Consistent element coupling in nonlinear static and dynamic analyses using explicit solvers

This paper develops and implements a new constraint formulation for treating nonlinear beam-to-shell, beam-to-solid, and shell-to-solid connections in explicit finite element analyses. The traditional methods commonly adopted to treat element couplings, namely transition elements or multi-point constraints, are investigated and their limitations are outlined and discussed. The newly proposed generalised constraint formulation enforces the kinematical and dynamic consistency across the element coupling interface simultaneously, and a method for implementing them in the explicit central difference integration algorithm is devised. Particular attention is devoted to the treatment of problems involving large rotations and deformations. To validate our constraint method, a number of finite element test cases are examined. Comparison of results of the new method and existing commercial codes against analytical results reveals good accuracy and robustness of the new algorithms in the treatment of both static and dynamic problems encountering large deformations and rotations.