基于工程限值约束的结构拓扑优化设计分析

基于固体各向同性材料惩罚密度插值模型，建立近似支撑框架模型，以最大刚度为优化目标，以优化体积比及工程限值为约束条件，对支撑框架结构进行了优化。工程限值约束包括最大、最小尺寸约束，对称性约束以及顶点位移约束等。研究结果表明：当支撑框架中斜撑的斜交角度为39°~59°时，框架具有较好的抗侧刚度；当优化体积比为0.3时，优化后结构顶点位移较原设计域增加19%。引入工程限值约束条件能使拓扑优化后的结果有效应用于实际工程，优化后结构具有框架形态，无不易建造的细微结构，减少了低效材料分布，从而降低造价。

Application of topology optimization based on engineering limited constraints

Based on the SIMP (solid isotropic microstructures with penalization) interpolation model, braced frame simulation models were constructed for stiffness maximization, where the constraints included volume fraction and engineering limited constraints. The engineering limited constraints incorporated maximum/minimum dimension constraint, symmetric constraint, and peak displacement constraint. Research shows that the optimum diagonal angle is between 39° and 59° to maximize the lateral stiffness of braced frame structure. The top drift increases by 19%, while the volume fraction is 0.3 after optimization. The optimum structure has the feature of braced frame without detailed microstructure difficulty to build. Thus appropriate engineering limited constraints are necessary to advance topology optimization towards more practical designs for construct ability, decrease inefficient material distribution, reduce the cost accordingly.