Isogeometric buckling analysis of orthotropic thin-walled laminated beams using the Carrera unified formulation

Abstract

The current work presents the combination of isogeometric approach (IGA) and Carrera unified formulation (CUF) to perform the buckling analysis of isotropic thin-walled and orthotropic beams. Toward this end, the layerwise (LW) theory based CUF and B-spline basis functions in IGA have been used. The LW theory uses Lagrangian expansion (LE) to estimate the displacement field in the cross-section. However, in the present study, B-spline basis functions in both longitudinal direction and cross-section have substituted the corresponding functions. The CUF expresses the 3 D displacement fields as a set of 1 D generalized unknown displacement. Combined model in the present study obliterates the costly use of 3 D finite element analysis with its high accuracy and loyalty to 3 D problems. The principle of virtual displacement (PVD) is used to obtain the fundamental nuclei. One of the features of CUF is that it’s higher-order expansion is free of the Poisson locking phenomenon. Also, there is no need to use the shear correction factor. Some examples of the isogeometric analysis of laminated composite beams with different geometries and boundary conditions are conducted and comparison of the critical buckling load results illustrate the proper validation and formulation of the present study.