控制网格变形的动力松弛法膜结构找形分析

Form finding of membrane structures by dynamic relaxation controlling mesh distortion

采用动力松弛法对膜结构找形分析时,为了防止节点的聚集以获得更精确的膜曲面,提出了一种新的控制网格变形的找形技术.膜单元采用平面三角形单元描述,在单元每两节点间引入了与单元边长变化速率成正比的阻尼项,通过阻尼项产生的节点力来控制网格在找形过程中的变形.对悬链面找形时发现,当黏性系数不大于0.7时,动力松弛法收敛,网格节点分布较无阻尼时均匀.对Scherk-like曲面找形时发现,能够控制网格变形且满足收敛性的黏性系数的上限为1.5.此方法能够有效地解决膜结构找形分析中网格的大变形问题,保证了单元密度,特别是克服了曲率较小处网格过于稀疏的缺陷.

For good representation of the surface and preventing the congregation of mesh nodes, a new technique for controlling mesh distortion during the form-finding of membrane structures by dynamic relaxation method was presented. In the course of form-finding, the plane triangle element was applied. The damp proportion to the velocity of element borderline deformation between each two nodes was introduced. The node force corresponding to damp was used to control mesh distortion. During form-finding of catenoid, when the viscosity coefficient was not more than 0.7, the dynamic relaxation method taking damp into account had good convergence and the nodes distributed more even. For convergence and controlling mesh distortion, during form-finding of Scherk-like surface, it was found that the upper limit of viscosity coefficient was 1.5. The method can successfully control the severe distortion of mesh and retain the density of elements, especially can avoid the sparseness of mesh in the location of lower curvature.