基于等几何方法的功能梯度Mindlin板结构拓扑优化设计

提出一种基于等几何分析的功能梯度Mindlin板结构拓扑优化方法，实现了沿着板面内方向梯度材料渐变与结构拓扑协同设计。基于等几何分析中的非均匀有理B样条(non-uniform rational B-spline， NURBS)基函数，保证了板结构建模、仿真分析和优化设计的参数化统一。由于等几何方法基函数的高阶连续性、非负性、规范性等特点，建立了合理的设计变量与梯度材料相对密度的分布关系。为了克服Mindlin板仿真分析的数值闭锁问题，采用NURBS等几何分析单元的缩减积分策略。数值算例展示了该方法的有效性，且获得了具有清晰细节特征的功能梯度板新型设计方案。结果表明，相比于预先定义材料配比，该方法可以实现功能梯度材料属性与结构拓扑的协同优化设计。

Topology Optimization Design of Functionally Graded Mindlin Plate Structures Based on Isogeometric Method

In this paper, a topology optimization approach of functionally graded Mindlin plate structures based on isogeometric analysis is proposed, in order to realize the collaborative design of material gradient along the in-plane direction and structure topology. Based on the non-uniform rational B-spline (NURBS) basis function in isogeometric analysis, the parametric unification of modeling, simulation analysis and optimization design of plate structures is ensured. Due to the high-order continuity, non-negative and normative characteristics of the basis functions, a reasonable distribution relationship between the design variable and the relative density of the gradient material is established. In order to overcome the numerical locking problem of Mindlin plate analysis, the reduced integration strategy of NURBS isogeometric elements is adopted. Numerical examples show the effectiveness of the proposed method, and the design scheme of functionally graded plate with clear and detailed features is obtained.The results show that compared with the pre-defined material ratio, the proposed method can realize the simulaneous optimization design of functionally graded material properties and structure topology.