Inhalt des Dokuments
Preprint 25-2005
Energy conserving spatial discretisation methods for the peridynamic
equation of motion in non-local elasticity theory
Author(s) :
Etienne Emmrich
,
Olaf Weckner
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 25-2005
MSC 2000
- 74B99 None of the above, but in this section
-
74H15 Numerical approximation of solutions
-
74S30 Other numerical methods
-
65R20 Integral equations
-
65N99 None of the above, but in this section
Abstract :
In this paper, different spatial discretisation methods for solving the
peridynamic equation of motion are suggested.
Based upon the Gau\ss-Hermite quadrature, the composite midpoint rule,
and linear finite elements,
respectively, the integral over the spatial domain appearing
in the governing partial integro-differential equation
is approximated.
The methods proposed are tested
for a homogeneous, linear
microelastic, pairwise equilibrated material of infinite length in
one spatial dimension
with a particular micromodulus
function and initial
displacement field whereas the velocity initially is zero.
The different approaches are compared with respect to the error between the
numerical and the exact solution.
Moreover, the conservation of the total energy
is studied. It is proved that general quadrature formula and Galerkin methods
conserve the discrete total energy if the external forces are autonomous.
This is justified by numerical experiments.
Keywords :
Peridynamic theory, long-range interaction,microelastic material,integro-diffe\-ren\-tial equation, numerical approximation, quadrature,energy conservation