An isogeometric method for linear nearly-incompressible elasticity with local stress projection

• Published in: Computer methods in applied mechanics and engineering Vol. 316; pp. 694 - 719
• Main Authors: Antolin, Pablo, Bressan, Andrea, Buffa, Annalisa, Sangalli, Giancarlo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2017; Elsevier BV
• Subjects: [formula omitted]-method; Computational fluid dynamics; Elasticity; Inf–sup stability; Isogeometric analysis; Materials elasticity; Nearly-incompressible elasticity; Numerical analysis; Poisson distribution; Spline functions; Splines and NURBS; Stability analysis; Stiffness matrix; Stress-strain curves; Studies; Volumetric strain; Isogeometric analysis; Inf–sup stability; B̄-method; Splines and NURBS; Nearly-incompressible elasticity
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.09.033

In this paper, we propose an isogeometric method for solving the linear nearly-incompressible elasticity problem. The method is similar to the B̄  formulation where the volumetric strain is projected on a lower degree spline space in order to prevent volumetric locking. In our method, we adopt a local projection on a coarser mesh, chosen in order to guarantee optimal convergence. Moreover the locality of the projector allows to maintain the sparsity of the stiffness matrix, that is, the efficiency of the method. The analysis of the method is based on the inf–sup stability of the associated mixed formulation via a macro-element technique for spline functions. The numerical tests confirm the theory of the method. •An IGA locking-free method for nearly-incompressible linear elasticity is introduced.•Volumetric strain is approximated using piecewise lower degree discontinuous spaces.•The method provides high-order optimally-accurate solutions for all Poisson ratios.•It is purely based on displacements and preserves the locality of the operators.•The inf–sup stability is analyzed both theoretically and numerically.