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IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints


IASS Symposium 2014

SESSION: General 9: Computational Tools, Shape Finding and Optimization

Shape finding and form-optimization of freeform surfaces and discrete grids

< Table of Contents for General 9: Computational Tools, Shape Finding and Optimization
  • Proceedings Name: IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints
  • ISSN: (Electronic Version) 2518-6582
  • Session: General 9: Computational Tools, Shape Finding and Optimization
  • Title: Shape finding and form-optimization of freeform surfaces and discrete grids
  • Author(s): Qi ZHANG, Bin YANG, Yan YU, Zheng ZHANG, Lu LI
  • Keywords: free form surface; optimization; shape finding
Abstract
As a new tendency of modern spatial structures, freeform surfaces have been widely adopted nowadays because of their predominant architectural representation. In this paper, the shape -finding and optimization method of a freeform surface used in an engineering project were introduced. After the optimal surface was found, discrete grids were generated as designed by the architect. And then the concept of force density was introduced into the optimization of discrete grids. Valley shaped columns were used in an engineering project located in shanghai, rhombus grids were used to form the freeform surface. In order to meet the artistic requirements of architect and at the same time get a reasonable mechanical form, several key problems should be solved. First, shape finding and optimization. In this project, the bottom boundary of the valley shaped column was given circle and the top boundary of the column was given space oblique ellipse. The position of these two boundaries was fixed. In this paper, three ellipses were set between the top boundary and the bottom boundary. The vertexes of the ellipses were used as the control points and basing on these control points and NURBS curve construction and NURBS surface construction technologies, continuous surface can be constructed. Take the geometric parameters as the optimization variables and the minimum strain energy as the optimization objective, by using the conjugate gradient methods, several reasonable freeform surfaces can be found and provided for the architect to choose. Second, after the optimal surface was found, discrete grids were generated as required by architect. In this paper, rhombus grids were generated using RHINO. Third, the grids generated by RHINO should be optimized in order to get a more reasonable form. In this paper, the concept of FORCE DENTISY generally used in cable net shape finding theory were introduced into the optimization of rigid grid structure in order to get a more reasonable and beautiful grid form. Suppose that the discrete grids were cable net, restrict the grid point displacement outside the surface, and the normal vector at certain points of the surface can be calculated by programming. Take that every cable has the same force density as the Iterative Target and use ANSYS to calculate. By changing the value of force density, different grid forms can be achieved. The methods and procedure used in this paper can also be used in other engineering projects.

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