Abstract
The author’s method of design sensitivity analysis of nonlinear coincident buckling load factors and corresponding optimization method of finite dimensional elastic structures are shown to be applicable to a structure with moderately large number of degrees of freedom. The sensitivity formulations are written in general form for coincident buckling load factors including limit points and bifurcation points. Optimum designs are found for a spherical latticed dome subjected to a concentrated load and distributed loads, respectively. The results are compared with those by linear eigenvalue formulation. An approximate optimal solution against nonlinear buckling can be obtained by only scaling the solution under linear eigenvalue formulation even for the case where the effect of prebuckling deformation is very large. It is shown that the proposed method is practically applicable to optimum design with coincident critical points especially for the case of hill-top branching where bifurcation points are located at the limit point. In this case, imperfection sensitivity is not enhanced as a result of optimization. The reduction of maximum load factor due to a minor imperfection is shown to be in the same order as that to a major imperfection. Therefore symmetric imperfection as well as asymmetric imperfection should be considered in estimating the maximum loads.
Similar content being viewed by others
References
N.S. Khot, V.B. Venkayya and L. Berke, Optimum structural design with stability constraints. Int. J. Numer. Meth. Engng.,10 (1976), 1097–1114.
R. Levy and H. Perng, Optimization for nonlinear stability. Comp. & Struct.,30, No. 3 (1988), 529–535.
N. Olhoff and S.H. Rasmussen, On single and bimodal optimum buckling loads of clamped columns. Int. J. Solids Struct.,13 (1977), 605–614.
E.J. Haug and K.K. Choi, Systematic occurrence of repeated eigenvalues in structural optimization. J. Optimization Theory and Appl.,38 (1982), 251–274.
A.P. Seyranian, E. Lund and N. Olhoff, Multiple eigenvalues in structural optimization problem. Structural Optimization,8 (1994), 207–227.
N.S. Khot and M.P. Kamat, Minimum weight design of truss structures with geometric nonlinear behavior. AIAA J.,23 (1985), 139–144.
R.H. Plaut, P. Ruangsilasingha and M.P. Kamat, Optimization of an asymmetric two-bar truss against instability. J. Struct. Mech.,12, No. 4 (1984), 465–470.
M.P. Kamat, N.S. Khot and V.B. Venkayya, Optimization of shallow trusses against limit point instability. AIAA J.,22, No. 3 (1984), 403–408.
C.C. Wu and J.S. Arora, Design sensitivity analysis of non-linear buckling load. Comp. Mech.,3 (1988), 129–140.
M. Ohsaki and T. Nakamura, Optimum design with imperfection sensitivity coefficients for limit point loads. Structural Optimization,8 (1994), 131–137.
J.M.T. Thompson, A general theory for the equilibrium and stability of discrete conservative systems. ZAMP,20 (1969), 797–846.
J. Roorda, On the buckling of symmetric structural systems with first and second order imperfections. Int. J. Solids Struct.,4 (1968), 1137–1148.
M. Ohsaki and K. Uetani, Sensitivity analysis of bifurcation load of finite dimensional symmetric systems. Int. J. Numer. Meth. Engng.,39 (1996), 1707–1720.
J.M.T. Thompson and G.W. Hunt, Elastic Instability Phenomena. John Wiley and Sons, 1984.
M. Ohsaki, Optimization of geometrically nonlinear symmetric systems with coincident critical points. Int. J. Numer. Meth. Engng.,48 (2000), 1345–1357.
D. Ho, Buckling load of nonlinear systems with multiple eigenvalues. Int. J. Solids Struct.,10 (1974), 1315–1330.
M. Ohsaki, K. Uetani and M. Takeuchi, Optimization of imperfection-sensitive symmetric systems for specified maximum load factor. Comp. Meth. Appl. Mech. Engng.,166 (1998), 349–362.
C.C. Wu and J.S. Arora, Design sensitivity analysis and optimization of nonlinear structural response using incremental procedure. AIAA J.,25, No. 8 (1986), 1118–1125.
J.S. Park and K.K. Choi, Design sensitivity analysis of critical load factor for nonlinear structural systems. Comp. & Struct.,36, No. 5 (1990), 823–838.
H. Noguchi and T. Hisada, Development of a sensitivity analysis method for nonlinear buckling load. JSME Int. J.,38, No. 3 (1995), 311–317.
Y. Kanno, M. Ohsaki, K. Fujisawa and N. Katoh, Topology optimization for specified multiple linear buckling load factors by using semidefinite programming. Proc. 1st Int. Conf. on Struct. Stability and Dynamics (ICSSD 2000), 2000, 267–272.
K.J. Bathe, E. Ramm and E.J. Wilson, Finite element formulations for large deformation dynamic analysis. Int. J. Numer. Meth. Engng.,9 (1974), 353–386.
K.M. Heal, M.L. Hansen and K.M. Rickard, Maple V Programming Guide. Springer, 1998.
DOT User’s Manual, Ver. 4.20. Vanderplaats Research & Development, Inc., Colorado Spring, 1995.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Ohsaki, M. Structural optimization for specified nonlinear buckling load factor. Japan J. Indust. Appl. Math. 19, 163–179 (2002). https://doi.org/10.1007/BF03167452
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03167452