TY - JOUR
T1 - High order thin-walled solid finite elements applied to elastic spring-back computations
AU - Muthler, Alexander
AU - Düster, Alexander
AU - Volk, Wolfram
AU - Wagner, Marcus
AU - Rank, Ernst
N1 - Funding Information:
This research has been supported by the BMW Group, Munich, Germany to which the authors are grateful.
PY - 2006/8/15
Y1 - 2006/8/15
N2 - In this paper we present a new approach for computing elastic spring-back based on a strictly three-dimensional, high order, solid, finite element formulation for curved, thin-walled structures allowing for an anisotropic discretization. In combination with appropriate mesh design, the p-version yields an exponential rate of convergence in the error in energy norm in contrast to low-order elements, which yield only an algebraic rate of convergence. Anisotropic Ansatz spaces based on high order elements lead to very efficient discretizations. The structural behavior of three-dimensional thin-walled continua can be predicted with a similar number of degrees of freedom as in the two-dimensional case, yet significantly more accurately because of the three-dimensional model. We also introduce an approach for the efficient computation of the relevant geometrically nonlinear problem. Furthermore the paper describes the necessary model conversion from a low-order deep drawing simulation to a spring-back computation based on the p-version of the FEM.
AB - In this paper we present a new approach for computing elastic spring-back based on a strictly three-dimensional, high order, solid, finite element formulation for curved, thin-walled structures allowing for an anisotropic discretization. In combination with appropriate mesh design, the p-version yields an exponential rate of convergence in the error in energy norm in contrast to low-order elements, which yield only an algebraic rate of convergence. Anisotropic Ansatz spaces based on high order elements lead to very efficient discretizations. The structural behavior of three-dimensional thin-walled continua can be predicted with a similar number of degrees of freedom as in the two-dimensional case, yet significantly more accurately because of the three-dimensional model. We also introduce an approach for the efficient computation of the relevant geometrically nonlinear problem. Furthermore the paper describes the necessary model conversion from a low-order deep drawing simulation to a spring-back computation based on the p-version of the FEM.
KW - Geometric modeling
KW - Spring-back
KW - p-FEM
UR - http://www.scopus.com/inward/record.url?scp=33745417208&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2005.08.019
DO - 10.1016/j.cma.2005.08.019
M3 - Article
AN - SCOPUS:33745417208
SN - 0045-7825
VL - 195
SP - 5377
EP - 5389
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 41-43
ER -