Research of Virtual Design System for Spatial Structures by Meshfree Method

为了降低大型膜结构的建造成本和工期，迫切需要一套准确、高效的膜结构设计系统。采用无单元体系而不是传统的有限元体系的原因如下。该方法不需要对复杂结构进行网格划分，利用移动最小二乘插值法可以得到精确、连续的应力应变状态。由于在有限元网格中很难定义位移场的连续条件，因此可以很容易地确定切割线在膜面上的测地线，本文还提出了膜上滑索的分析方法。用来加强强度的拉索往往会使大型膜结构变得紧张。在分析拉索加筋膜结构时，必须考虑拉索处的折叠膜，它会产生不连续的坡度。此外，这些缆索通常以一种允许其自身滑过薄膜表面的方式连接，以便缆索能够在施加的重力荷载、风荷载等作用下找到平衡状态。在传统的有限元方法中，坡度的不连续性只存在于单元的边界上，因此需要重新划分网格或对折叠单元进行特殊的发展来模拟这种移动的不连续性；在无单元方法中，不需要将分析模型细分为单元，因此可以在膜表面的任意点上模拟折叠，并且通过重新定义节点排列可以在表面上自由移动。最后，本文提出了基于移动最小二乘插值法的膜结构无网格设计分析系统。数值算例表明了该方法的有效性。

In order to reduce cost and period of constructing large-scale membrane structures, an accurate and efficient system for designing membrane structures is anticipated. The reason why the element free system was adopted rather than the conventional finite element system are as follows. It requires no generating meshes of complicated structures, accurate and continuous stress and strain state is obtained by using the moving least squares interpolation. Also the geodesic lines on the surface of membrane for the cutting lines can easily determined due to the C 1 continuity condition of displacement field, which are hardly defined in the finite element meshes.In this study, adding to the above characteristics, the analysis method for sliding cables on membrane is also proposed. Cables to reinforce their strength often tense large membrane structures. In order to analyze cable-reinforced membrane structures, folding membrane at cable, which yields discontinuity of slope, has to be taken into account. Furthermore, these cables are often attached in a way that permits themselves to slide over the surface on the membrane so that the cables could find equilibrium form under the applied gravity load, wind load and so on. In the conventional finite element method, discontinuity of slope can exists only at the boundary of elements, so re-meshing or special development of folding element is necessary to model this moving discontinuity.In the element free method, it is not necessary to subdivide analysis model into elements, therefore, folding can be modeled at arbitrary points on membrane surface and it can move freely on the surface by redefining the nodal arrangement.Finally, in this study, the design and analysis system using mesh free method based on the moving least squares interpolation for membrane structures is proposed. Several numerical examples have been demonstrated to show the validity of the proposed method.