NURBS-based three-dimensional analysis of geometrically nonlinear elastic structures

• NURBS-based analysis is employed to deal with nonlinear problems in solid mechanics.
• Kinematical description with a corotational-based approach is proposed.
• The rate form of state equation is formulated within framework of large rotations.
• Several examples of shells structures are analyzed numerically.

A comprehensive kinematical description with a corotational approach, which is based on exact polar decomposition for solid elements using isogeometric analysis is the main objective of this work. A numerical model using NURBS-based FEM is developed to deal with nonlinear problems in solid mechanics involving large rotations.From the theoretical viewpoint, the rate type form of state equation is formulated within the framework of isotropic infinitesimal elasticity. It is shown in particular that the state equation relates the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.Illustrative examples are analyzed to verify the efficiency in solving a wide variety of strong nonlinear problems.