Generalized Timoshenko modelling of composite beam structures: sensitivity analysis and optimal design

Abstract

This article describes a new approach to design the cross-section layer orientations of composite laminated beam structures. The beams are modelled with realistic cross-sectional geometry and material properties instead of a simplified model. The VABS (the variational asymptotic beam section analysis) methodology is used to compute the cross-sectional model for a generalized Timoshenko model, which was embedded in the finite element solver FEAP. Optimal design is performed with respect to the layers’ orientation. The design sensitivity analysis is analytically formulated and implemented. The direct differentiation method is used to evaluate the response sensitivities with respect to the design variables. Thus, the design sensitivities of the Timoshenko stiffness computed by VABS methodology are imbedded into the modified VABS program and linked to the beam finite element solver. The modified method of feasible directions and sequential quadratic programming algorithms are used to seek the optimal continuous solution of a set of numerical examples. The buckling load associated with the twist–bend instability of cantilever composite beams, which may have several cross-section geometries, is improved in the optimization procedure.

Keywords:

• variational asymptotical method
• design sensitivity analysis
• structural optimization
• finite element method

Acknowledgements

This study was supported by the Portuguese Foundation for Science and Technology and FSE under a post doctoral scholarship. The views and findings contained herein are those of the author and should not be interpreted as necessarily representing the theoretical policies or endorsement, either expressed or implied, of the Portuguese Foundation for Science and Technology.