&nbsp;&nbsp; &nbsp;The Absolute Nodal Coordinate Formulation (ANCF) is a nonlinear finite element method that is well suited for flexible multibody dynamics that can support both geometric and material nonlinearities. &nbsp;For many elements, this formulation results in a constant expression for the mass matrix, but a relatively complex expression for the generalized internal force vector. &nbsp;This first part of a two-part presentation will focus on the implementation details for a new method for computing the generalized internal force vector and its Jacobian for continuum mechanics based ANCF elements with a linear viscoelastic material model. &nbsp;The second presentation will compare the computational performance of this new method against several other existing efficient methods in the literature across five different ANCF elements. 
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&nbsp;&nbsp; &nbsp;The generalized internal force vector for ANCF elements can be calculated using either a structural mechanics or a continuum mechanics formulation. &nbsp;Since the continuum mechanics formulation is the more general of the two and it can be applied to the majority of ANCF elements, this work focuses on optimizing these calculations. &nbsp;Although many different types of materials can be used with ANCF elements, a linear viscoelastic material model is assumed for this work due its simplicity and its ability to include some damping effects, which commonly need to be accounted for in dynamic simulation models. &nbsp;This material model assumes a linear elastic material law coupled with a single coefficient linear Kelvin-Voigt damping model that depends solely on the Green strain rates. &nbsp; 
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&nbsp;&nbsp; &nbsp;When calculating the generalized internal force vector within a continuum mechanics based ANCF element, two general approaches can be taken. &nbsp;The first approach, which this new method follows, is to make the integration across the volume of the element of the partial derivative of the strain energy density with respect to the nodal coordinates as efficient as possible. &nbsp;For this approach, which will be referred to as ``Continual Integration'', integration across the volume of the element occurs every time the generalized internal force needs to be calculated and the computational effort depends on the number of quadrature points used for the numerical integration. &nbsp;The second approach is to factor out the terms that must be integrated across the volume of the element from the nodal coordinates so that integration across the volume of the element only needs to occur once prior to the start of the simulation. &nbsp;The computational effort for this ``Pre-Integration'' approach during the simulation is independent of the number of quadrature points used for the numerical integration across the volume of the element. &nbsp;As will be shown in the second part of the presentation, there are advantages for each of these two approaches.

Implementation Implications on the Performance of Ancf Simulations

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

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