A new hybrid fuzzy-goal programming scheme for multi-objective topological optimization of static and dynamic structures under multiple loading conditions

This work presents a hybrid fuzzy-goal multi-objective programming scheme for topological optimization of continuum structures, in which both static and dynamic loadings are considered. The proposed methodology fortopological optimization first employs a fuzzy-goal programming scheme at the top level for multi-objective problems with static and dynamic objectives. For the static objective with multi-stiffness cases in the fuzzy-goal formulation, a hybrid approach, involving a hierarchical sequence approach or a hierarchical sequence approach coupled with a compromise programming method, is especially suggested for the statically loaded multi-stiffness structure at the sublevel. Concerning dynamic optimization problems of freevibration cases, nonstructural mass, oscillation of the objective function, and repeated eigenvalues are also discussed. Solid Isotropic Material with Penalization density–stiffness interpolation scheme is used to indicate the dependence ofmaterial modulus upon regularized element densities. The globally convergent version of the method of moving asymptotes and the sequential linear programming method areboth employed as optimizers. Several applications have been applied to demonstrate the validation of the presented methodologies.

[1]  M. Zhou,et al.  Checkerboard and minimum member size control in topology optimization , 2001 .

[2]  O. Sigmund,et al.  Checkerboard patterns in layout optimization , 1995 .

[3]  N. Olhoff,et al.  Multiple eigenvalues in structural optimization problems , 1994 .

[4]  M. Bendsøe,et al.  Optimal design of material properties and material distribution for multiple loading conditions , 1995 .

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

[6]  G. Rozvany.  Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics , 2001 .

[7]  Jared L. Cohon,et al.  Multiobjective programming and planning , 2004 .

[8]  James P. Ignizio,et al.  Generalized goal programming An overview , 1983, Comput. Oper. Res..

[9]  Alexander P. Seyranian,et al.  Sensitivity Analysis of Multiple Eigenvalues , 1993 .

[10]  Erik Lund,et al.  Reliable and Efficient Finite Element Based Design Sensitivity Analysis of Eigenvalues , 1993 .

[11]  C. S. Jog,et al.  A new approach to variable-topology shape design using a constraint on perimeter , 1996 .

[12]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[13]  H. Zimmermann.  Fuzzy programming and linear programming with several objective functions , 1978 .

[14]  Noboru Kikuchi,et al.  TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS USING THE HOMOGENIZATION METHOD , 1998 .

[15]  N. L. Pedersen.  Maximization of eigenvalues using topology optimization , 2000 .

[16]  B. Bourdin.  Filters in topology optimization , 2001 .

[17]  N. Olhoff,et al.  Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives , 1999 .

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

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

[20]  N. Kikuchi,et al.  Topological design for vibrating structures , 1995 .

[21]  Noboru Kikuchi,et al.  Unified topology design of static and vibrating structures using multiobjective optimization , 2000 .

[22]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[23]  Ting-Yu Chen,et al.  Multiobjective optimal topology design of structures , 1998 .

[24]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[25]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[26]  J. Petersson,et al.  Slope constrained topology optimization , 1998 .

[27]  T. A. S. Vijayaraghavan,et al.  A multi-objective programming problem and its equivalent goal programming problem with appropriate priorities and aspiration levels: A fuzzy approach , 1995, Comput. Oper. Res..

[28]  Waiel F. Abd El-Wahed,et al.  A hybrid fuzzy-goal programming approach to multiple objective decision making problems , 2001, Fuzzy Sets Syst..

[29]  J. Petersson,et al.  Topology optimization using regularized intermediate density control , 2001 .

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

[31]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .