A General Co-simulation Framework Based on a Novel Weak Formulation at the Interface Level

Co-simulation techniques are widely used to enable global simulation of a coupled mechanical system via composition of simulators. In the present work, the focus is initially placed on presenting a new scheme for the numerical integration of each subsystem. Subsequently, new co-simulation techniques are introduced. Specifically, a novel coupling strategy for satisfying the coupling conditions in their integral form, in the time domain, is proposed. This formulation constitutes a general framework for the generation of coupling condition schemes with varying accuracy and stability properties, based on the choice of basis and order of polynomials for the involved quantities, thus creating a whole new perspective on the field of co-simulation. Moreover, the point-collocation method, which is mainly employed in the literature, is easily recognized as a subcase of this general formulation, by selecting the test functions as Dirac delta functions that are nonzero at the macro-time points only. The core ideas of the new techniques are initially introduced by using a simple linear model of two masses, constrained with a fixed joint. Following that, nonlinear models of single planar and double planar pendulums are examined to verify the accuracy of the new numerical integration and co-simulation techniques, respectively. The examined models are relatively simple, but the developed methods have general validity and can be applied for coupling arbitrary multibody or structural solvers.