A Dissipation-Based Algorithm With Energy Control For Geometrically Nonlinear Elastodynamics Using Eight-Node Finite Elements And One-Point Quadrature

A formulation for the geometrically nonlinear dynamic analysis of elastic structures is presented in this paper. It is well known that the Newmark`s method, which is considered the most popular time-stepping scheme for structural dynamics, exhibits unconditional stability in the case of linear dynamical systems. However, this characteristic is lost in the nonlinear regime owing to the lack of an energy balance within each time step of the integration process. In order to obtain a numerical scheme with energy-conserving and controllable numerical dissipation properties a new algorithm is proposed in this work. The formulation is based on the Generalized-α method, adjusting optimized time integration parameters and the addition of an algorithmic control of the energy balance restriction, which is introduced in the Newton-Raphson iterative process within each time step of the time marching. The Finite Element Method (FEM) is employed in the present model for spatial discretizations using an eight-node hexahedral isoparametric element with one-point quadrature. In order to avoid the excitation of spurious modes an efficient hourglass control technique is used and therefore volumetric locking as well as shear locking are not observed. Some examples are analyzed in order to validate the present algorithm.

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