A new technique to simulate nonsmooth motions occurring in vibro-impacting continuous systems is proposed. Sticking motions that are encountered during vibro-impact simulation are imposed exactly using a Lagrange multiplier, which represents the normal reaction force between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The developed theory is demonstrated by numerically simulating the forced response of a pinned-pinned beam impacting a point-like rigid obstacle.

This paper presents the development of a two-dimensional (2D) multibody foot contact model consisting of a volumetric model of foot pad. The volumetric model employs nonlinear springs and linear dampers to represent the complex material behavior of the foot pad, typical of a visco-hyperelastic material. The nonlinear springs of the foot contact model are motivated by an Ogden-type material that can describe the nonlinear constitutive behavior of a wide variety of biological tissues and rubbers. The geometry of the foot pad is modeled as three simplified ellipse which represent the heel, balls of the feet, and toe. The efficacy of the developed foot contact model is established by driving the simulation model with kinematics observed from walking experiments and comparing the generated ground reaction force with the experimental data.

In this work we propose a new methodology to simulate sticking motions occurring in vibro-impacting continuous systems. We have developed this method in the framework of the coefficient of restitution approach. During the sticking phase, the sticking constraints are imposed exactly using a Lagrange multiplier, which represents the reaction between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The proposed method does not require the mode-shapes during the sticking phase, unlike the mode-switching method. The developed methodology is supported by illustrative numerical simulations.

Partitioned dynamic simulation of multibody systems offers the benefit of increased modularity over direct simulation, thereby allowing for the use of softwares tailored to the needs of each physical subsystem. In this paper, the partitioned simulation of multibody systems is accomplished by deriving an explicit expression for the constraint forces acting between subsystems. These constraint forces form the basis of a coupling module that communicates results between subsystems, each of which can be simulated independently using tailored numerical solvers. We provide details of how this partitioned solution approach can be implemented in the framework of implicit and explicit time integrators. The computational efficiency of the proposed partitioned simulation approach is established, in comparison with direct simulation, by solving three suitable problems containing both rigid and deformable components.

In this paper a highly scalable parallel formulation of the primal-dual technique is presented for index-3 constrained flexible multi-body dynamics system. The key features of the primal-dual approach are constraint preservation, preserving the original order of accuracy of time integration operators that are employed, and faster convergence rates of nonlinear iterations for the solution of flexible multi-body dynamical systems. In addition, this technique not only preserves the underlying properties of time integration operators for ordinary differential equations, but also eliminates the need for index reduction, constraint stabilization and regularization approaches. The key features of the parallel formulation of rigid and flexible modeling and simulation technology are capabilities such as adaptive high/low fidelity modeling that is useful from the initial design concept stage to the intermediate and to the final design stages in a single seamless simulation environment. The examples considered illustrate the capabilities and scalability of the proposed high performance computing (HPC) approach for large-scale simulations.