B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements
TEXAS UNIV AT AUSTIN
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This paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of Isogeometric Analysis. After reviewing some fundamentals of isogeometric analysis we investigate the use of higher-order Non-Uniform Rational B-Splines NURBS within the B projection method. The higher-continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results. A new nonlinear F projection method, based on a modified minimum potential energy principle and inspired by the B method is proposed for the large-deformation case. It leads to a symmetric formulation for which the consistent linearized operator for fully nonlinear elasticity is derived and used in a Newton-Raphson iterative procedure. The performance of the methods is assessed on several numerical examples, and results obtained are shown to compare favorably with other published techniques.
- Theoretical Mathematics