A hybrid path-following approach for constrained nonlinear-buckling optimization of variable stiffness composite shells with shape imperfections

Nonlinear buckling optimization of variable stiffness (VS) composite shells is computationally expensive due to frequent nonlinear analyses. Although the generalized path-following method can serve to reduce the redundant computation, it is weakened by two kinds of discontinuity. First, the design variables may not always be searched continuously in the constrained optimization. Second, the critical buckling states may not be continuous at singular points on the search path. To address this issue, a hybrid path-following approach is proposed to trace the critical buckling states in the nonlinear-buckling optimization with constraints on the realizability of the lamination parameters and the amplitude range of geometric imperfections. Firstly, the optimal search direction is determined with the sensitivity analysis of the critical buckling equations in the isogeometric continuum shell model. Then, a continuous following strategy is adopted to provide a proper initial estimate for the Newton iterations at a disconnected point. Moreover, an investigation into the singularity of the critical buckling equations is conducted to identify the discontinuous points of the critical states in a line-search. Upon detection of the singularity, a segment of path in state space is inserted to recover the continuity. Numerical experiments show that the continuity of the critical states in the optimization is well maintained, which leads to a more efficient optimization for the VS shell with shape imperfections.