含有Heaviside密度映射的构型平稳变化的柔性机构拓扑优化设计

Optimizing Topological Design of Compliant Mechanism with Steady Change in its Configuration with Heaviside Density Projection

现有柔性机构拓扑优化方法在解决柔性机构拓扑优化的类铰链和灰度问题仍存在一些困难。为获得清晰和不含类铰链的优化拓扑,提出了一种构型平稳变化的结构拓扑优化求解方法。首先,构建了一种能综合表征柔性机构输入和输出端的局部刚度特性的加权组合柔顺度函数;而后,引入加权组合柔顺度的小量变化约束、Heaviside密度映射和变约束限方案,建立了柔性机构构型平稳变化的优化模型;最后结合MMA算法,形成了一种构型平稳变化的柔性机构拓扑优化方法。给出的算例结果表明,相比于现有方法,该方法计算公式简单,可获得清晰且无类铰链的拓扑构型。

The existing methods for the topological optimization of a compliant mechanism still have some difficulties in optimizing its hinge-like and grey topology.In order to obtain a clear and optimal topology without any hinge,a structural topological optimization method is proposed.Firstly,we construct a weighted combination compliance function,which can comprehensively characterize the local stiffness characteristics of the input and output ends of the compliant mechanism.Then,by introducing the small change constraints of the weighted combination mechanism,the Heaviside density projection and a varied constraint scheme,we establish an optimization model with steady changes in the configuration of the compliant mechanism.Finally,in combination with the MMA algorithm,a topological optimization method for compliant mechanism with steady changes in configuration is formulated.The numerical simulation results show that,compared with the existing methods,the proposed method has simple calculation formulae and can obtain a clear optimal topology without hinges.