考虑承载面最大位移约束的结构拓扑优化方法

在实际工程问题中，存在着一类承受分布力载荷作用的工程结构。为了实现此类结构的刚度设计要求，提出限制承载面变形的拓扑优化设计新模型。模型采用KS包络函数对承载面节点位移进行凝聚化处理，并推导了相应的伴随方程和敏度表达式。遵循独立连续映射法建模方式，采用一阶和二阶泰勒展开分别得到约束函数和目标函数的显式表达式。由此将优化问题转换为一系列标准二次规划子问题，采用序列二次规划算法进行高效、稳健求解。通过二维、三维数值算例验证了提出模型的可行性和有效性。结果表明，所提出的列式和相应的优化求解算法能有效控制结构局部区域的最大变形量。

Structural topology optimization method with maximum displacement constraint on load-bearing surface

In practical engineering problems, there exists a class of engineering structures sustaining distributed force. To satisfy the requirement of the stiffness design for this kind of structure, a new topological design formulation is proposed to restrict the deflection on the load-bearing surface. The KS aggregation function is applied to integrate a mass of the displacement constraints on load-bearing surface into one single constraint. The corresponding adjoin equation and sensitivity expressions are conducted. Following the construction of the independent continuous mapping method, the explicit expressions of the objective function and constraint function are obtained by first-order and second-order Taylor expansion. Consequently, the optimization problem is transformed into a series of standard quadratic programs, which can be solved efficiently and robustly using the sequential quadratic programming. The feasibility and effectiveness of the proposed method are then verified by 2D and 3D numerical examples. The optimized results clearly demonstrate that the proposed formulation and corresponding optimization algorithm can effectively control the maximum deflection of local region.