基于B样条的自由曲面结构形态创构方法研究

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。

Structure morphogenesis of free-form surfaces based on B-spline

Given the key points on B-spline and introducing the reference plane, the internal and external boundaries were determined using B-spline curved surface formed by the key points and parametric B-spline curve on reference plane, which was divided by Delaunay triangular. Then the initial structure with complicated boundary was obtained. The strain energy sensitivity to the key points was derived using the relationship between the strain energy and the key points. A new method was established to minimize the strain energy, which avoided the low computation efficiency if node was set as the variable and the optimized surface needed secondary processing for smoothing. Results show that the proposed method can solve the structure morphogenesis of the free-form surfaces with complex boundary in practical engineering. A variety of flexible and reasonable free-form surfaces can be created using the method. The resulting structure has higher stiffness and higher ultimate capacity. The generation of bending moment is avoided. The effect of initial imperfections on the mechanical property is decreased.