Discussion on some convergence problems in buckling optimisation

This note reports and briefly discusses some of the numerous reasons for bad convergence in linear buckling optimisation. Above all, it highlights that erratic convergence history can be avoided when the design optimisation problem includes enough buckling modes (and not only the first ones as it is the usual case), which keep the whole structure sensitive to the design restriction. This strategy is illustrated with an example and shows that possible significant improvement in the convergence speed can also be achieved by simply considering a large number of buckling modes in the optimisation problem. The selection of a suitable approximation scheme is also discussed.

[1]  Grant P. Steven,et al.  Evolutionary structural optimization for dynamic problems , 1996 .

[2]  Michaël Bruyneel,et al.  A general and effective approach for the optimal design of fiber reinforced composite structures , 2006 .

[3]  R. Haftka,et al.  A discourse on sensitivity analysis for discretely-modeled structures , 1991 .

[4]  Raphael T. Haftka,et al.  A comparison of two types of structural optimization procedures for satisfying flutter requirements , 1974 .

[5]  Shijun Guo,et al.  Optimiz ation of Composite Wing Structures for Maximum Flutter Speed , 2005 .

[6]  J. Thompson,et al.  Elastic Instability Phenomena , 1984 .

[7]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[8]  C. Fleury,et al.  A family of MMA approximations for structural optimization , 2002 .

[9]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[10]  Y. Radovcic,et al.  BOSS QUATTRO: an open system for parametric design , 2002 .

[11]  Erik Lund,et al.  Buckling topology optimization of laminated multi-material composite shell structures , 2009 .

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

[13]  C. M. Mota Soares,et al.  Buckling sensitivity analysis and optimal design of thin laminated structures , 1997 .

[14]  Niels Olhoff,et al.  Th World Congresses of Structural and Multidisciplinary Optimization Topology Optimization of Continuum Structures with Respect to Simple and Multiple Eigenfrequencies , 2022 .

[15]  Erik Lund.  Buckling Topology Optimization of Laminated Multi-Material Composite Structures , 2006 .

[16]  Ramana V. Grandhi,et al.  Structural optimization with frequency constraints - A review , 1992 .

[17]  W. J. Anderson,et al.  Mode Tracking Issues in Structural Optimization , 1995 .

[18]  Weihong Zhang,et al.  Characteristics of Sensitivity Analysis of Repeated Frequencies , 2004 .

[19]  N. Olhoff,et al.  Multiple eigenvalues in structural optimization problems , 1994 .

[20]  D. Wallerstein,et al.  Modal design sensitivities for multiple eigenvalues , 1988 .