偶应力介质结构的最优强度拓扑优化

在等应变能密度分布的意义下给出了偶应力介质结构最优强度的拓扑优化设计方法。优化模型的设计变量为单元的密度,约束函数为许用材料的体积用量,目标函数通过等应变能密度准则隐式地给出。该方法的优点在于将强度约束/目标的显式应力形式进行转化,避免了应力函数优化问题中的奇异性、强非线性及约束的局部性等困难。数值算例表明,基于优化模型,偶应力介质的最优结果依赖于结构的最小局部尺寸与偶应力介质特征长度的比值。当宏观结构的尺寸远大于特征长度时,偶应力介质的结果趋于经典连续介质的相应结果。

Structural Topology Optimization of Couple-stress Continuum with Maximum Strength

The topology optimization formulation of a couple-stress continuum structure with maximum strength is studied under the principle of uniform density of strain energy. The design variable is the element density and the constraint function is the permitted material volume in this formulation. Besides, the objective function is presented implicitly through the principle of uniform strain energy density. Compared with the traditional objective/constraint function in explicit stress expressions, this implicit objective avoids the difficulties such as singularity, the high nonlinearity and the locality of constraints. The numerical example shows that the optimal topology of couple-stress continuum based on the present optimization formulation relies on the size ratio of the local structure to the characteristic length. The topology of the couple-stress continuum tends to that of the classical continuum model.