Shape And Topology Optimization Of Single Layer Free-Form Grid Shell

The main form of free-form surface used on architecture is the roof of various public buildings, among the many forms of single layer grid structure, the triangulated grids has great development potential for it’s succinct modeling, simple joints, good stiffness, and better suitability compared to the quadrilateral grids.Currently in practical application, the surface form is usually given by the architect and then followed by the structural engineers’ design of mechanical components, but this process gives little consideration of structural efficiency of the given surface. It is a new research subject of how to design it’s skin and grid configuration on the given surface. In this paper, in view of the existing problems of free-form surface single-layer lattice structures in practical use, we carried on the exploration from the following several aspects:For any free-form surface triangular grid structure, shape optimization of the initial surface given by architect is needed to enhance its mechanical performance. However, this kind of grid structure has such large number of nodes, there are difficulties for traditional shape optimization method to deal with it. This article uses reduced gradient method for shape optimization algorithm, in each iteration the problem to be solved was dealed with dimension reduction, so it can be applied to optimization problems with a great number of variables.The height of nodes on surface is used as design variable, the maximum stress and displacement adopted as state variables, strain energy is taken as optimization object, several examples showed that this method is not only suitable for minor adjustment of a given initial surface, but also can be used for form-finding of surface whitout a initial given shape.and compared to the original lattice structure, the optimized grid structure’s mechanical properties under static and dynamic load have dramatically improved.A two-phase approach for single-layer grid shell topology optimization design is presented that:Phase 1 involves a form-finding to achieve a optimal pattern of the gride shell under given loads and boundary conditions with numerical inverse suspension method, Phase 2 is topology optimization of grid structures based on genetic algorithms, through the adjustment of grid nodes and the removal of bars with low nominal stress in the structure in each iteration step,to enable internal forces of all elements of the optimized grid structure reaches the set limit value, eliminate low stress rods to improve material utilization, reduce structural costs, and always maintain the mechanical properties of structural indicators meet the code limits in the optimization process.Meshing is always the main factors that discourage a wide range use of free surface grid structure, the grid formatted by commonly used meshing method(manual or automatic meshing method)was difficult to ensure the uniformity of the structure, grid uniformity is mainly reflected in the length uniformity of rods and shape uniformity of elements. In order to solve this situation, in this paper automated mesh uniformity optimizer was programmed, the program automatically recognized and created the information matrix of the grid structure, and to achieve uniformity optimization of the length of grid bars through the adjustment of nodes on surface. Node adjusting direction was achieved by learning force density, adjusting distance was dicided by golden section method, the entire surface mesh uniform was achieved by adjustment of homogenization of a single node-link bars, and uses Rhino’s internal functions to pull back node detached from the surface to ensure the invariance of the surface in the calculate process.Examples showed that after node adjustment, grid uniformity is greatly enhanced,all bars basically reached same length, their differences meet the needs of engineering errors.Througt the analysis of mechanical properties of structure before and after adjustment, Homogenization does not cause significantly weaken to the structure, and some changes have appeared of the structure collapse mode under the ultimate load.This paper researched the problems in the practical application of free-form surface of single-layer space grid structure, conducted optimization study in three levels of shape, topology and grid, provides some methods and technical support for the application of this kind of structure.