A Parametric Study on Nonlinear Elastodynamics Using Isogeometric Analysis and a Dissipative Energy-Momentum Conserving Algorithm

Abstract

A parametric study is performed in this work in order to investigate the computational performance of a numerical model based on isogeometric analysis for applications in nonlinear elastodynamics. It is well known that finite element models cannot represent accurately the higher vibration modes of a dynamic response due to deficiencies associated with the spatial discretization procedure. In addition, time integration algorithms with unconditional stability in the linear range are frequently subject to numerical instability when they are applied to nonlinear problems. In this sense, it is expected that a formulation utilizing isogeometric analysis and a dissipative energy-momentum conserving scheme for time discretization can significantly improve numerical stability. In the present paper, a numerical model for dynamic analysis is presented considering the isogeometric formulation based on NURBS (non-uniform rational B-splines). The kinematical description is performed using the corotational approach formulated in the context of isogeometric analysis and the constitutive equation is written in terms of corotational variables according to the hypoelastic theory, where the small strain hypothesis is adopted. Large displacements and large rotations may be also considered in the present scheme. A dissipative energy-momentum conserving algorithm is adopted to solve the equation of motion by using the generalized-α method and algorithmic conservation of energy as well as linear and angular momentum. Numerical examples are analyzed with the numerical formulation proposed in this work and results are compared with predictions obtained from a finite element model in order to quantify computational aspects such as efficiency and accuracy.