Recent Advances in Approximation Concepts for Optimum Structural Design

This paper reviews the basic approximation concepts used in structural optimization. It also discusses some of the most recent developments in that area since the introduction of approximation concepts in the mid-seventies. The paper distinguishes between local, medium-range and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It appears also that some new methodologies emerge which could greatly benefit from the introduction of new computer architectures.

[1]  U. Kirsch,et al.  Approximate Behavior Models for Optimum Structural Design , 1981 .

[2]  M. Fuchs,et al.  A family of homogeneous analysis models for the design of scalable structures , 1990 .

[3]  B. Prasad,et al.  Novel Concepts for Constraint Treatments and Approximations in Efficient Structural Synthesis , 1983 .

[4]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[5]  Vassili Toropov,et al.  Simulation approach to structural optimization , 1989 .

[6]  Hirokazu Miura,et al.  New approximation of frequency response for structural synthesis and parameter identification , 1991 .

[7]  G. N. Vanderplaats,et al.  Arch shape optimization using force approximation methods , 1990 .

[8]  Raphael T. Haftka,et al.  First and second order constraint approximations in structural optimization , 1988 .

[9]  R. H. Ricketts,et al.  Simplified and refined structural modeling for economical flutter analysis and design , 1977 .

[10]  M. Zhou,et al.  Two‐level approximation concept in structural synthesis , 1990 .

[11]  Claude Fleury,et al.  Convex Approximation Strategies in Structural Optimization , 1989 .

[12]  James L. Rogers,et al.  Shuttle solid rocket booster bolted field joint shape optimization , 1988 .

[13]  J. Sobieszczanski-Sobieski,et al.  Structural optimization by multilevel decomposition , 1983 .

[14]  R. Lust,et al.  Structural optimization with crashworthiness constraints , 1992 .

[15]  Garret Vanderplaats,et al.  Improved Approximations for Static Stress Constraints in Shape Optimal Design of Shell Structures , 1990 .

[16]  R. Canfield.  High-quality approximation of eigenvalues in structural optimization , 1990 .

[17]  Raphael T. Haftka,et al.  Preliminary design of composite wings for buckling, strength and displacement constraints , 1979 .

[18]  Hirokazu Miura,et al.  Second order approximation of natural frequency constraints in structural synthesis , 1978 .

[19]  G. Box,et al.  Empirical Model-Building and Response Surfaces. , 1990 .

[20]  Garret N. Vanderplaats,et al.  Two-level approximation method for stress constraints in structural optimization , 1990 .

[21]  J. Arora.  Survey of Structural Reanalysis Techniques , 1976 .

[22]  Claude Fleury,et al.  Efficient approximation concepts using second order information , 1989 .

[23]  L. A. Schmit,et al.  Behavior sensitivities for control augmented structures , 1987 .

[24]  Ahmed K. Noor,et al.  Structural reanalysis via a mixed method , 1975 .

[25]  D. V. Murthy,et al.  Approximations to eigenvalues of modified general matrices , 1987 .

[26]  R. Haftka.  Combining global and local approximations , 1991 .

[27]  J. Barthelemy,et al.  Two point exponential approximation method for structural optimization , 1990 .

[28]  J. A. Nachlas,et al.  Structural Optimization of Laminated Conical Shells , 1985 .

[29]  R. Haftka,et al.  Approximation methods for combined thermal/structural design , 1979 .

[30]  S Edelman,et al.  THE SHOCK AND VIBRATION BULLETIN , 1969 .

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

[32]  P. Hajela,et al.  Further developments in the controlled growth approach for optimal structural synthesis , 1982 .

[33]  L. A. Schmit,et al.  Alternative approximation concepts for space frame synthesis , 1985 .

[34]  Garret N. Vanderplaats,et al.  An Efficient Approximation Method for Structural Synthesis with Reference to Space Structures , 1987 .

[35]  John Rasmussen.  Accumulated approximation: A new method for structural optimization by iterative improvement , 1990 .

[36]  Erdal Atrek,et al.  On stress constraints in structural optimization , 1981 .

[37]  Garret N. Vanderplaats,et al.  An efficient approximation technique for frequency constraints in frame optimization , 1988 .

[38]  William T. Hollowell,et al.  Simulation Optimization of the Crashworthiness of a Passenger Vehicle in Frontal Collisions using Response Surface Methodology , 1985 .

[39]  Biren Prasad,et al.  Explicit constraint approximation forms in structural optimization. Part 2: Numerical experiences , 1984 .

[40]  Ajg Bert Schoofs.  Experimental Design and Structural Optimization , 1988 .

[41]  Prabhat Hajela,et al.  Neurobiological Computational Models in Structural Analysis and Design , 1990 .

[42]  S. Kodiyalam,et al.  Shape optimization of 3D continuum structures via force approximation techniques , 1988 .

[43]  Garret N. Vanderplaats,et al.  Structural optimization using beam elements , 1988 .

[44]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[45]  C. Fleury.  First and second order convex approximation strategies in structural optimization , 1989 .

[46]  Lucien A. Schmit,et al.  Advances in dual algorithms and convex approximation methods , 1988 .

[47]  G. Vanderplaats.  Approximation concepts for numerical airfoil optimization , 1979 .

[48]  Richard J. Balling,et al.  Approximation of Computationally Expensive and Noisy Functions for Constrained Nonlinear Optimization , 1987 .

[49]  Lucien A. Schmit,et al.  Influence of analysis and design models on minimum weight design , 1984 .

[50]  Yunliang Ding,et al.  OPTIMUM DESIGN OF FRAMES WITH BEAMS OF DIFFERENT CROSS-SECTIONAL SHAPES , 1986 .

[51]  Moshe B. Fuchs,et al.  Linearized homogeneous constraints in structural design , 1980 .

[52]  A. J. Morris,et al.  APPROXIMATE HIGHER-ORDER SENSITIVITIES IN STRUCTURAL DESIGN , 1984 .

[53]  J. H. Starnes,et al.  Applications of a quadratic extended interior penalty function for structural optimization , 1975 .

[54]  V. Braibant,et al.  An approximation-concepts approach to shape optimal design , 1985 .

[55]  Lucien A. Schmit,et al.  Approximations Method for Space Frame Synthesis , 1983 .

[56]  Raphael T. Haftka,et al.  Applications of a Quadratic Extended Interior for Structural Optimization Penalty Function , 1976 .

[57]  B. Prasad.  Explicit constraint approximation forms in structural optimization Part 1: Analyses and projections , 1983 .

[58]  Garret N. Vanderplaats,et al.  An approximation method for configuration optimization of trusses , 1988 .

[59]  G. N. Vanderplaats.  An efficient algorithm for numerical airfoil optimization , 1979 .

[60]  F. Mistree,et al.  AN OPTIMIZATION METHOD FOR THE DESIGN OF LARGE, HIGHLY CONSTRAINED COMPLEX SYSTEMS , 1981 .

[61]  X. Renwei,et al.  Structural optimization based on second-order approximations of functions and dual theory , 1987 .

[62]  Jaroslaw Sobieszczanski,et al.  A Mixed Optimization Method for Automated Design of Fuselage Structures , 1972 .

[63]  A. Morris.  Structural optimization by geometric programming , 1972 .

[64]  A.S.L. Chan,et al.  An approximate method for structural optimisation , 1978 .

[65]  A. J. Morris,et al.  Higher-order updates for dynamic responses in structural optimization , 1985 .

[66]  P. Hajela.  Geometric programming strategies in large-scale structural synthesis , 1986 .

[67]  Clarence Zener,et al.  Geometric Programming , 1974 .

[68]  Prabhat Hajela,et al.  The controlled growth method - A tool for structural optimization , 1981 .

[69]  G. N. Vanderplaats,et al.  Efficient Algorithm for Numerical Optimization , 1979 .

[70]  Jayant Rajgopal,et al.  Exponential approximations in optimal design , 1990 .

[71]  L. A. Schmit,et al.  BASIS REDUCTION CONCEPTS IN LARGE SCALE STRUCTURAL SYNTHESIS , 1981 .

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

[73]  L. A. Schmit,et al.  Structural optimization with dynamic behavior constraints , 1985 .

[74]  Yunliang Ding,et al.  Optimum design of sandwich constructions , 1987 .

[75]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[76]  Tze Hsin Woo,et al.  Space frame optimization subject to frequency constraints , 1987 .

[77]  Layne T. Watson,et al.  Two-point constraint approximation in structural optimization , 1987 .

[78]  Claude Fleury,et al.  Dual methods for optimizing finite element flexural systems , 1983 .

[79]  Abdon Sepulveda,et al.  Improved approximations for control augmented structural synthesis , 1992 .

[80]  E. Salajegheh,et al.  New Approximation Method for Stress Constraints in Structural Synthesis , 1989 .

[81]  L. Schmit,et al.  Approximation concepts for efficient structural synthesis , 1976 .

[82]  Olaf O. Storaasli,et al.  On the Accuracy of the Taylor Approximation for Structure Resizing , 1974 .

[83]  Pauli Pedersen,et al.  The Integrated Approach of FEM-SLP for Solving Problems of Optimal Design , 1981 .

[84]  G. Kreisselmeier,et al.  SYSTEMATIC CONTROL DESIGN BY OPTIMIZING A VECTOR PERFORMANCE INDEX , 1979 .

[85]  Raphael T. Haftka,et al.  Integrated structural analysis and design using three-dimensional finite elements , 1991 .

[86]  Lucien A. Schmit,et al.  Improved approximations for dynamic displacements using intermediate response quantities , 1990 .

[87]  Howard M. Adelman,et al.  Differential equation based method for accurate approximations in optimization , 1990 .