An efficient MITC9 shell element for large-deformation analysis of laminated composite shells

Abstract

Laminated composite shells are widely used in lightweight structures for their high specific strength and stiffness. However, analyzing their mechanical behavior under large deformations is challenging due to anisotropy, material heterogeneity, and ply-coupling. To address this, we propose a reformulated MITC9 formulation based on geometrically exact shell theory for large-deformation analysis of laminated shells. The Mixed Interpolation of Tensorial Components (MITC) concept is used to construct a nine-node quadrilateral shell element where selected covariant components of the Green-Lagrange strain tensor are independently interpolated at optimally placed tying points and then projected back onto the displacement field. This formulation mitigates both shear and membrane locking even under large-deformation. An orthotropic laminate constitutive model is formulated using equivalent single-layer theory, analytically integrating lamina stiffnesses through the thickness. This yields the classical extensional, coupling, bending, and transverse shear stiffness matrices for arbitrary stacking sequences. The formulation is validated through several benchmark problems involving highly anisotropic laminates and large rotations. In all cases, the MITC9 element accurately reproduces reference load–displacement curves and displacement contours, is locking-free even on relatively coarse meshes, and supports flexible ply sequence modeling. These findings confirm the method’s effectiveness and high accuracy for nonlinear analysis of laminated composite shells.