Co-simulation techniques are widely used to enable global simulation of a coupled mechanical syst... more Co-simulation techniques are widely used to enable global simulation of a coupled mechanical system via composition of simulators. Within this work, the focus is initially placed on a new scheme for the numerical integration of each subsystem since the corresponding accuracy affects directly the correct solution of a decomposed model. Following that, the new co-simulation methods are introduced. Specifically, a novel coupling strategy for satisfying the coupling conditions in their integral (weak) 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. In addition, the point-collocation method, which is mainly employed in the literature, is easily recognized as a degenerate case of this general weak formula...
International Journal of Non-Linear Mechanics, 2021
Abstract This work presents a new numerical integration method for determining dynamics of a clas... more Abstract This work presents a new numerical integration method for determining dynamics of a class of multibody systems involving impact and friction. Specifically, these systems are subject to a set of equality constraints and can exhibit single frictional impact events. Such events are associated to significant numerical stiffness, appearing in the equations of motion. The new method is a time-stepping scheme, involving proper incorporation of a novel return mapping into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints only. Namely, when an impact is detected during a time step, this map is applied at the end of the step in order to bring the system position back to the configuration manifold with the allowable motions. The construction of this map is based on the concept of Jacobi fields on non-flat manifolds. Moreover, once an impact event is detected, the post-impact state is determined by employing a combination of analytical and numerical tools. First, a proper coordinate transformation is performed, bringing the system into a new set of coordinates, which are suitable for describing the impact dynamics. In these coordinates, the dominant dynamics is described by a system of three equations of motion only, which are valid during the short contact interval. In addition, these equations are geometrically discretized by using appropriate cubic splines on the configuration manifold. In this way, the inherent numerical stiffness of the class of systems examined is properly addressed, since it is restricted to a space with a much smaller dimension and a much shorter time scale. Finally, the accuracy and efficiency of the new method is demonstrated by applying it to a selected set of mechanical examples.
Journal of Computational and Nonlinear Dynamics, 2018
A systematic theoretical approach is presented, revealing dynamics of a class of multibody system... more A systematic theoretical approach is presented, revealing dynamics of a class of multibody systems. Specifically, the motion is restricted by a set of bilateral constraints, acting simultaneously with a unilateral constraint, representing a frictional impact. The analysis is carried out within the framework of Analytical Dynamics and uses some concepts of differential geometry, which provides a foundation for applying Newton's second law. This permits a successful and illuminating description of the dynamics. Starting from the unilateral constraint, a boundary is defined, providing a subspace of allowable motions within the original configuration manifold. Then, the emphasis is focused on a thin boundary layer. In addition to the usual restrictions imposed on the tangent space, the bilateral constraints cause a correction of the direction where the main impulse occurs. When friction effects are negligible, the dominant action occurs along this direction and is described by a sin...
A new numerical integration method is presented for a class of multibody systems, which exhibit s... more A new numerical integration method is presented for a class of multibody systems, which exhibit single frictional impacts. The new method is a time-stepping scheme, involving incorporation of a novel return map into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints. When an impact is detected, this map is applied at the end of the step and brings the system position back to the configuration manifold with the allowable motions. In addition, the equations of motion during impact are geometrically discretized by appropriate cubic splines on the configuration manifold. Finally, the accuracy and efficiency of the method is demonstrated by a set of mechanical examples.
Co-simulation techniques are widely used to enable global simulation of a coupled mechanical syst... more Co-simulation techniques are widely used to enable global simulation of a coupled mechanical system via composition of simulators. Within this work, the focus is initially placed on a new scheme for the numerical integration of each subsystem since the corresponding accuracy affects directly the correct solution of a decomposed model. Following that, the new co-simulation methods are introduced. Specifically, a novel coupling strategy for satisfying the coupling conditions in their integral (weak) 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. In addition, the point-collocation method, which is mainly employed in the literature, is easily recognized as a degenerate case of this general weak formula...
International Journal of Non-Linear Mechanics, 2021
Abstract This work presents a new numerical integration method for determining dynamics of a clas... more Abstract This work presents a new numerical integration method for determining dynamics of a class of multibody systems involving impact and friction. Specifically, these systems are subject to a set of equality constraints and can exhibit single frictional impact events. Such events are associated to significant numerical stiffness, appearing in the equations of motion. The new method is a time-stepping scheme, involving proper incorporation of a novel return mapping into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints only. Namely, when an impact is detected during a time step, this map is applied at the end of the step in order to bring the system position back to the configuration manifold with the allowable motions. The construction of this map is based on the concept of Jacobi fields on non-flat manifolds. Moreover, once an impact event is detected, the post-impact state is determined by employing a combination of analytical and numerical tools. First, a proper coordinate transformation is performed, bringing the system into a new set of coordinates, which are suitable for describing the impact dynamics. In these coordinates, the dominant dynamics is described by a system of three equations of motion only, which are valid during the short contact interval. In addition, these equations are geometrically discretized by using appropriate cubic splines on the configuration manifold. In this way, the inherent numerical stiffness of the class of systems examined is properly addressed, since it is restricted to a space with a much smaller dimension and a much shorter time scale. Finally, the accuracy and efficiency of the new method is demonstrated by applying it to a selected set of mechanical examples.
Journal of Computational and Nonlinear Dynamics, 2018
A systematic theoretical approach is presented, revealing dynamics of a class of multibody system... more A systematic theoretical approach is presented, revealing dynamics of a class of multibody systems. Specifically, the motion is restricted by a set of bilateral constraints, acting simultaneously with a unilateral constraint, representing a frictional impact. The analysis is carried out within the framework of Analytical Dynamics and uses some concepts of differential geometry, which provides a foundation for applying Newton's second law. This permits a successful and illuminating description of the dynamics. Starting from the unilateral constraint, a boundary is defined, providing a subspace of allowable motions within the original configuration manifold. Then, the emphasis is focused on a thin boundary layer. In addition to the usual restrictions imposed on the tangent space, the bilateral constraints cause a correction of the direction where the main impulse occurs. When friction effects are negligible, the dominant action occurs along this direction and is described by a sin...
A new numerical integration method is presented for a class of multibody systems, which exhibit s... more A new numerical integration method is presented for a class of multibody systems, which exhibit single frictional impacts. The new method is a time-stepping scheme, involving incorporation of a novel return map into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints. When an impact is detected, this map is applied at the end of the step and brings the system position back to the configuration manifold with the allowable motions. In addition, the equations of motion during impact are geometrically discretized by appropriate cubic splines on the configuration manifold. Finally, the accuracy and efficiency of the method is demonstrated by a set of mechanical examples.
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Papers by Elias Paraskevopoulos