Development of a family of explicit algorithms for structural dynamics with unconditional stability

A new family of explicit integration algorithms is developed based on discrete control theory for solving the dynamic equations of motion. The proposed algorithms are explicit for both displacement and velocity and require no factorisation of the damping matrix and the stiffness matrix. Therefore, for a system with nonlinear damping and stiffness, the proposed algorithms are more efficient than the common explicit algorithms that provide only explicit displacement. Accuracy and stability properties of the proposed algorithms are analysed theoretically and verified numerically. Certain subfamilies are found to be unconditionally stable for any system state (linear elastic, stiffness softening or stiffness hardening) that may occur in earthquake engineering of a practical structure. With dual explicit expression and excellent stability property, the proposed family of algorithms can potentially solve complicated nonlinear dynamic problems.