Robust path-following and branch-switching in isogeometric nonlinear bifurcation analysis of variable angle tow panels with cutouts under compression

Abstract

In this paper, an isogeometric nonlinear analysis framework integrating robust path-following and branch-switching techniques is specifically developed to investigate the nonlinear bifurcation behaviors of variable angle tow composite panels containing cutouts under compressive loads. The framework integrates Reddy’s third-order shear deformation theory with von Kármán’s nonlinearity into an isogeometric analysis formulation. The inherent $C^1$ continuity requirement of Reddy’s plate model is naturally satisfied via non-uniform rational B-splines basis functions. Geometric discontinuities arising from complex cutouts are efficiently addressed using the finite cell method with adaptive quadrature refinement. Nonlinear equilibrium equations under force- or displacement-controlled edge loads are first derived from the principle of virtual work and subsequently solved through robust path-following and branch-switching algorithms. The framework distinguishes itself through three core capabilities: (i) handling snap-through and snap-back instabilities using force- or displacement-controlled arc-length scheme; (ii) locating singular points with quadratic convergence via force- or displacement-controlled pinpointing scheme; and (iii) switching to secondary branches at bifurcation points without artificial perturbations. Its potential applicability can extend to more complex shell structures; however, the present study focuses exclusively on plate structures. The effectiveness and robustness of the proposed framework are validated against finite element solutions from ABAQUS. Effects of load condition, hole size and fiber angle on the nonlinear bifurcation behaviors of variable-stiffness composite panels with cutouts loaded in compression are also discussed in numerical examples. Results demonstrate that favourable variable-stiffness configurations retain their beneficial load redistribution mechanisms even in the presence of cutouts. These findings may provide valuable insights for the design of perforated thin-walled structures.