High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Abstract

The computation cost of matrix formation in isogeometric analysis can be drastically reduced by employing tensor decomposition, but the performance like accuracy and robustness still depends on the approach used to realize the low‐rank approximation for the nonpolynomial integral kernels. In the buckling analysis of laminated shells with solid‐shell model, the integral kernels are not smooth in the thickness direction due to their material and stress distribution and have a high complexity because the curvilinear coordinate systems are involved in the representation of anisotropic constitutive relations, which makes it more difficult to guarantee the decomposition accuracy. This paper proposes a robust high‐fidelity tensor‐decomposition based matrix formation method for stiffness matrix and geometric stiffness matrix of the isogeometric buckling analysis problem. The proposed method avoids using a spline approximation and employs the hierarchical block‐wise decomposition approach (HBD) to obtain a determinate decomposition result, which saves more time without loss of accuracy and produces less canonical ranks with a reliable procedure. Besides, the matrix calculation is partly independent of the number of layers, showing a higher efficiency when the number of layers is larger. Finally, several experiments with various Gaussian curvatures are implemented to validate the proposed method.