Strength optimized designs of thermoelastic structures
Strength optimized designs of thermoelastic structures
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DOI：
10.1007/s00158-010-0535-5
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发表时间：
2010-11
影响因子：
3.9
通讯作者：
P. Pedersen;N. L. Pedersen
中科院分区：
文献类型：
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作者：
P. Pedersen;N. L. Pedersen
对于热弹性结构，相同的优化设计不会同时导致最小柔度和最大强度。合规性可能是一个值得怀疑的目标，本文的重点是强度的重要方面，量化为最大冯米塞斯应力的最小化。柔度定义为位移和总载荷的乘积，那么对于热弹性问题，柔度就不同于总弹性能。这种差异的一个显式公式推导和优化的例子中的数值说明。作为一种替代数学规划，这与大量的设计变量和强度约束，被发现是不切实际的，我们选择简单的递归迭代，以获得均匀的能量密度，并通过实例发现，所获得的设计也接近满足强度最大化。在顺应性最小化中，减少总体积可能是有利的，但对于强度最大化，有人认为保持总允许体积是有利的。与热弹性分析直接在有限元公式，简单的显式公式等效热弹性载荷附加。
For thermoelastic structures the same optimal design does not simultaneously lead to minimum compliance and maximum strength. Compliance may be a questionable objective and focus for the present paper is on the important aspect of strength, quantified as minimization of the maximum von Mises stress. With compliance defined as the product of resulting displacements and their corresponding total loads, then for thermoelastic problems compliance is different from total elastic energy. An explicit formula for this difference is derived and numerically illustrated in the optimized examples. As an alternative to mathematical programming, which with a large number of both design variables and strength constraints, is found non-practical, we choose simple recursive iterations to obtain uniform energy density and find by examples that the obtained designs are close to fulfilling also strength maximization. In compliance minimization it may be advantageous to decrease the total volume, but for strength maximization it is argued that it is advantageous to keep the total permissible volume. With the thermoelastic analysis presented directly in a finite element formulation, simple explicit formulas for equivalent thermoelastic loads are appended.