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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.

74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
65D07 Numerical computation using splines
Full Text: DOI
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