The purpose of the paper is to apply monotone multigrid methods to static and dynamic biomechanical contact problems. In space, a finite element method involving a mortar discretization of the contact conditions is used. In time, a new contact–stabilized Newmark scheme is presented. Numerical experiments for a two body Hertzian contact problem and a biomechanical application are reported.

CALIBRATION AND RANKING OF COARSE-GRAINED MODELS IN MOLECULAR SIMULATIONS USING BAYESIAN FORMALISM Hadi Meidani,1,∗ Justin B. Hooper,2 Dmitry Bedrov,2 & Robert M. Kirby3 1Department of Civil and Environmental Engineering, 1211 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61822, USA 2Department of Materials Science & Engineering, 206 Civil and Mate...

When simulating the behavior of a mechanical system, the time evolution of the generalized coordinates used to represent the configuration of the model is computed as the solution of a combined set of ordinary differential and algebraic equations (DAEs). There are several ways in which the numerical solution of the resulting index 3 DAE problem can be approached. The most well-known and time-ho...

We focus on a simple implicit time integration scheme for the transient response solution of structures when large deformations and long time durations are considered. Our aim is to have a practical method of implicit time integration for analyses in which the widely used Newmark time integration procedure is not conserving energy and momentum, and is unstable. The method of time integration di...

A time-accurate procedure to model fluid/structure interactions of helicopter blades is presented. The Navier-Stokes equations in conjunction with the one-equation SpalartAllmaras turbulence model are used to compute the flow. Structural dynamics is modeled using the modal equations. The aerodynamic and structural dynamic equations are coupled time-accurately using the linear acceleration metho...

During the last few years, di erent approaches for integrating ordinary di erential equations on manifolds have been published. In this work, we consider two of these approaches. We present some numerical experiments showing bene ts and some pitfalls when using the new methods. To demonstrate how they work, we compare with well known classical methods, e.g. Newmark and Runge-Kutta methods. AMS ...

An implicit integration strategy for use with the Material Point Method (MPM) is described. This strategy uses an incremental–iterative solution strategy based on a Newton method to solve the equations of motion and Newmark integration to update the kinematic variables. An example problem was used to compare the implicit integration scheme to the traditional explicit integration scheme used wit...

This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses viscoelastic structures characterized by generalized Maxwell model. We depart from scheme developed three-parameter model Hatada et al. [1], which we extend to generic chain and demonstrate that resulting algorithm can be derived suitably discretized Hamilton variational principle. structure manifests its...