Abstract

In this paper we present a structural optimization approach that is based on explicit B-spline representation of the design, conforming with CAD standards. The methodology and implementation are general and can accommodate arbitrary B-spline degrees. The spline-based parametrization enables to incorporate explicit constraints on minimum and maximum areas of holes and on curvatures of boundaries. Therefore, practical design considerations such as flexibility with respect to locations and sizes of holes, can be embedded into the optimization problem. Furthermore, control over curvatures can simplify machining processes and lead to more efficient manufacturing, as well as influence the peak stresses in the structure. The presented method is applied to several stiffness optimization problems. The results demonstrate the capabilities of this approach to incorporate explicit geometric constraints in a straightforward manner. The utilization of curvature constraints as an efficient alternative to stress constraints is demonstrated as well.

摘要

在本文中，我们提出了一种结构优化方法，该方法基于设计的显式 B 样条表示，符合 CAD 标准。方法和实现是通用的，可以适应任意 B 样条度数。基于样条的参数化能够结合对孔的最小和最大区域以及边界曲率的显式约束。因此，实际的设计考虑，例如关于孔的位置和尺寸的灵活性，可以嵌入到优化问题中。此外，对曲率的控制可以简化加工过程并提高制造效率，并影响结构中的峰值应力。所提出的方法适用于几个刚度优化问题。结果证明了这种方法能够以直接的方式结合显式几何约束。曲率约束作为应力约束的有效替代方案也得到了证明。