A time discontinuous formulations preserving a consistent high-order of accuracy for nonlinear/linear structural dynamics

Given a time integrator of a prescribed level of accuracy for integrating step-by-step the linear equations of motion, the key objective of the present paper is to design consistent high-order of accuracy time discretized operators for nonlinear dynamic situations based on a generalized bi-discontinuous weakform formulation. Emanating from a generalized bi-discontinuous time weighted residual formulation, a new unified set of energy dissipating time discretized operators for the equations of motion in the two-field form are presented that are fundamentally useful for non-linear structural dynamic computations. A consistent theoretical development is provided such that the order of convergence of the time integrators for linear situations are also preserved for non-linear situations. The theoretical developments and stability, accuracy, and convergence are described via various non-linear single degree-of-freedom dynamic systems representative of many practical applications.