Coupled form-finding and grid optimization approach for single layer grid shells

Abstract This paper demonstrates a novel two-phase approach to the preliminary structural design of grid shell structures, with the objective of material minimization and improved structural performance. The two-phase approach consists of: (i) a form-finding technique that uses dynamic relaxation with kinetic damping to determine the global grid shell form, (ii) a genetic algorithm optimization procedure acting on the grid topology and nodal positions (together called the ‘grid configuration’ in this paper). The methodology is demonstrated on a case study minimizing the mass of three 24 × 24 m grid shells with different boundary conditions. Analysis of the three case studies clearly indicates the benefits of the coupled form-finding and grid configuration optimization approach: material mass reduction of up to 50% is achieved.

[1]  Robert L. Taylor,et al.  FEAP - - A Finite Element Analysis Program , 2011 .

[2]  K. Deb,et al.  Design of truss-structures for minimum weight using genetic algorithms , 2001 .

[3]  Johannes Wallner,et al.  Architectural geometry , 2007, Comput. Graph..

[4]  Fan Zijie,et al.  Truss Topology Optimization Using Genetic Algorithm with Individual Identification Technique , 2009 .

[5]  Sophia Lefantzi,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. , 2011 .

[6]  Santiago Huerta Fernández.  El cálculo de estructuras en la obra de Gaudí , 2003 .

[7]  P. Hajela,et al.  Genetic algorithms in truss topological optimization , 1995 .

[8]  V. Toğan,et al.  Optimization of 3d trusses with adaptive approach in genetic algorithms , 2006 .

[9]  Philippe Block,et al.  THRUST NETWORK ANALYSIS : A NEW METHODOLOGY FOR THREE-DIMENSIONAL EQUILIBRIUM , 2007 .

[10]  Axel Kilian,et al.  PARTICLE-SPRING SYSTEMS FOR STRUCTURAL FORM FINDING , 2005 .

[11]  Siamak Talatahari,et al.  Geometry and topology optimization of geodesic domes using charged system search , 2011 .

[12]  Claude Fleury,et al.  A primal-dual approach in truss topology optimization , 1997 .

[13]  Luciano Lamberti,et al.  An efficient simulated annealing algorithm for design optimization of truss structures , 2008 .

[14]  Hiroshi Ohmori,et al.  Truss topology optimization by a modified genetic algorithm , 2002 .

[15]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[16]  H. Schek.  The force density method for form finding and computation of general networks , 1974 .

[17]  M. Ohsaki.  Genetic algorithm for topology optimization of trusses , 1995 .

[18]  David P. Billington.  The Art of Structural Design: A Swiss Legacy , 2003 .

[19]  Sigrid Adriaenssens,et al.  Finding the Form of an Irregular Meshed Steel and Glass Shell Based on Construction Constraints , 2012 .

[20]  Michael S. Eldred,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's reference manual. , 2010 .

[21]  Paolo Ermanni,et al.  Evolutionary truss topology optimization using a graph-based parameterization concept , 2006 .

[22]  Sigrid Adriaenssens,et al.  Tensegrity Spline Beam and Grid Shell Structures , 2001 .

[23]  Ph. Bouillard,et al.  Review: Multicriteria optimization of lightweight bridge structures with a constrained force density method , 2011 .

[24]  Philippe Bouillard,et al.  Multiobjective topology optimization of truss structures with kinematic stability repair , 2012, Structural and Multidisciplinary Optimization.

[25]  Neil Leach,et al.  Digital Tectonics , 2004 .

[26]  Pauli Pedersen,et al.  Optimal Joint Positions for Space Trusses , 1973 .

[27]  Mathias Stolpe,et al.  Global optimization of discrete truss topology design problems using a parallel cut-and-branch method , 2008 .

[28]  L. Gil,et al.  Shape and cross-section optimisation of a truss structure , 2001 .

[29]  Hartmut Noltemeier.  Computational Geometry and its Applications , 1988 .

[30]  Sergio Pellegrino,et al.  Multi-objective optimization of free-form grid structures , 2009 .

[31]  Marta B. Rosales,et al.  Shell form-finding: Physical and numerical design tools , 2009 .

[32]  Rolf Klein,et al.  Abstract Voronoi Diagrams and their Applications , 1988, Workshop on Computational Geometry.

[33]  A. Nemirovski,et al.  Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint , 2000 .

[34]  Afonso C. C. Lemonge,et al.  A genetic algorithm for topology optimization of dome structures , 2008 .

[35]  Mehmet Polat Saka,et al.  Optimum topological design of geometrically nonlinear single layer latticed domes using coupled genetic algorithm , 2007 .

[36]  Paolo Basso,et al.  Computational morphogenesis in Architecture: the cost optimization of free form grid shells , 2009 .