Coupled flexural torsional analysis and buckling optimization of variable stiffness thin-walled composite beams

Abstract

Present work examines flexural–torsional coupling for static and stability analysis of thin-walled composite beams having variable stiffness. Variable stiffness composites (VSCs), manufactured with curvilinear fibers, are considered in this work. Compared to straight fiber laminates, variable angle tow (VAT) sections may significantly improve structural response as they redistribute the in-plane stresses. A generalized beam kinematic model which considers the effect of flexural, torsional and, warping deformation is adopted and using the principle of minimum potential energy, governing equations are derived. The variable fiber angles can be defined using a general Lagrangian polynomial and as a particular case, the solution is presented for linearly varying fiber angles. Stability analysis considers geometric nonlinearity. The present model neglects transverse shear deformations, and governing equations are numerically solved using a set of C¹ continuous finite elements. Important observations are made on the coupled response of thin-walled VSCs for static and stability analysis, which indicates the necessity of optimization study. An efficient ‘Teaching Learning Based Optimization’ (TLBO) algorithm is applied to obtain the most efficient curvilinear fiber path. The results show that lateral torsional buckling load capacity can be increased by approximately 15% in optimized VSCs compared to unidirectional fiber composites. The present kinematic model and numerical scheme can be easily extended to the optimization studies considering manufacturing constraints, which may be further implemented in commercial designs.

Keywords:

• Flexural–torsional
• lateral buckling
• teaching learning based optimization
• thin-walled
• variable stiffness