Research of Virtual Design System for Spatial Structures by Meshfree Method

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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.