Optimization for Maximum Buckling Load of a Lattice Space Frame with Nonlinear Sensitivity Analysis

Abstract

The paper presents an optimization analysis method to find the optimum shape of a lattice space frame with maximum buckling load. The buckling load of the lattice space frame is determined by a geometrically nonlinear analysis. The mathematic analysis of the optimization is based on Generalised Reduced Gradient method (GRG) [1], in which the slope of the objective function (the load parameter at buckling point) with respect to the design parameters is required. In order to determine the slope, the authors introduced a so-called Stiffness Sensitivity Tensor in the nonlinear structural analysis, such that the sensitivity analysis can be carried out simultaneously with the incremental iteration of the geometrically nonlinear structural analysis. A single layer lattice dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that for the initial shape.

Keywords

Shape optimization maximum buckling load sensitivity analysis Stiffness Sensitivity Tensor nonlinear analysis lattice space frame lattice dome

References

Minoux

, “Mathematical Programming (Theory and Algorithms)”, John Wiley and Sons, 1983.

Reitinger

Ramm

, “Optimization of geometrically nonlinear buckling sensitive structures”, Optimization of Structural System, pp. 525–540.

Reitinger

Bletzinger

K. -U.

Ramm

, “Shape optimization of buckling sensitive structures”, Computing System in Engineering, Vol. 5, No.11994, pp. 65–75.

Pei Shan Chen Mamoru Kawaguchi Masaru Abe , “An application of inverse problem techniques to spatial structures”, Spatial/Lattice and Tension Structures (Atlanta, Georgia), April 1994, pp. 113–122.

Pei Shan Chen Mamoru Kawaguchi , “Shape of a Space Frame With Maximum Buckling Load”, Journal of Structural and Construction Engineering, AIJ, No. 489. November, 1996, pp. 41–46.

Riks

, “An Incremental Approach To the Solution of Snapping and Buckling Problems”, Int. J. Solids Structures, Vol. 15, 1979, pp. 529–551.

Riks

, Bifurcation and Stability, a Numerical Approach, “Proceeding of the international conference on innovative methods for nonlinear problems”, Lui

W. K.

Belytschko

Park

K. C.

(Eds.), Pineridge Press International Limited, 1984, pp. 313–344.

Riks

, “Some computational aspects of the stability analysis of nonlinear structures”, Computer Methods in Applied Mechanics and Engineering, 1984, 47, pp. 219–259.