Abstract
The present paper reviews recent developments in two major areas of structural sensitivity analysis: sensitivity of static and transient response; and sensitivity of vibration and buckling eigenproblems. Recent developments from the standpoint of computational cost, accuracy, and ease of implementation are presented.
In the area of static response, current interest is focused on sensitivity to shape variation and sensitivity of nonlinear response. Two general approaches are used for computing sensitivities: differentiation of the continuum equations followed by discretization, and the reverse approach of discretization followed by differentiation. It is shown that the choice of methods has important accuracy and implementation implications.
In the area of eigenproblem sensitivity, there is a great deal of interest and significant progress in sensitivity of problems with repeated eigenvalues. The paper raises the issue of differentiability and continuity that is inherent to the repeated eigenvalue case.
Similar content being viewed by others
References
Adelman, H.M.; Haftka, R.T. 1986: Sensitivity analysis for discrete structural systems.AIAA J. 24, 823–832 [1]
Andrew, A.L. 1978: Convergence of an iterative method for derivatives of eigensystems.J. of Comput. Phys. 26, 107–112 [2]
Arora, J.S.; Wu, C.C. 1987: Design sensitivity analysis and optimization of nonlinear structures. In: Mota Soares, C.A (ed.)Computer aided optimal design: structures and mechanical systems, pp. 589–604. Berlin, Heidelberg, New York: Springer [3]
Atrek, E. 1985: Theorems of structural variations: a simplification.Int. J. Num. Meth. Eng. 21, 481–485 [4]
Barone, M.R.; Yang, R.-J. 1988: Boundary integral equations for recovery of design sensitivity in shape optimization.AIAA J. 26, 589–594 [5]
Barthelemy, B.; Chon, C.T.; Haftka, R.T. 1986: Sensitivity approximation of static structural response. Presented at theFirst World Cong. Computational Mechanics (held in Austin, Texas, Sept. 6–8), published inFinite Elements in Analysis and Design 4, 249–265, 1988 [6]
Barthelemy, B.; Haftka, R.T. 1988: Accuracy analysis of the semi-analytical method for shape sensitivity calculation. AIAA Paper 88-2284,Proc. AIAA/ASME/ASCE/AHS/ASC 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 1, pp. 572–581 [7]
Barthelemy B.; Haftka, R.T.; Cohen, G.A. 1989: Physically based sensitivity derivatives for structural analysis programs.Comp. Mech. (in press) [8]
Belegundu, A.D. 1985: Lagrangian approach to design sensitivity analysis.J. Eng. Mech. ASCE 111, 680–695 [9]
Belegundu, A.D. 1989: Muller Breslau's principle in adjoint design sensitivity analysis.Mech. Struct. Mach. (to appear) [10]
Belegundu, A.D.; Rajan, S.D. 1988: Shape optimal design using isoparametric elements. AIAA Paper 88-2300,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 2, pp. 696–701 [11]
Bendsøe, M.P.; Olhoff, N.; Sokolowski, J. 1985: Sensitivity analysis of elasticity with unilateral constraints.J. Struct. Mech. 13, 201–222 [12]
Bendsøe, M.P.; Sokolowski, J. 1987a: Sensitivity analysis and optimal design of elastic plates with unilateral point supports.Mech. Struct. Mach. 15, 383–393 [13]
Bendsøe, M.P.; Sokolowski, J. 1987b: Sensitivity analysis and optimization of elastic-plastic structures.Eng. Opt. 11, 31–38 [14]
Bendsøe, M.P.; Sokolowski, J. 1988: Design sensitivity analysis of elastic-plastic analysis problems.Mech. Struct. Mach. 16, 81–102 [15]
Bindolino, G.; Mantegazza, P. 1987: Aeroelastic derivatives as a sensitivity analysis of nonlinear equations.AIAA J. 25, 1145–1146 [16]
Botkin, M.E. 1988: Shape optimization with multiple loading conditions and mesh refinement. AIAA Paper 88-2299, Proc.AIAA/ASME/ASCE/AHS/ASC 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 2, pp. 689–695 [17]
Braibant, V. 1986: Shape sensitivity by finite elements.J. Struct. Mech. 14, 209–228 [18]
Braibant, V.; Fleury, C. 1984: Shape optimal design using B-Splines.Comp. Meth. Appl. Mech. Eng. 44, 247–267 [19]
Braibant, V.; Sander, G. 1987: Optimization techniques: synthesis of design and analysis.Finite Elements in Analysis and Design 3, 57–78 [20]
Camarda, C.J.; Adelman, H.M. 1984: Static and dynamic structural sensitivity derivatives calculations in the finite-element based engineering analysis language (EAL) system.NASA TM-85743 [21]
Cardoso, J.B.; Arora, J.S. 1988: Variational method for design sensitivity analysis of nonlinear structural mechanics.AIAA J. 26, 595–605 [22]
Chang, C.-O.; Chou, C.-S. 1988: Dynamic analysis and optimal design of the viscous ring nutation damper for a freely precessing gyroscope. AIAA Paper 88-2264,Proc. AIAA/ASME/ASCE/AHS/ 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 1, pp. 411–419 [23]
Chen, S.-H.; Pan, H.H. 1986: Design sensitivity analysis of vibration modes by finite element perturbation.Proc. 4th Int. Modal Analysis Conf. (held in Los Angeles, Ca.), I, pp. 38–43 [24]
Chen, S.-H., Wei, F.-S. 1985: Systematic approach for eigensystem analysis. AIAA Paper 85-0635,Proc. AIAA/ASME/ASCE/AHS/ 26th Structures, Structural Dynamics and Materials Conf. (held in Orlando, Florida, April 15–17), Part 2, pp. 178–183 [25]
Chenais, D. 1987: Shape optimization in shell theory: design sensitivity of the continuous problem.Eng. Opt. 11, 289–303 [26]
Chenais, D. 1989: Optimal design of midsurface shells: differentiability proof and sensitivity computation.Appl. Math. and Applications (to be published) [27]
Chenais, D.; Rousselet, B.; Benedict, R. 1988: Design sensitivity for arch structures with respect to midsurface shape under static loading.J. Opt. Theory Appl. 28, 225–239 [28]
Cheng, G.; Yingwei, L. 1987: A new computation scheme for sensitivity analysis.Eng. Opt.,12, 219–234 [29]
Choi, K.K. 1987: Shape design sensitivity analysis and optimal design of structural systems. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structures and mechanical systems, pp. 439–492. Berlin, Heidelberg, New York: Springer [30]
Choi, K.K.; Haug, E.J. 1983: Shape design sensitivity analysis of elastic structures.J. Struct. Mech.,11, 231–269 [31]
Choi, K.K.; Santos, J.L.T. 1987, 1988: Design sensitivity analysis of non-linear structural systems, Part I: theory. Part II: numerical methods.Int. J. Num. Meth. Eng. 24, 2039–2055,26, 2097–2114 [32]
Choi, K.K.; Santos, J.L.T.; Frederick, M.C. 1987: Implementation of design sensitivity analysis with existing finite element codes.ASME J. Mechanisms, Transmissions, and Automation in Design 109, 385–391 [33]
Choi, K.K.; Seong, H.G. 1986a: A domain method for shape design sensitivity of built-up structures.Compt. Meth. Appl. Mech. and Eng. 57, 1–15 [34]
Choi, K.K.; Seong, H.G. 1986b: Design component method for sensitivity analysis of built-up structures.J. Struct. Mech. 14, 379–399 [35]
Choi, K.K.; Twu, S.-L. 1989: On eigenvalue of continuum and discrete methods of shape design sensitivity analysis.AIAA J. (to appear) [36]
Chon, C.T. 1987: Sensitivity of total strain energy of a vehicle structure to local joint stiffness.AIAA J. 25, 1391–1395 [37]
Cohen, G.A.; Haftka, R.T. 1989: Sensitivity of buckling loads of anisotropic shells of revolution to geometric imperfections and design changesComp. Struct. 31, 985–995 [38]
Dailey, R.L. 1989: Eigenvector derivatives with repeated eigenvalues.AIAA J. 27, 486–491 [39]
Dems, K. 1986: Sensitivity analysis in thermal problems — I: variation of material parameters within a fixed domain.J. of Thermal Stresses 9, 303–324 [40]
Dems, K. 1987a: Sensitivity analysis in thermal problems — II: structure shape variation.J. of Thermal Stresses 10, 1–16 [41]
Dems, K. 1987b: Sensitivity analysis in thermoelasticity problems. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structures and mechanical systems, pp. 563–572. Berlin, Heidelberg, New York: Springer [42]
Dems, K.; Haftka, R.T. 1989: Two approaches to sensitivity analysis for shape variation of structures.Mech. Struct. Mach. (in press) [43]
Dems, K.; Mróz, Z. 1984: Variational approach by means of adjoint systems to structural optimization and sensitivity analysis — II structural shape variation.Int. J. Solids Struct. 20, 527–552 [44]
Dems, K.; Mróz, Z. 1985: Variational approach to first- and second-order sensitivity analysis of elastic structures.Int. J. Num. Meth. Eng. 21, 637–661 [45]
Dems, K.; Mróz, Z. 1986: On a class of conservation rules associated with sensitivity analysis in linear elasticity.Int. J. Solids Struct. 22, 737–758 [46]
Dems, K.; Mróz, Z. 1987a: Variational approach to sensitivity analysis in thermoelasticity.J. Thermal Stresses 10, 283–306 [47]
Dems, K.; Mróz, Z. 1987b: A variational approach to sensitivity analysis and structural optimization of plane arches.Mech. Struct. Mach. 15, 297–321 [48]
Dopker, B.; Choi, K.K. 1987: Sizing and shape sensitivity analysis using a hybrid finite element code.Finite Elements in Analysis and Design 3, 315–331 [49]
Fox, R.L.; Kapoor, M.P. 1968: Rates of change of eigenvalues and eigenvectors.AIAA J. 6, 2426–2429 [50]
Freudenberg, J.S.; Looze, D.P.; Cruz, J.B. 1982: Robustness analysis using singular value sensitivities.Int. J. Control 35, 95–116 [51]
Giles, G.L.; Rogers, J.L. 1982: Implementation of structural response sensitivity calculations in a large scale finite-element analysis system. AIAA Paper 82-0714,Proc. AIAA/ASME/ASCE/AHS/ 23rd Structures, Structural Dynamics and Materials Conf. (held in New Orleans, LA, May), Part II, pp. 348–359 [52]
Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H. 1983: Computing forward-difference intervals for numerical optimization.SIAM J. Sci. and Stat. Comput. 4, 310–321 [53]
Grabacki, J. 1988: Shape optimization and shape sensitivity analysis of elastic plates.SM Archives 13, 103–120 [54]
Grandhi, R.V.; Haftka, R.T.; Watson, L.T. 1986: Efficient identification of critical stresses in structures subject to dynamic loads.Comp. Struct. 22, 373–386 [55]
Greene, W.H.; Haftka, R.T. 1988: Computational aspects of sensitivity calculations in transient structural analysis.NASA TM-100589 [56]
Haber, R.B. 1987: A new variational approach to structural shape design sensitivity analysis. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structures and mechanical systems, pp. 573–588. Berlin, Heidelberg, New York: Springer [57]
Haftka, R.T. 1983: Design for temperature and thermal buckling constraints employing non-eigenvalue formulation.J. of Spacecraft and Rockets 20, 363–367 [58]
Haftka, R.T. 1985: Sensitivity calculations for iteratively solved problems.Int. J. Num. Meth. Eng. 21, 1535–1546 [59]
Haftka, R.T.; Barthelemy, B. 1988: On the accuracy of shape sensitivity derivatives. In: Eschenauer, H.A.; Thierauf, G. (eds.)Discretization methods in engineering — procedures and applications, pp. 136–144. Berlin, Heidelberg, New York: Springer [60]
Haftka, R.T.; Cohen, G.A.; Mróz, Z. 1989: Derivatives of buckling loads and vibration frequencies with respect to stiffness and initial strain parameters.J. Appl. Mech (to be published) [61]
Haftka, R.T.; Grandhi, R.V. 1986: Structural shape optimization — a survey.Comp. Meth. Appl. Mech. Eng. 57, 91–106 [62]
Haftka, R.T.; Kamat, M.P. 1985:Elements of structural optimization. The Hague: Martinus Nijhoff [63]
Haftka, R.T.; Malkus, D.S. 1981: Calculation of sensitivity derivatives in thermal problems by finite differences.Int. J. Num. Meth. Eng., 1811–1821 [64]
Haftka, R.T.; Mróz, Z. 1986: First- and second-order sensitivity derivatives of linear and nonlinear structures.AIAA J. 24, 1187–1192 [65]
Haug, E.J.; Choi, K.K.; Komkov, V. 1986:Design sensitivity analysis of structural systems. New York: Academic Press [66]
Herendeen, D.L.; Hoesly, R.L.; Johnson, E.H.; Venkayya, V.B. 1986: Astros — an advanced software environment for automated design. AIAA Paper 86-0856,Proc. AIAA/ASME/ASCE/AHS 27th Structures, Structural Dynamics and Materials Conf. (held in San Antonio, Texas, May 19–21), Part 1, pp. 59–66 [67]
Herrera-Vaillard, A.; Paduano, J.; Downing, D. 1986: Sensitivity analysis of automatic flight control systems using singularvalue concepts.J. of Guidance, Control and Dynamics 9, 621–626 [68]
Hou, J.W.; Yuan, J.Z. 1988: Calculation of eigenvalue and eigenvectro derivatives for nonlinear beam vibrations.AIAA J. 26, 872–880 [69]
Hou, J.W.; Chen, J.L.; Sheen, J.S. 1986: Computational method for optimization of structural shapes.AIAA J. 24, 1005–1012 [70]
Hou, J.W.; Mei, C.; Xue, Y.X. 1987: On the design sensitivity analysis of beams under free and forced nonlinear vibrations. AIAA Paper 87-0936,Proc. AIAA Dynamics Specialist Conf. (held in Monterey, California, April 9–10), Part 2B, pp. 836–843 [71]
Hou, J.W.; Sheen, J.S. 1988: On the design velocity field in the domain and boundary methods for shape optimization. AIAA Paper 88-2238, Presented atAIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20) [72]
Hsieh, C.C.; Arora, J.S. 1985: Structural design sensitivity analysis with general boundary conditions: dynamic problem.Int. J. Num. Meth. Eng. 21, 267–283 [73]
Hsieh, C.C.; Arora, J.S. 1986: Algorithms for point-wise state variable constraints in structural optimization.Comp. Struct. 22, 225–238 [74]
Ibrahim, R.A. 1987: Structural dynamics with parameter uncertainties.Appl. Mech. Rev. 40, 309–328 [75]
Iott, J.; Haftka, R.T.; Adelman, H.M. 1985: Selecting step sizes in sensitivity analysis by finite differences.NASA TM-86382 [76]
Jankovic, M.S. 1988: Analytical solution for then-th derivatives of eigenvalues and eigenvectors for a nonlinear eigenvalue problem.AIAA J. 26, 204–205 [77]
Juang, J.-N.; Ghaemmaghami, P.; Lim, K.B. 1988: On the eigenvalues and eigenvector derivatives of a non-defective matrix. AIAA Paper 88-2352,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 3, pp. 1124–1231 [78]
Kamat, M.P. 1987: Optimization of shallow arches against instability using sensitivity derivatives.Finite Elements in Analysis and Design 3, 277–284 [79]
Kane, J.H.; Saigal, S. 1988: Design sensitivity analysis of solids using BEM.J. Eng. Mech. ASCE 114, 1703–1722 [80]
Kane, J.H.; Stabinsky, M. 1988: Simultaneous computation of multiple sensitivities by a boundary element structural analysis formulation.3rd Int. Conf. on CAD/CAM, Robotics and Factories of the Future (held in Southfield, Michigan, August 14–17) [81]
Kwak, B.M.; Choi, J.H. 1988: Numerical implementation of shape design sensitivity analysis by boundary integral equation for fillet design problem. In: Atluri, S.N.; Yagawa, G. (eds.)Computational mechanics '88, pp. 45.V.1–45.V.2,2. Berlin, Heidelberg, New York: Springer [82]
Lancaster, P. 1964: On eigenvalues of matrices dependent on a parameter.Numerische Mathematik 6, 377–387 [83]
Liefooghe, D.; Shyy, Y.K.; Fleury, C. 1988: Shape sensitivity analysis using low and high order finite elements. AIAA Paper 88-2431,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 3, pp. 1656–1666 [84]
Lim, J.; Chopra, I. 1987: Design sensitivity analysis for an aeroelastic optimization of a helicopter blade. AIAA Paper 87-0923,Proc. AIAA Dynamics Specialist Conf. (held in Monterey, California, April 9–10), Part 2B, pp. 1093–1102 [85]
Lim, K.B.; Juang, J.-N.; Ghaemmaghami, P. 1989: Eigenvector derivative of repeated eigenvalue using singular value decomposition.J. Guidance, Control and Dynamics 12, 282–283 [86]
Lim, K.B.; Junkins, J.L.; Wang, B.P. 1987: A re-examination of eigenvector derivatives.J. Guidance, Control and Dynamics 10, 581–587 [87]
Liu, W.K.; Besterfield, G.; Lawrence, M.; Belytschko, T. 1988: Use of adjoint methods in the probabilistic finite element approach to fracture mechanics. AIAA Paper 88-2420,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Virginia, April 18–20), Part 3, pp. 1631–1634 [88]
Mani, N.K.; Haug, E.J. 1985: Singular value decomposition for dynamic system design.Eng. Comp.,1, 103–109 [89]
Meric, R.A. 1986: Material and load optimization of thermoelastic solids, Part I: sensitivity analysis.J. Thermal Stresses 9, 359–372 [90]
Meric, R.A. 1987a: Boundary elements in shape design sensitivity analysis of thermoelastic solids. In: Mota Soares, C.A. (ed.) Computer aided optimal design: structures and mechanical systems, pp. 643–652. Berlin, Heidelberg, New York: Springer [91]
Meric, R.A. 1987b: Sensitivity analysis for a general performance criterion in micropolar thermoelasticity.Int. J. Eng. Sci. 25, 265–276 [92]
Meric, R.A. 1987c: Dynamic sensitivity analysis of material and load parameters in nonlocal elasticity.Int. J. Eng. Sci. 25, 915–922 [93]
Meric, R.A. 1988a: Shape design sensitivity analysis of dynamic structures.AIAA J. 26, 206–212 [94]
Meric, R.A. 1988b: Sensitivity analysis of functionals with respect to shape for dynamically loaded nonlocal thermoelastic solids.Int. J. Eng. Sci. 26, 703–711 [95]
Meyer, C.D.; Stewart, G.W. 1988: Derivatives and perturbations of eigenvectors.SIAM J. on Numerical Analysis 25, 679–691 [96]
Mills-Curran, W.C. 1988: Calculation of derivatives for structures with reapeated eigenvalues.AIAA J. 26, 867–871 [97]
Mota Soares, C.A.; Pereira Leal, R.; Choi, K.K. 1987: Boundary elements in shape optimal design of structural components. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structures and mechanical systems, pp. 605–632. Berlin, Heidelberg, New York: Springer [98]
Mota Soares, C.A.; Pereira Leal, R. 1987: Mixed elements in the sensitivity analysis of structures.Eng. Opt. 11, 227–237 [99]
Mróz, Z. 1987: Sensitivity analysis and optimal design with account for varying shape and support conditions. In: Mota Soares, C.A. (ed.)Computer aided optimal design: structures and mechanical systems, pp. 407–438. Berlin, Heidelberg, New York: Springer [100]
Mróz, Z.; Haftka, R.T. 1988: Sensitivity of buckling loads and vibration frequencies of plates. In: Elishakoff, I. (ed.)Buckling of structures, pp. 255–266. Berlin, Heidelberg, New York: Springer [101]
Mróz, Z.; Kamat, M.P.; Plaut, R.H. 1985: Sensitivity analysis and optimal design of nonlinear beams and plates.J. Struct. Mech. 13, 245–266 [102]
Mukherjee, S.; Chandra, A 1989: A boundary element formulation for design sensitivity in materially nonlinear problems.Acta Mechanica (to appear) [103]
Muhkopadhyay, V.; Newsom, J.R. 1984: A multiloop system stability margin study using matrix singular values.J. Guidance, Control and Dynamics 7, 582–587 [104]
Murthy, D.V.; Haftka, R.T. 1988: Derivatives of eigenvalues and eigenvectors of a general complex matrix.Int J. Num. Meth. Eng. 26, 293–311 [105]
Murthy, D.V.; Kaza, K.R.V. 1988: Application of a semianalytical technique for sensitivity and analysis of unsteady aerodynamic computations. AIAA Paper 88-2377,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 3, pp. 1307–1316 [106]
Nagendra, G.K.; Fleury, C. 1987: Sensitivity and optimization of composite structures using MSC/NASTRAN. In: Adelman, H.M.; Haftka, R.T. (eds.)Sensitivity analysis in engineering, pp. 147–166.NASA CP-2457 [107]
Nagendra, G.K.; Wallerstein, D.V. 1988: Grid sensitivity capability for large scale structures. In: Barthelemy, J.-F.(ed.),Proc. Second NASA/Air Force Symp. on Recent Advances in Multidisciplinary Analysis and Optimization (held in Hampton, Virginia, September 28–30) Part 2, pp. 697–712.NASA CP-3031 [108]
Nakagiri, S. 1987: Fluctuation of structural response why and how.JSME Int. J. 30, pp. 369–374 [109]
Neittaanmäki, P.; Sokolowski, J.; Zolesio, J.P. 1988: Optimization of the domain in elliptic variational inequalities.Appl. Math. and Optimiz. 18 [110]
Nelson, R.B. 1976: Simplified calculation of eigenvector derivatives.AIAA J. 14, 1201–1205 [111]
Nguyen, D.T. 1987a: Multilevel substructuring sensitivity analysis.Comp. Struct. 25, 191–202 [112]
Nguyen, D.T. 1987b: Practical implementation of an accurate method for multilevel design sensitivity analysis.Proc. AIAA/ASME/ASCE/AHS 28th Structures, Structural Dynamics and Material Conf. (held in Monterey, California, April 6–8), Part I, pp. 76–87 [113]
Nogis, R. 1986: Design sensitivity analysis for buckling load of elastic structures.ZAMM, Z. Angew., Math. Mech. 66, 775–776 [114]
Ojalvo, I.U. 1987: Efficient computation of mode-shape derivatives for large dynamic systems.AIAA J. 25, 1386–1390 [115]
Pedersen, P.; Cheng, G.; Rasmussen, J. 1987: On accuracy problems for semi-analytical sensitivity analysis.DCAMM Report 367, Technical University of Denmark [116]
Pierre, C. 1987: Eigensolution perturbation for systems with perturbed boundary conditions.J. Sound and Vibr. 112, 167–172 [117]
Prasad, B.; Emerson, J.F. 1982: A general capability of design sensitivity for finite element systems. AIAA Paper 82-0680,Proc. AIAA/ASME/ASCE/AHS/ 23rd Structures, Structural Dynamics and Materials Conf. (held in New Orleans, LA, May), Part II, pp. 175–186 [118]
Pritchard, J.I.; Adelman, H.M.; Haftka, R.T. 1987: Sensitivity analysis and optimization of nodal point placement for vibration reduction.J. Sound and Vibr. 119, 277–289 [119]
Raisdzadek, F.; Dwyer, H.A. 1985: Sensitivity analysis of turbulent variable density round jet and diffusion flame flows. In: Bowen, J.R.; Leyer, J.C.; Soloukhin, R.I. (eds.)Progress in astronautics and aeronautics 105, pp. 3–17. Presented at the 10th Int. Colloq. on Dynamics of Explosions and Reactive Systems (held in CA, August) [120]
Rajan, M.; Nelson, H.D.; Chen, W.J. 1986: Parameter sensitivity in the dynamics of rotor bearing systems.ASME J. of Vibration, Acoustics, Stress and Reliability in Design 108, 197–206 [121]
Rajan, M.; Budiman, J. 1987: A study of two-dimensional plane elasticity finite elements for optimal design.Mech. Struct. Mach. 15, 185–207 [122]
Reuven, Y.; Smooke, M.D.; Rabitz, H. 1986: Sensitivity analysis of boundary value problems: application to nonlinear reaction — diffusion systems.J. Comput. Phys. 64, 27–55 [123]
Rudisill, C.S.; Chu, Y.Y. 1975: Numerical methods for evaluating the derivatives of eigenvalues and eigenvectors.AIAA J. 13, 834–837 [124]
Ryu, Y.S.; Hariran, M.; Wu, C.C.; Arora, J.S. 1985: Structural design sensitivity of nonlinear response.Comp. Struct. 21, 245–255 [125]
Saigal, S.; Aithal, R.; Kane, J.H. 1989: Conforming boundary elements in plane elasticity for shape design sensitivity.Int. J. Num. Meth. Eng. (to appear) [126]
Sandridge, C.A.; Haftka, R.T. 1987: Accuracy of derivatives of control performance using a reduced structural model. AIAA Paper 87-0905,Proc. AIAA/ASME/ASCE/AHS 28th Structures, Structural Dynamics and Materials Conf. and AIAA Dynamics Specialists Conf., Part 2B, pp. 622–628 [127]
Santos, J.L.T. 1989: Sizing design sensitivity analysis of linear steady heat transfer systems using established FE codes.Numerical Heat Transfer (to be published) [128]
Santos, J.L.; Choi, K.K. 1987: Design sensitivity analysis of nonlinear structural systems with an established finite element code. Presented atANSYS Conf. (held in Newport Beach, CA, March 31–April 3) [129]
Seong, H.G.; Choi, K.K. 1987: Boundary layer approach to shape design sensitivity analysis.J. Struct. Mech. 15, 241–263 [130]
Sobiesczanski-Sobieski, J. 1988: On the sensitivity of complex, internally coupled systems.NASA TM 100537 [131]
Sobiesczanski-Sobieski, J.; Bloebaum, C.L.; Hajela, P. 1988: Sensitivity of control augmented structure obtained by a system decomposition method. AIAA Paper 88-2205,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20) [132]
Sokolowski, J.; Zolesio, J.P. 1987: Shape design sensitivity of plates and plane elastic solids under unilateral constraints.J. Opt. Theory and Applications 54, 361–382 [133]
Sutter, T.R.; Camarda, C.J.; Walsh, J.L.; Adelman, H.M. 1988: A comparison of several methods for the calculation of vibration modes shape derivatives.AIAA J. 26, 1506–1511 [134]
Szefer, G.; Mróz, Z.; Demkowicz, L. 1989: Variational approach to sensitivity analysis in nonlinear elasticity.Arch. Mech. (in press) [135]
Tan, R.C.E. 1986: Accelerating the convergence of an iterative method for derivatives of eigensystems.J. Comput. Phys. 67, 230–235 [136]
Tan, R.C.E. 1987a: Computing derivatives of eigensystems by the vectorε-algorithm.IMA J. Num. Analysis 7, 484–495 [137]
Tan, R.C.E. 1987b: An extrapolation method for computing derivatives of eigensystems.Int. J. Comput. Math. 22, 63–73 [138]
Tan, R.C.E. 1987c: Computing derivatives of eigensystems by the topologicalε-algorithm.Appl. Num. Math. 3, 539–550 [139]
Tsay, J.J.; Arora, J.S. 1988: Variational methods for design sensitivity analysis of nonlinear response with history dependent effects. In: Atluri, S.N.; Vagawa, G. (eds.)Computational mechanics '88, pp. 45.vi. Berlin, Heidelberg, New York: Springer [140]
Tseng, C.H.; Arora, J.S. 1988: Optimum design of systems for dynamic and control using sequential quadratic programming. AIAA Paper 88-2303,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 2, pp. 739–748 [141]
Wacholder, E.; Dayan, J. 1984: Application of the adjoint sensitivity method for the analysis of a supersonic ejector.ASME J. Fluid Eng. 106, 425–429 [142]
Wang, B.P. 1985: An improved approximate method for computing eigenvalue derivatives. Paper presented at a work-in-progress session,AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conf. (held in Orlando, Florida, April) [143]
Wang, S.-Y.; Sun. Y.; Gallagher, R.H. 1985: Sensitivity analysis in shape optimization of continuum structures.Comp. Struct. 20, 855–867 [144]
Wexler, A.S. 1987: Automatic evaluation of derivatives.Appl. Math. Comput. 24, 19–46 [145]
Wu, C.C.; Arora, J.S. 1987: Design sensitivity analysis of nonlinear response using incremental procedure.AIAA J. 25, 1118–1125 [146]
Wuu, T.L.; Becker, R.G.; Polak, E. 1986: On the computation of sensitivity functions of linear time-invariant system responses via diagonalization.IEEE Transactions on Automatic Control AC-31, pp. 1141–1143 [147]
Yang, R.J. 1989: A three-dimensional shape optimization system- SHOP 3D.Comp. Struct. 31, 881–890 [148]
Yang, R.J.; Botkin, M.E. 1986: Comparison between the variational and implicit differentiation approaches to shape design sensitivities.AIAA J. 24, 1027–1032 [149]
Yang, R.J.; Botkin, M.E. 1987: Accuracy of the domain material derivative approach to shape design sensitivity.AIAA J. 25, 1606–1610 [150]
Yoon, B.G.; Belegundu, A.D. 1988: Iterative methods for design sensitivity analysis. In: Barthelemy, J.-F. (ed.)Proc. 2nd NASA/Air Force Symp. on Recent Experiences in Multidisciplinary Analysis and Optimization, NASA CP-3031 (held in Hampton, Va., September), Vol. 2, 713–726; to appear inAIAA J. [151]
Yuan, K.; Wu, C. 1988: Sensitivity calculations for the numerically integrated degenerate axisymmetric shell element. AIAA Paper 88-2285,Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Va., April 18–20), Part 1, pp. 582–589 [152]
Zhong, W.; Cheng, G. 1986: Second-order sensitivity analysis of multimodal eigenvalues and related optimization techniques.J. Struct. Mech 14, 421–436 [153]
Zimoch, S. 1987: Sensitivity analysis of vibrating systems.J. Sound Vib. 115, 447–458 [154]
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Haftka, R.T., Adelman, H.M. Recent developments in structural sensitivity analysis. Structural Optimization 1, 137–151 (1989). https://doi.org/10.1007/BF01637334
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01637334