Direct strain measure for large displacement analyses on hinge connected beam structures

A multibody dynamics formulation based on a nonlinear finite element method is presented, particularly targeting beams connected with hinges. A nonlinear kinematics, called direct strain measure, is employed to extract the strains of beams subjected to large displacement, including finite rotations but small strain. Hinges are mathematically expressed in terms of the relation between connecting nodes, rather than Lagrange multipliers. The resultant dynamic equation is a differential equation of minimum set of degree of freedom, while the sparsity of mass and stiffness matrices are preserved. Computational examples prove the validity of the proposed method.