Sensitivity analysis of thin-walled members, problems and applications

A review of problems related to sensitivity analysis of thin walled members with open monosymmetric or bisymmetric cross-section is presented. The restraints imposed on angle of cross-section rotation, transverse displacement and cross-section warping are taken into account. The consideration is based upon the classical theory of thin-walled beams with nondeformable cross-section. The first variations of state variables due to a change of the design variable are investigated. Arbitrary displacement, internal force or reaction of the member subject to static load, critical buckling load, frequency and mode of torsional vibration are assumed to be the state variables. The dimensions of the cross-section, the material constants, the restraints stiffness, and their locations, position of the member ends are taken as the design variables. Accuracy of the approximate changes of the state variables achieved by sensitivity analysis is also discussed.

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

[2]  Tomasz Mikulski,et al.  NUMERICAL SIMULATION OF BEHAVIOUR OF THIN-WALLED FRAMES SUBJECTED TO STATIC LOADS , 2002 .

[3]  John T. DeWolf,et al.  Beams with Torsional Stiffeners , 1983 .

[4]  Bożena B. Budkowska,et al.  Sensitivity analysis of critical torsional buckling load of thin-walled I-columns resting on elastic foundation , 1992 .

[5]  Steen Krenk,et al.  Warping of joints in I-beam assemblages , 1991 .

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

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

[8]  Yeong-bin Yang,et al.  A procedure for analysing space frames with partial warping restraint , 1984 .

[9]  C. Szymczak.  Sensitivity analysis of critical loads of flexural-torsional buckling of thin-walled I beam , 1999 .

[10]  Carsten Munk Plum,et al.  Stiffener Effects on Torsional Buckling of Columns , 1983 .

[11]  V. Vlasov.  Thin-walled elastic beams , 1961 .

[12]  Nicholas S. Trahair,et al.  Elastic biaxial bending and torsion of thin-walled members , 1990 .

[13]  C. Szymczak,et al.  Sensitivity Analysis of Thin-Walled I-Beams Resting on Elastic Foundation , 1992 .

[14]  Zenon Mróz,et al.  Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—I: Variation of material parameters within fixed domain , 1983 .

[15]  Buckling and initial post-buckling behavior of thin-walled I columns , 1980 .