Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples J. Comput. Nonlinear Dynam. 2012;8(2):021004-021004-7. doi:10.1115/1.4006787 Figure Legend: A cantilever beam under a vertical tip load F is tested to show the performance for in-plane bending problems. Therefore, the displacement in the third direction uz is zero.

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples J. Comput. Nonlinear Dynam. 2012;8(2):021004-021004-7. doi:10.1115/1.4006787 Figure Legend: Comparison of convergence of the different beam formulations: With respect to the converged reference solution of the proposed quadratic CMF (locking free) and considering Poisson ratio ν = 0.3, the standard cubic continuum mechanics based ANCF beam element [6] shows convergence of order two, while the proposed quadratic CMF (locking free) shows convergence of order four. The standard quadratic CMF, which suffers from Poisson locking, does not converge to the correct solution. With respect to the converged solution of Simo-Vu-Quoc (Maple) [10] and considering Poisson ratio ν = 0.3, the proposed quadratic SMF converges with order four as well. In addition, the plot shows that the standard cubic continuum mechanics based ANCF beam element [6] does not converge to the solution of the proposed CMF (locking free), while considering Poisson ratio ν = 0.

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples J. Comput. Nonlinear Dynam. 2012;8(2):021004-021004-7. doi:10.1115/1.4006787 Figure Legend: A cantilever beam under a bending and a torsional moment is tested to analyze a general bending problem

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples J. Comput. Nonlinear Dynam. 2012;8(2):021004-021004-7. doi:10.1115/1.4006787 Figure Legend: Simply supported beam in Sec. 4.5 investigated for eigenfrequency analysis

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples J. Comput. Nonlinear Dynam. 2012;8(2):021004-021004-7. doi:10.1115/1.4006787 Figure Legend: Instead of position and slope vectors, here the respective displacement-based quantities are chosen as degrees of freedom

Date of download: 10/31/2017 Copyright © ASME. All rights reserved. From: Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples J. Comput. Nonlinear Dynam. 2012;8(2):021004-021004-7. doi:10.1115/1.4006787 Figure Legend: Different configurations of the finite beam element: (a) scaled straight reference element and (b) the reference element depicted in the global coordinate system