钢筋混凝土结构的应力拓扑优化方法研究

STUDY ON STRESS BASED TOPOLOGY OPTIMIZATION FOR REINFORCED CONCRETE STRUCTURES

基于预测混凝土失效行为的Drucker-Prager(D-P)屈服准则,研究了进行钢筋混凝土结构配筋设计的应力拓扑优化方法。结合扩展的双材料密度惩罚模型,优化问题构造为以单元人工密度为设计变量、混凝土材料Drucker-Prager屈服函数为约束条件的钢筋用量最小化问题。为合理定义混凝土应力并防止应力奇异解现象,采用局部应力插值模型和-松弛方法对混凝土应力约束条件进行处理。推导约束函数的伴随法灵敏度计算公式,运用基于梯度的连续性优化算法求解优化问题。数值算例验证了所提优化模型的正确性及数值算法的有效性,并通过与传统最小柔顺性拓扑优化结果的比较,说明了该文方法能够充分利用混凝土的抗压能力和钢筋的抗拉能力,设计结果更为实用。

Based on the Drucker-Prager （D-P） criterion for the failure of concrete, a stress based topology optimization method for the design of reinforced concrete structures is studied. Following an extended two-material density penalization scheme, elemental artificial densities are set as the design variables in the optimization problem. The proposed optimization model is constructed as to minimize the steel material volume under concrete Drucker-Prager yield constraints. In order to give a reasonable definition of concrete stress and prevent the stress singularity, the local stress interpolation function and the e-relaxation technique are employed. With the adjoint-variable sensitivity information of stress constraints, the optimization problem is solved by the gradient-based continuous optimization algorithm. Numerical examples show the validity of the proposed optimization model as well as the efficiency of the numerical techniques. Compared with the conventional compliance minimization method, the obtained optimal solutions are more practicable since they make the best use of the compression strength of concrete and the tensile strength of steel.