Isogeometric collocation: Neumann boundary conditions and contact

• Neumann boundary conditions in isogeometric collocation are discussed.
• Two alternative formulations to standard isogeometric collocation are proposed.
• The alternative formulations are more accurate than the standard one for non-uniform meshes.
• A contact formulation for isogeometric collocation is proposed.
• The contact formulation is shown to pass the contact patch test.

Isogeometric collocation methods have been proposed recently and their accuracy and efficiency demonstrated for elastostatics and explicit dynamics. This paper addresses two important aspects in the development of the isogeometric collocation technology, namely, the imposition of Neumann boundary conditions and the enforcement of contact constraints, which are both treated within the same framework. It is shown that the strong imposition of Neumann boundary conditions may lead to a significant loss of accuracy in some situations, in particular when non-uniform meshes are used. Two possible remedies are proposed to restore the desired level of accuracy while keeping the computational cost virtually unchanged, i.e. a hybrid collocation–Galerkin approach and an enhanced collocation (EC) approach. A frictionless contact formulation suitable for the collocation framework is further proposed and shown to pass the contact patch test to machine precision. When combined with the EC approach, the formulation is shown to deliver accurate results and to perform robustly also for highly non-uniform meshes. For all the collocation formulations, contact pressures are greater than or equal to zero pointwise, in contrast with standard Lagrange finite elements.