Date:

2025-04-30

Title of Paper:

Development and implementation of geometrically accurate reduced-order models: Convergence properties of planar beams

Journal:

Journal of Sound and Vibration

Summary:

A geometrically accurate infinitesimal-rotation planar beam element is developed and
implemented in this study. The performance of the element, which is suited for developing
reduced-order models for both structural and multibody systems (MBS), is evaluated using
an eigenvalue analysis. Unlike conventional infinitesimal-rotation finite elements (FE), the
new element is compatible with the computer-aided design (CAD) B-spline and NURBS
(Non-Uniform Rational B-Spline) representations and allows for a straightforward linear
transformation of CAD solid models to FE analysis meshes. The absolute nodal coordinate
formulation (ANCF) elements, which are related to B-splines and NURBS by linear mapping,
are used as the basis for developing the planar beam element. The new element has a
shape function matrix expressed in terms of geometric coefficients obtained using the
ANCF position vector gradients in the reference configuration. The change in the position
vector gradients is written in terms of infinitesimal rotation coordinates using a velocity
transformation that defines constant element mass and stiffness matrices. Using this
approach, initially straight and curved configurations can be modeled using the same
displacement field. The eigenvalue analysis is used to evaluate the element performance
and examine the effect of shear locking on the predicted frequencies. Several elastic force
formulations are used to evaluate the convergence characteristics, including the direct
displacement method (DDM), general continuum mechanics (GCM) approach, elastic line (EL)
approach, and strain split method (SSM). The element performance is compared with the
conventional Euler-Bernoulli and Timoshenko elements as well as the analytical solutions.

Co-author:

Zhang Z, Wang T, Shabana A A

Volume:

439

Page Number:

457-478

Translation or Not:

No

Date of Publication:

2018-10-09