摘要
针对复杂空间曲面提出了一种基于单元变形能的优化展开算法。算法以拓扑等价映射得到的结果为初始值,以曲面网格单元由平面状态到空间状态的总变形能最小为目标,对展开网格的尺寸与形状进行优化,得到使变形能达到最小值的优化展开平面。计算结果表明,优化过程使变形能收敛于稳定的最小值,变形分布趋于均匀。
This paper presents an algorithm for the optimal development of doubly curved surfaces into planar shapes based on element deformation energy. The optimization process is divided into two stages： （1） the triangular mesh of the discretized surface is mapped into a planar shape homo-topologically on the assumption that the deformation distributed within the surface is continuous and homogeneous; （2） as non-developable surface can only be approximately developed, when the approximately developed planar shape is forced into the designed non-developable surface, the existence of deformation energy is unavoidable; the optimization model proposed by us is such that, when the approximately developed planar shape is forced into its designed shape, the energy of the deformation is the minimum. In the deformation energy model of each element, both stretching strain and shearing strain are considered. The optimized development shape and strain distribution are obtained by solving a functional differential equation iteratively. The convergence property of the algorithm is analyzed theoretically and numerically. Examples are given to show the effectiveness of the algorithm.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2006年第2期270-274,共5页
Journal of Northwestern Polytechnical University
关键词
曲面展开
优化展开
复杂曲面
surface development, optimal development, doubly curved surface
