A High-Order Method for 3D Nonlinear Elastodynamics

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.

Speaker: Steve Dong, Purdue University

Abstract: 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

Room Number: 106 McAllister

Date: 10/10/2008

Time: 3:35pm - 4:25pm