Topology Optimization of Strut-and-Tie Models in Reinforced Concrete Structures Using an Evolutionary Procedure

This paper presents a performance based evolutionary topology optimization method for automatically generating optimal strut-and-tie models in reinforced concrete structures with displacement constraints. In the proposed approach, the element virtual strain energy is calculated for element removal, while a performance index is used to monitor the evolutionary optimization process. By systematically removing elements that have the least contribution to the stiffness from the discretized concrete member, the load transfer mechanism in the member is gradually characterized by the remaining elements. The optimal topology of the strut-and-tie model is determined from the performance index history, based on the optimization criterion of minimizing the weight of the structure while the constrained displacements are within acceptable limits. Several examples are provided to demonstrate the capability of the proposed method in finding the actual load transfer mechanism in concrete members. It is shown that the proposed optimization procedure can produce optimal strut-and-tie models that are supported by the existing analytical solutions and experimental evidence, and can be used in practice, especially in the design of complex reinforced concrete members where no previous experience is available.

[1]  Fabio Biondini,et al.  Optimisation of Strut and-Tie Models in Reinforced Concrete Structures , 1998 .

[2]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[3]  Jorg Schlaich,et al.  Design and detailing of structural concrete using strut-and-tie models , 1991 .

[4]  Yi Min Xie,et al.  A performance index for topology and shape optimization of plate bending problems with displacement constraints , 2001 .

[5]  Grant P. Steven,et al.  Evolutionary structural optimization for dynamic problems , 1996 .

[6]  J Schlaich,et al.  TOWARD A CONSISTENT DESIGN OF STRUCTURAL CONCRETE , 1987 .

[7]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[8]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[9]  W. Ritter,et al.  Die Bauweise Hennebique , 1904 .

[10]  Uri Kirsch,et al.  Optimal Design Based on Approximate Scaling , 1982 .

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

[12]  Yi Min Xie,et al.  Optimal topology selection of continuum structures with displacement constraints , 2000 .

[13]  B. H. V. Topping,et al.  Topology Design of Discrete Structures , 1993 .

[14]  A. J. Morris,et al.  Foundations of Structural Optimization: A Unified Approach , 1982 .

[15]  Yi Min Xie,et al.  Optimal selection of topologies for the minimum-weight design of continuum structures with stress constraints , 1999 .

[16]  Y. Xie,et al.  Evolutionary structural optimization for problems with stiffness constraints , 1996 .

[17]  Harvey J. Greenberg,et al.  Automatic design of optimal structures , 1964 .

[18]  null null,et al.  Recent Approaches to Shear Design of Structural Concrete , 1998 .

[19]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .

[20]  Peter Marti,et al.  BASIC TOOLS OF REINFORCED CONCRETE BEAM DESIGN , 1985 .

[21]  G. R. Sharp,et al.  Structural idealization for deep beams with web openings , 1977 .

[22]  M. Z. Cohn,et al.  Application of Structural Optimization , 1994 .

[23]  William L. Gamble,et al.  RECENT APPROACHES TO SHEAR DESIGN OF STRUCTURAL CONCRETE. DISCUSSIONS AND CLOSURES , 2000 .

[24]  Prabhat Kumar.  Optimal force transmission in reinforced concrete deep beams , 1978 .

[25]  Yi Min Xie,et al.  Evolutionary Structural Optimization , 1997 .