A VFIFE-DKMT Formulation for Nonlinear Motion Analysis of Laminated Composite Thick Shells

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Abstract
This study presents a new formulation for laminated composite thick shells by incorporating the discrete Kirchhoff–Mindlin triangular (DKMT) element into the vector form intrinsic finite element (VFIFE) method. This integration enables the accurate modeling of transverse shear effects, which are difficult to capture using conventional VFIFEs. In this framework, the shell is discretized into particles whose motions are analyzed over discrete time intervals, referred to as path elements. Euler’s law of motion governs particle dynamics, while triangular elements connect the particles and describe local deformation and internal forces. Quaternions represent rigid body rotations within the convected material frame, and internal forces are obtained from the shape functions of the VFIFE–DKMT element. The formulation is validated through numerical examples involving geometrically nonlinear displacements, dynamic responses, and large deformations in isotropic and composite shells. The results demonstrate the accuracy and robustness of the proposed method in predicting the nonlinear motion of thick shell structures.

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