按应变能处理应力约束的连续体结构拓扑优化

 对每个单元都引入应变比能系数，通过追求对局部应力约束的高精度逼近，使独立·连续·映射（Independent Continuous and Mapping，ICM）方法中全局化应变比能约束的表达更为可靠，同时采取放松初始应变比能系数的手段加速优化迭代。利用结构最大Mises应力对许用应力比值的幂函数对全局化处理后的应变比能约束限进行修正，或者控制结构的最大应力，或者加速优化迭代。为了使拓扑构型向合理方向演变，每次迭代都对拓扑变量履行从连续到离散的反演，反演阈值自动计算。各算例均以较少的结构重分析次数，优化得到了类似理论最优解Michell桁架的拓扑图形，表明本文处理应力约束下结构拓扑优化问题的方法是合理和高效的。

Topology Optimization of Continuum Structure with Stress Constraint Handled by Strain Energy Density

The coefficients of strain energy density are incorporated in every finite element, which makes the expression of the globalized strain energy density constraint in the ICM method more reliable by enforcing the local stress constraint with high accuracy. Furthermore, the original coefficients of strain energy density are relaxed in order to accelerate the optimization iteration convergence. A power function formed as the ratio of the maximal structural von Mises stress and the allowable stress is applied to modify the constraint value of the globalized constraint to control the structural maximal stress or to accelerate the optimization iteration convergence. For the topology configuration to evolve in a reasonable direction, the continuous topological design variables are converted to discrete ones by using of a dynamic filter criterion computed automatically. Some examples show that the method proposed in this paper is reasonable and efficient. The optimal topology configurations are similar to the Michell truss, which is known as the theoretical optimal solution.