Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
Computer Methods in Applied Mechanics and Engineering
Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
SIAM Journal on Numerical Analysis
Asynchronous contact mechanics
ACM SIGGRAPH 2009 papers
Long-Run Accuracy of Variational Integrators in the Stochastic Context
SIAM Journal on Numerical Analysis
A comparison of structure-preserving integrators for discrete thermoelastic systems
Computational Mechanics
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This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green-Naghdi theory of type II for thermo-elastic solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to finite element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples.