Research of Virtual Design System for Spatial Structures by Meshfree Method

为了降低大型膜结构的造价和工期，提出了一套准确、高效的膜结构设计体系。采用无单元系统而不是传统有限元系统的原因如下：该方法不需要生成复杂结构的网格，采用移动最小二乘插值法获得精确连续的应力应变状态。此外，由于位移场的c1连续性条件，可以很容易地确定膜表面切割线的测地线，这在有限元网格中很难定义。结合上述特点，本文还提出了膜上滑动索的分析方法。为了增强钢索的强度，通常会拉紧大型膜结构。在分析拉索加筋膜结构时，必须考虑拉索处的折叠膜引起的边坡不连续。此外，这些电缆通常以一种允许自己在膜表面滑动的方式连接，以便电缆在施加的重力载荷，风载荷等下能够找到平衡形式。在传统的有限元方法中，边坡的不连续面只能存在于单元的边界处，因此需要对这种移动的不连续面进行重新网格划分或对折叠单元进行特殊展开。在无单元法中，不需要将分析模型细分为单元，因此，折叠可以在膜表面的任意点上建模，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的无网格法膜结构设计与分析系统。算例验证了该方法的有效性。

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.