Research Of Shape, Topology And Grid Optimization Design About Free-form Structures Based On Robustness

So far, space latticed structures including space trusses, reticulated shells have been applied to culture, sports and exhibition architectures in quantity. But, these structures mostly have simple surface shape, such as spherical, parabolic, cylindrical, etc. People have developed the aesthetic fatigue. At home and abroad in recent years, a lot of free-form architectures appeared which are characterized by appearance of freedom to change. These new architectures have become landmarks from the time they appeared because of their unique appearance. Now, more and more architects are willing to adopt this new kind of spatial structures.Because such architectures have complex appearance and mechanical performance which need high reliability, it has become a pressing problem that how to ensure the safety of the class structures. Simultaneously, uniform morphology and force performance, reasonable topological arrangement of rods and mesh grid uniformity are three key problems in designing the class structures. This paper will discuss the contents of preliminary solutions to the above problems.For safety assessment method of free-form structures, this paper established a robustness evaluation index based on H∞control theory. This index can characterize structural sensitivity to outside interference, reflecting the robust degree of structures. By buckling analysis of hexagonal star dome, this paper compared the contact and difference between robustness index with structural strain energy.NURBS (non-uniform rational B-spline) has been a major method to create the morphology of free-form surface. The method can achieve any surface expression, and surface control parameters can be easily extracted for structural parametric design. This paper introduced the basic principles of NURBS, analyzed control principle and distinction of NURBS control points, weight, node vector on the shape construction.Based on the above theories, H∞robustness index was used as optimization objective, coordinates of NURBS control points and weights were used as shape optimization variables. DE (differential evolution algorithm) conducted free-form shape optimization under constraints. Then, features of control points and weights as shape optimization variables were contrasted. For a given surface, this paper added a tiny fluctuate surface in the original curved surface to achieve shape fine-tuning, dramatically improving the mechanical properties.In addition to shape, topology is another major factor affecting the mechanical properties of free-form grid structures. Reasonably determined topology configuration can guide meshing, providing a theoretical basis for the arrangement of rods. Currently, due to the complexity of this type of structures in shape and unclear force law, research on their topology is barely lack. In this paper, topology optimization variables were introduced into the mechanical optimization based on thickness or SIMP model. Combined optimization of the shape and topology was achieved by joining shape variables and topology variables. Practice has proved that this method can get the optimal structure, compared to the traditional shape optimization alone, topology optimization alone. This method can maximize the mechanical properties of the structure.Meshing is a major factor in the promotion of such structures. Manual or automatic meshing is hard to ensure grid uniformity. Grid uniformity is mainly reflected in the length uniformity of rods and shape uniformity of elements. Based on Rhinoceros software, automated mesh uniformity optimizer was programed. The program automatically recognized surface mesh and created grid information matrix. Uniformity of the grid was achieved by individually adjusting the position of the nodes. Node adjusting direction was achieved by learning force density. So, three-dimensional node adjustment was reduced to be one-dimensional. Then, one-dimensional searching technology was used to lock position of nodes. Examples showed that through few optimization steps, grid uniformity quality can be greatly improvedThis paper researched the major practical application issues of free-form structures, conducted optimization study in three levels of shape, topology and grid and achieved structural robust design, providing theoretical basis and technical support for the application of such structures.