考虑自重载荷作用的连续体结构拓扑优化

TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES SUBJECTED TO SELF WEIGHT LOADS

针对自重载荷作用下连续体结构拓扑优化中常遇到的柔顺度随单元密度变化的非单调性、非有效的材料体积约束和材料低密度区出现的"附属"效应等主要困难,提出了RAMP材料插值模型和平均敏度过滤技术相结合的求解策略,并采用MMA方法进行了优化求解.研究了惩罚因子的选择对最优拓扑以及材料体积约束的影响.结果表明,合理增大RAMP材料模型中惩罚因子(例如取值达到20.0),可使材料体积约束达到有效约束.此外,通过与Sigmund提出的敏度过滤技术比较表明,当引入平均敏度过滤技术时,结果0/1化程度较Sigmund的敏度技术高,可获得清晰的黑白拓扑.

The topology optimization of continuum structures with self weight loads is investigated in this paper. Such difficulties as non-monotonous behavior of the compliance, inactive volume constraint of the optimal topology and the parasitic effect of low density regions are often arisen in topology optimization problems with self weight loads. Solution strategies based on the RAMP material model and the mean sensitivity filtering technique are proposed to get rid of the difficulties and MMA code is used to solve the optimization problem. The influence of penalty factors of the RAMP model on the optimal topology results is investigated. Research results show that the material resource constraint turn to active when the penalty factor is set to an appropriate value （for example, 20.0）. In addition, compared with the sensitivity filtering suggested by Sigmund, discrete 0/1 design can be obtained by the mean sensitivity filtering technique.