Geometrically Nonlinear Analysis of Composite Beam Based on Space-Time Finite Element Method

This paper presents a time-continuous Galerkin finite element method for the fully intrinsic geometrically exact beam equations that is energy consistent. Within the grid of space and time, this study derives the governing equations for elements using the Galerkin method and Time finite element method, implements variable-order interpolation of variables by Legendre functions, and establishes an assembly process for sapce-time finite element equations. Additionally, by introducing kinematical equations of the rotation with Lagrange operators completely impose the conservative loads into fully intrinsic equations. Through a set of illustrative examples, our algorithm demonstrates effectiveness in addressing conservative forces, static deformation, dynamic response which means the capabilities to analyze elastically coupled dynamic problems of helicopter rotor. Meanwhile, by increasing interpolation orders effectively enhances computational accuracy and reduces discrete grid requirements.