A new spacetime variational integration approach integrated with ANCF for thin shells and plates with large deformations

With the rapid development of lightweight space structures, dynamic modeling and analysis of thin shells and plates with large deformations are attractive. However, the long-time simulations usually suffer from energy dissipation due to the numerical damping of the algorithm, which puts forward high requirements for computational accuracy. Aiming at this, a new spacetime variational integration approach is developed for thin shells and plates with large deformations in this work to possess excellent energy–momentum preserving behavior. The shell or plate is spatially discretized using the absolute nodal coordinate formulation, thus the mass matrix is retained as constant while large displacements and large deformations can be accurately described. Furthermore, the complex representations and operations for large rotations are naturally avoided. The present variational integration approach is much simpler and more easy-to-implementation than the classical ones, since the manually summing up discrete action integral at a certain time is replaced by the numerical integration over a time domain within its neighborhood. Numerical simulations for benchmark examples are conducted to demonstrate the performances of the present method, where the second-order convergence rate and good energy–momentum preserving characteristics are observed. The present approach has shown its capability and potential to handle long-time simulations of thin shell and plate structures experiencing large displacements, rotations, and deformations.