曲线变换型自由曲面结构的形态创建

Computational morphogenesis method of curve-generated freeform structures

基于结构形态学的基本概念,通过将结构几何形状的建立方法与寻找合理受力性能的数值优化方法相结合,提出了一种适用于曲线变换型自由曲面结构的形态创建方法。以B样条函数表达母线和准线,以应变能作为评价结构受力性能的指标,基于梯度法推导出结构应变能与B样条函数曲线控制点坐标间的导数关系,根据应变能的变化梯度确定控制点坐标的调整方向,通过逐步调整控制点坐标,获得一系列具有较小应变能的合理曲面形状。利用FORTRAN语言编制了相应的形态创建程序,并通过具体算例验证了方法的有效性。结果表明:该方法可保证结构在形态创建过程中,曲面上曲线的相对位置关系保持不变,为进一步实现连续壳体的离散化提供了条件;且由于控制点的数量远少于曲面上离散点的数量,因此相比于直接调整曲面坐标的形态创建方法,该方法计算效率更高。

Based on the principle of structural morphology, a new computational morphogenesis method lor curve- generated freeform structures was put forward, which combines the geometrical modeling method and the optimal method. The basic idea of this method can be illustrated as follow： B-spline technique is adopted to describe the generatrices and directrices of curve-generated surface, and the structural strain energy is taken as the evaluating indicator of structural performance ; based on the gradient method, the relationship between the differential of structural strain energy and the differential of the coordinate of the control points of generatrices and directrices is deduced, thus the adjusted direction of control points can be determined according to the gradient of structural strain energy; by adjusting control points gradually, the profile of freeform structures can be modified to achieve a series of freeform surface structures with lower structural strain energy. This morphogenesis method was programmed using FORTRAN language and some examples were carried out to verify the efficiency of this method. It shows that this method can keep the constant relationship between generatrices and directrices in the process of morphogenesis, since the morphogenesis process starts from the generatrices and directrices rather than the generated surfaces, which makes this method more suitable for the application of grid shells. Moreover, as the amount of control points are far less than the amount of points on surface, the adjusting of surface by control points is more efficient than some computational morphogenesis methods which adjust the surface directly.