Structural reanalysis for topological modifications – a unified approach

Abstract.A unified approach for structural reanalysis of all types of topological modifications is presented. The modifications considered include various cases of deletion and addition of members and joints. The most challenging problem where the structural model is itself allowed to vary is presented. The two cases, where the number of degrees of freedom is decreased and increased, are considered. Various types of modified topologies are discussed, including the common conditionally unstable structures. The solution procedure is based on the combined approximations approach and involves small computational effort. Numerical examples show that accurate results are achieved for significant topological modifications. Exact solutions are obtained efficiently for modifications in a small number of members.

[1]  U. Kirsch,et al.  Efficient reanalysis for topological optimization , 1993 .

[2]  Martin P. Bendsøe,et al.  Topology design of structures , 1993 .

[3]  Uri Kirsch,et al.  Structural Optimization: Fundamentals and Applications , 1993 .

[4]  K. Svanberg The method of moving asymptotes—a new method for structural optimization , 1987 .

[5]  Zhong‐sheng Liu,et al.  Structural Approximate Reanalysis for Topological Modifications of Finite Element Systems , 1998 .

[6]  George I. N. Rozvany,et al.  Layout Optimization of Structures , 1995 .

[7]  Leonard Spunt,et al.  Optimum structural design , 1971 .

[8]  U. Kirsch Combined approximations – a general reanalysis approach for structural optimization , 2000 .

[9]  Panos Y. Papalambros,et al.  Exact and accurate solutions in the approximate reanalysis of structures , 2001 .

[10]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary aerospace design optimization - Survey of recent developments , 1996 .

[11]  L. Leu,et al.  A reduced basis method for geometric nonlinear analysis of structures , 1998 .

[12]  T Haftka Raphael,et al.  Multidisciplinary aerospace design optimization: survey of recent developments , 1996 .

[13]  L. A. Schmit,et al.  Some approximation concepts for structural synthesis , 1973 .

[14]  M. F. Rubinstein,et al.  Automated Structural Synthesis Using a Reduced Number of Design Coordinates , 1973 .

[15]  Uri Kirsch,et al.  Efficient, Accurate Reanalysis for Structural Optimization , 1999 .

[16]  Ahmed K. Noor,et al.  Recent Advances and Applications of Reduction Methods , 1994 .

[17]  U. Kirsch,et al.  Exact structural reanalysis by a first-order reduced basis approach , 1995 .

[18]  Raphael T. Haftka,et al.  Fast exact linear and non‐linear structural reanalysis and the Sherman–Morrison–Woodbury formulas , 2001 .

[19]  Uri Kirsch,et al.  Optimal Topologies of Structures , 1989 .

[20]  Uri Kirsch,et al.  Structural Reanalysis for General Layout Modifications , 1997 .

[21]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[22]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .