Adrian Lew
Aeronautics, 105-50
California Institute of Technology
Pasadena, CA 91125
lewa@caltech.edu
Abstract:
Time integration algorithms widely used in
finite elements fail to preserve the energy balance
equation at the element level, although some of them
do conserve the total energy in some situations. Time adaptivity
is also an issue that has been addressed before with
partial degree of success. In the present work we start from a
discrete action sum, and by rendering it stationary with respect to the
nodal coordinates and the time step of each element, we obtain discrete linear
momentum and energy balance equations. We developed an algorithm to
solve them. It naturally makes each element advance with its own time
step chosen to satisfy the energy equation. A two dimensional
numerical example in nonlinear large deformations elasticity is shown.