Sensitivity Analysis of Discrete Structural Systems

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

[1]  W. H. Wittrick Rates of Change of Eigenvalues, With Reference to Buckling and Vibration Problems , 1962, The Journal of the Royal Aeronautical Society.

[2]  H. Kelley Method of Gradients , 1962 .

[3]  Rajko Tomović,et al.  Sensitivity analysis of dynamic systems , 1963 .

[4]  P. Lancaster On eigenvalues of matrices dependent on a parameter , 1964 .

[5]  R. Fox,et al.  Constraint surface normals for structural synthesis techniques , 1965 .

[6]  Sensitivity of an eigenvalue to changes in the matrix , 1965 .

[7]  B. Morgan Computational procedure for the sensitivity of an eigenvalue , 1966 .

[8]  G. W. Stewart,et al.  A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives , 1967, JACM.

[9]  J. P. LaSalle,et al.  Sensitivity Methods in Control Theory , 1967 .

[10]  R. Fox,et al.  Rates of change of eigenvalues and eigenvectors. , 1968 .

[11]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[12]  R. L. Barnett,et al.  High performance structures , 1968 .

[13]  L. C. Rogers Derivatives of eigenvalues and eigenvectors , 1970 .

[14]  C. D. Mote,et al.  Optimization methods for engineering design , 1971 .

[15]  K. G. Bhatia,et al.  Second derivatives of the flutter velocity and the optimization of aircraft structures. , 1972 .

[16]  G. Stewart On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$ , 1972 .

[17]  Singiresu S Rao,et al.  Rates of change of flutter Mach number and flutter frequency. , 1972 .

[18]  Raymond H. Plaut,et al.  Derivatives of eigenvalues and eigenvectors in non-self-adjoint systems. , 1973 .

[19]  Subhash Garg,et al.  Derivatives of Eigensolutions for a General Matrix , 1973 .

[20]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

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

[22]  Anthony V. Fiacco,et al.  Computational experience in sensitivity analysis for nonlinear programming , 1974, Math. Program..

[23]  C. S. Rudisill,et al.  Derivatives of Eigenvalues and Eigenvectors for a General Matrix , 1974 .

[24]  J. I. Leonard,et al.  The application of sensitivity analysis to models of large scale physiological systems , 1974 .

[25]  Mehdi Farshad,et al.  Variations of Eigenvalues and Eigenfunctions in Continuum Mechanics , 1974 .

[26]  James H. Bigelow,et al.  Implicit function theorems for mathematical programming and for systems of inequalities , 1974, Math. Program..

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

[28]  Thomas R. Kane,et al.  Multiparameter Quadratic Eigenproblems , 1975 .

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

[30]  Yee-Yeen Chu,et al.  Numerical methods for evaluating the derivatives of eigenvalues and eigenvectors , 1975 .

[31]  Richard Flavell,et al.  An Approach to Sensitivity Analysis , 1975 .

[32]  E. M. Oblow,et al.  Sensitivity theory from a differential viewpoint , 1976 .

[33]  H. A. Dwyer,et al.  Sensitivity analysis applied to boundary layer flow , 1976 .

[34]  Anthony V. Fiacco,et al.  Sensitivity analysis for nonlinear programming using penalty methods , 1976, Math. Program..

[35]  J. Arora,et al.  Efficient optimal design of structures by generalized steepest descent programming , 1976 .

[36]  A. Simpson On the rates of change of sets of equal eigenvalues , 1976 .

[37]  Richard B. Nelson,et al.  Simplified calculation of eigenvector derivatives , 1976 .

[38]  Lyle G. Clark,et al.  Sensitivity analysis for a class of evolution equations , 1977 .

[39]  Itio Hirai,et al.  Derivatives of eigenvectors of locally modified structures , 1977 .

[40]  E. Haug,et al.  Sensitivity analysis in distributed-parameter mechanical system optimization , 1977 .

[41]  Jasbir S. Arora,et al.  Design Sensitivity Analysis with Substructuring , 1977 .

[42]  Edward J. Haug,et al.  Two-dimensional shape optimal design† , 1978 .

[43]  Edward J. Haug,et al.  Design sensitivity analysis of elastic mechanical systems , 1978 .

[44]  Karl S. Pister,et al.  Sensitivity analysis for hysteretic dynamic systems: Theory and applications , 1978 .

[45]  Herschel Rabitz,et al.  The Green’s function method of sensitivity analysis in chemical kinetics , 1978 .

[46]  K. Shuler,et al.  Nonlinear sensitivity analysis of multiparameter model systems , 1977 .

[47]  A. Fiacco,et al.  Nonlinear Programming Sensitivity Analysis Results Using Strong Second Order Assumptions. , 1978 .

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

[49]  A. Andrew Convergence of an Iterative Method for Derivatives of Eigensystems , 1978 .

[50]  Pertubation-magnitude Control for Difference-quotient Estimation of Derivatives , 1979 .

[51]  An exemplified semi-analytical approach to the transient sensitivity of nonlinear systems , 1979 .

[52]  Ali H. Dogru,et al.  Sensitivity analysis of partial differential equations with application to reaction and diffusion processes , 1979 .

[53]  J. Seinfeld,et al.  Automatic sensitivity analysis of kinetic mechanisms , 1979 .

[54]  Edward J. Haug,et al.  Methods of Design Sensitivity Analysis in Structural Optimization , 1979 .

[55]  Eugene P. Dougherty,et al.  A computational algorithm for the Green's function method of sensitivity analysis in chemical kinetics , 1979 .

[56]  A. Andrew Iterative Computation of Derivatives of Eigenvalues and Eigenvectors , 1979 .

[57]  P. Mantegazza,et al.  Calculation of Eigenvalue and Eigenvector Derivatives for Algebraic Flutter and Divergence Eigenproblems , 1979 .

[58]  Eugene P. Dougherty,et al.  Further developments and applications of the Green’s function method of sensitivity analysis in chemical kinetics , 1979 .

[59]  Herschel Rabitz,et al.  Further developments and applications of sensitivity analysis to collisional energy transfer , 1980 .

[60]  Eugene P. Dougherty,et al.  Computational kinetics and sensitivity analysis of hydrogen–oxygen combustion , 1980 .

[61]  Robert K. Brayton,et al.  Sensitivity and optimization , 1980 .

[62]  Edward J. Haug,et al.  Design Sensitivity Analysis in Structural Mechanics. I. Static Response Variations , 1980 .

[63]  Patrick Vanhonacker,et al.  Differential and Difference Sensitivities of Natural Frequencies and Mode Shapes of Mechanical Structures , 1980 .

[64]  Edward J. Haug,et al.  Design Sensitivity Analysis in Structural Mechanics.II. Eigenvalue Variations , 1980 .

[65]  Jasbir S. Arora,et al.  Analysis of optimality criteria and gradient projection methods for optimal structural design , 1980 .

[66]  T. Peterson,et al.  A study of turbulent flow with sensitivity analysis , 1980 .

[67]  Michael A. Saunders,et al.  Computing Finite-Difference Approximations to Derivatives for Numerical Optimization. , 1980 .

[68]  Ahmed K. Noor,et al.  Reduced Basis Technique for Nonlinear Analysis of Structures , 1980 .

[69]  L. A. Schmit,et al.  Structural synthesis - Its genesis and development , 1981 .

[70]  E. Haug A Unified Theory of Optimization of Structures with Displacement and Compliance Constraints , 1981 .

[71]  Edward J. Haug,et al.  Design Sensitivity Analysis of Planar Mechanism and Machine Dynamics , 1981 .

[72]  M. E. Botkin,et al.  Shape Optimization of Plate and Shell Structures , 1981 .

[73]  Jean-Paul Zolésio,et al.  Domain Variational Formulation for Free Boundary Problems , 1981 .

[74]  C. Irwin,et al.  Sensitivity analysis of thermodynamic calculations , 1981 .

[75]  Metin Demiralp,et al.  Chemical kinetic functional sensitivity analysis: Derived sensitivities and general applications , 1981 .

[76]  D. Cacuci Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach , 1981 .

[77]  Herschel Rabitz,et al.  Chemical sensitivity analysis theory with applications to molecular dynamics and kinetics , 1981, Comput. Chem..

[78]  E. Haug,et al.  Design Sensitivity Analysis of Shape Variation , 1981 .

[79]  Ali H. Dogru,et al.  Comparison of Sensitivity Coefficient Calculation Methods in Automatic History Matching (includes associated paper 10873 ) , 1981 .

[80]  Joseph M. Calo,et al.  An improved computational method for sensitivity analysis: Green's function method with ‘AIM’ , 1981 .

[81]  A. A. Schy,et al.  Multiobjective insensitive design of airplane control systems with uncertain parameters , 1981 .

[82]  Raphael T. Haftka,et al.  Calculation of sensitivity derivatives in thermal problems by finite differences , 1981 .

[83]  H. A. Dwyer,et al.  Study of Turbulent Flow with Sensitivity Analysis , 1981 .

[84]  Raphael T. Haftka,et al.  Techniques for thermal sensitivity analysis , 1981 .

[85]  Edward J. Haug,et al.  Second-order design sensitivity analysis of structural systems , 1981 .

[86]  Jean-Paul Zolésio,et al.  The Material Derivative (or Speed) Method for Shape Optimization , 1981 .

[87]  M. Koda,et al.  Sensitivity analysis of distributed parameter systems , 1982 .

[88]  R. Sandford,et al.  CH-47 Fiberglass Rotor Blade Design and Fabrication , 1982 .

[89]  John H. Seinfeld,et al.  Global sensitivity analysis—a computational implementation of the Fourier Amplitude Sensitivity Test (FAST) , 1982 .

[90]  Bo Ping Wang,et al.  Helicopter Vibration Reduction by Local Structural Modification , 1982 .

[91]  J. M. Calo,et al.  AIM: the analytically integrated magnus method for linear and second-order sensitivity coefficients , 1982 .

[92]  S.-S. D. Young,et al.  The Sensitivity Analysis of Cam Mechanism Dynamics , 1982 .

[93]  Bernard Rousselet Note on the Design Differentiability of the Static Response of Elastic Structures , 1982 .

[94]  G. L. Giles,et al.  Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system , 1982 .

[95]  Edward J. Haug,et al.  Design Sensitivity Analysis in Structural Mechanics. III. Effects of Shape Variation , 1982 .

[96]  K. M. Riley,et al.  Sensitivity of Optimum Solutions of Problem Parameters , 1982 .

[97]  Duc T. Nguyen,et al.  Fail-Safe Optimal Design of Complex Structures With Substructures , 1982 .

[98]  Dan G. Cacuci,et al.  Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method , 1982 .

[99]  Eigenvalue Derivatives for Damped Torsional Vibrations , 1982 .

[100]  Raphael T. Haftka,et al.  Second-order sensitivity derivatives in structural analysis , 1982 .

[101]  John H. Seinfeld,et al.  Sensitivity analysis of a mathematical model for photochemical air pollution , 1982 .

[102]  Biren Prasad,et al.  A GENERAL CAPABILITY OF DESIGN SENSITIVITY FOR FINITE ELEMENT SYSTEMS , 1982 .

[103]  Edward J. Haug,et al.  Second‐order design sensitivity analysis of mechanical system dynamics , 1982 .

[104]  H. Van Belle,et al.  Higher order sensitivities in structural systems , 1982 .

[105]  B Prasad,et al.  Organization of PARS — a structural resizing system , 1982 .

[106]  Alexander P. Seyranian,et al.  Sensitivity analysis and optimization of aeroelastic stability , 1982 .

[107]  B. P. Wang,et al.  REANALYSIS, MODAL SYNTHESIS AND DYNAMIC DESIGN. , 1983 .

[108]  P. Gill,et al.  Computing Forward-Difference Intervals for Numerical Optimization , 1983 .

[109]  C. C. Hauser,et al.  Optimization using sensitivity analysis , 1983 .

[110]  Kyung K. Choi,et al.  Shape Design Sensitivity Analysis of Elastic Structures , 1983 .

[111]  Alexander S. Bratus,et al.  Bimodal solutions in eigenvalue optimization problems , 1983 .

[112]  Terence P Coffee,et al.  Sensitivity analysis for premixed, laminar, steady-state flames. Technical report , 1983 .

[113]  Pauli Pedersen,et al.  Sensitivity analysis for problems of dynamic stability , 1983 .

[114]  A. A. Schy,et al.  Tradeoff studies in multiobjective insensitive design of airplane control systems , 1983 .

[115]  J. Sobieszczanski-Sobieski,et al.  Optimum sensitivity derivatives of objective functions in nonlinear programming , 1983 .

[116]  B. Rousselet,et al.  Shape design sensitivity of a membrane , 1983 .

[117]  Edward J. Haug,et al.  Shape Optimization of a Solid of Revolution , 1983 .

[118]  J. D. Hawk,et al.  Subsonic Panel Method for Designing Wing Surfaces From Pressure Distribution , 1983 .

[119]  J. Sobieszczanski-Sobieski,et al.  Extrapolation of Optimum Design Based on Sensitivity Derivatives , 1983 .

[120]  E. J. Haug,et al.  Structural design sensitivity analysis with generalized global stiffness and mass matrices , 1984 .

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

[122]  H. Adelman,et al.  Static and dynamic structural-sensitivity derivative calculations in the finite-element-based Engineering Analysis Language (EAL) system , 1984 .

[123]  D. V. Wallerstein,et al.  Design enhancement tools in MSC/NASTRAN , 1984 .

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

[125]  Jasbir S. Arora,et al.  Structural design sensitivity analysis with general boundary conditions: Dynamic problem , 1984 .

[126]  J. Arora,et al.  Design sensitivity analysis and optimization of dynamic response , 1984 .

[127]  Choon T. Chon Design Sensitivity Analysis Strain Energy via Distribution , 1984 .

[128]  Masataka Yoshimura Design Sensitivity Analysis of Frequency Response in Machine Structures , 1984 .

[129]  J. A. Brandon,et al.  Derivation and significance of second-order modal design sensitivities , 1984 .

[130]  Lucien A. Schmit,et al.  Optimum design sensitivity based on approximation concepts and dual methods , 1984 .

[131]  Zenon Mróz,et al.  Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—II: Structure shape variation , 1984 .

[132]  Kyung K. Choi,et al.  Shape Optimal Design of an Engine Connecting Rod , 1984 .

[133]  M. E. Botkin,et al.  Structural shape optimization with geometric description and adaptive mesh refinement , 1985 .

[134]  Kyung K. Choi,et al.  Accuracy of Finite Element Based Shape Design Sensitivity Analysis , 1985 .

[135]  Kyung K. Choi,et al.  Shape Design Sensitivity Analysis of Displacement and Stress Constraints , 1985 .

[136]  G. Vanderplaats,et al.  Efficient calculation of optimum design sensitivity , 1984 .

[137]  F. Wei,et al.  Systematic approach for eigensensitivity analysis , 1985 .

[138]  J. W. Hou,et al.  COMPUTATIONAL METHOD FOR SHAPE OPTIMIZATION. , 1985 .

[139]  R. Haftka,et al.  Sensitivity derivatives for static test loading boundary conditions , 1985 .

[140]  R. Haftka Sensitivity calculations for iteratively solved problems , 1985 .

[141]  Z. Mroz,et al.  Variational approach to first- and second-order sensitivity analysis of elastic structures , 1985 .

[142]  Edward J. Haug,et al.  Design Sensitivity Analysis of Structural Systems , 1986 .