrtle Beach,SC(US) >Global versus local statement of stress constraints in topology optimization of continuum structures
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Global versus local statement of stress constraints in topology optimization of continuum structures

机译：连续体结构拓扑优化中应力约束的全局和局部陈述

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摘要

Structural topology optimization problems have been traditionally set out in terms of maximum stiffness formulations. In this approach, the goal is to distribute a given amount of material in a certain region, so that the stiffness of the resulting structure is maximized for a given load case. Even though this approach is quite convenient, it also entails some serious conceptual and practical drawbacks. The authors, in common with other research groups, have been working for a few years on the possibility of stating these kinds of problems by means of a FEM-based minimum weight with stress (and/or displacement) constraints formulation. The physical meaning of this approach is closer to the engineering point of view. Furthermore, most of the above mentioned drawbacks could be removed this way. However, this also leads to more complicated optimization problems with much higher computational requirements, since a large number of highly non-linear (local) constraints must be taken into account to limit the maximum stress (and/or displacement) at the element level. In this paper, we explore the feasibility of defining a so-called global constraint, whose basic aim is to limit the maximum stress (and/or displacement) simultaneously within all the structure by means of one single inequality. Should this global constraint perform adequately, the complexity of the underlying mathematical programming problem should be drastically reduced. Finally, we compare the results provided by both types of constraints in some application examples.
机译：传统上已经根据最大刚度公式提出了结构拓扑优化问题。在这种方法中，目标是在给定的区域中分配给定数量的材料，以便在给定的载荷情况下使所得结构的刚度最大化。尽管此方法非常方便，但也带来一些严重的概念和实践缺陷。与其他研究小组一样，这些作者已经通过基于FEM的具有权重（和/或位移）约束的最小权重来阐明此类问题的可能性进行了数年的研究。这种方法的物理意义更接近工程学的观点。此外，大多数上述缺点可以通过这种方式消除。但是，由于必须考虑大量的高度非线性（局部）约束以限制单元级别的最大应力（和/或位移），因此这也会导致具有更高计算要求的更复杂的优化问题。在本文中，我们探索了定义所谓的全局约束的可行性，其基本目的是通过一个不等式同时限制所有结构内的最大应力（和/或位移）。如果此全局约束能够充分执行，则应大大降低基础数学编程问题的复杂性。最后，在一些应用示例中，我们比较了两种约束类型提供的结果。

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