In this paper, we study plane incompressible elastic problems by means of a “stream-function” formulation such that a divergence-free displacement field can be computed from a scalar potential. The numerical scheme is constructed within the framework of NURBS-based isogeometric analysis and we take advantage of the high continuity guaranteed by NURBS basis functions in order to obtain the displacement field from the potential differentiation. As a consequence, the obtained numerical scheme is automatically locking-free in the presence of the incompressibility constraint. A Discontinuous Galerkin approach is proposed to deal with multiple mapped, possibly multiply connected, domains. Extensive numerical results are provided to show the method capabilities.
A fully "locking-free" isogeometric approach for plane linear elasticity problems: a stream function formulation / F. Auricchio, L. Beirao da Veiga, A. Buffa, C. Lovadina, A. Reali, G. Sangalli. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - 197:1-4(2007), pp. 160-172.
A fully "locking-free" isogeometric approach for plane linear elasticity problems: a stream function formulation
L. Beirao da VeigaSecondo
;C. Lovadina;
2007
Abstract
In this paper, we study plane incompressible elastic problems by means of a “stream-function” formulation such that a divergence-free displacement field can be computed from a scalar potential. The numerical scheme is constructed within the framework of NURBS-based isogeometric analysis and we take advantage of the high continuity guaranteed by NURBS basis functions in order to obtain the displacement field from the potential differentiation. As a consequence, the obtained numerical scheme is automatically locking-free in the presence of the incompressibility constraint. A Discontinuous Galerkin approach is proposed to deal with multiple mapped, possibly multiply connected, domains. Extensive numerical results are provided to show the method capabilities.File | Dimensione | Formato | |
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