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A fully “locking-free” isogeometric approach for plane linear elasticity problems: a stream function formulation. (English) Zbl 1169.74643
Summary: 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.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
65D07 Numerical computation using splines
Software:
FEAP
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