For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.
|Title:||A High-Order Method for 3D Nonlinear Elastodynamics|
|Seminar:||Computational and Applied Mathematics Colloquium|
|Speaker:||Steve Dong, Purdue University|
|Spatial high-order accuracy and temporal unconditional stability are
crucial for accurate and long-time simulations of dynamic nonlinear
structural problems involving large deformations. In this talk we present
a high-order method employing Jacobi polynomial-based shape functions, as
an alternative to the typical Legendre polynomial-based shape functions in
solid mechanics, for solving 3D dynamic nonlinear elasticity equations.
Besides the more favorable numerical conditioning in the resulting
mass/stiffness matrices, Jacobi-based approach also provides a unified
treatment for elements of all commonly encountered geometric shapes (e.g.
hex, tet, prism, pyramid). For time integration, we present a composite
scheme combining a generalized BDF scheme and the trapezoidal rule for
nonlinear elastodynamic equations. The main advantage of the new composite
scheme lies in its unconditional stability, simplicity, and the symmetry
in the resultant tangential stiffness matrices (as opposed to the
non-symmetric tangent matrices with e.g. energy-momentum based methods).
We demonstrate the spatial exponential convergence rate and temporal
second-order accuracy of the above method for the four classes of problems
of linear/geometrically-nonlinear elastostatics/elastodynamics. Several 3D
nonlinear elastodynamic problems involving large deformations will be
employed for comparison with existing algorithms.|
Room Reservation Information
|Date:||10 / 10 / 2008|
|Time:||03:35pm - 04:25pm|