TY - GEN
T1 - Weakly enforced boundary conditions for the NURBS-based finite cell method
AU - Ruess, M.
AU - Bazilevs, Y.
AU - Schillinger, D.
AU - Zander, N.
AU - Rank, E.
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2012
Y1 - 2012
N2 - In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement.
AB - In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement.
KW - Fictitious domain
KW - Finite cell method
KW - NURBS
KW - Weakly enforced boundary conditions
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M3 - Conference contribution
AN - SCOPUS:84871630721
SN - 9783950353709
T3 - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
SP - 7119
EP - 7134
BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
T2 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Y2 - 10 September 2012 through 14 September 2012
ER -