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在B样条曲面上设定关键点并引入参考平面,利用所设定的关键点形成B样条曲面与参考平面上参数化B样条曲线确定的内外边界,采用Delaunay网格划分技术进行三角划分,生成能够适应复杂边界的自由曲面初始结构。利用关键点坐标的变化与自由曲面应变能的关系,推导了应变能对关键点的敏感度,建立了结构应变能最小化的自由曲面结构形态创构的方法,解决了以节点为优化变量计算效率低且优化后曲面不光滑需要二次加工的问题。研究结果表明,所提出的方法可以解决在实际工程应用中具有复杂边界的自由曲面形态创构问题,可以创构出自由、灵活的多种合理自由曲面结构,由此获得的曲面结构具有刚度大、承载力高,同时最大限度地抑制了弯矩的产生,且具有初始缺陷对结构受力性能影响减小的特点。
The key points are set on the B-spline surface and the reference plane is introduced. The key points are used to form the internal and external boundaries defined by the B-spline curves and the parameterized B-spline curves on the reference plane. The Delaunay meshing technique is used to triangulate the triangles Divide and generate the initial structure of freeform surface that can adapt to the complicated boundary. Based on the relationship between the change of the coordinate of the key point and the strain energy of the freeform surface, the sensitivity of the strain energy to the key points is deduced, and the method of constructing the freeform surface structure with minimized strain energy is established. Low efficiency and optimization of the surface is not smooth secondary processing problems. The results show that the proposed method can solve the problem of creating a free-form surface with complex boundaries in practical engineering applications, and can create a variety of free and flexible free-form surface structures. The surface structure obtained by this method has a large stiffness , Bearing capacity is high, while minimizing the generation of bending moment, and with the initial defects on the structure of the reduced force characteristics.