The curved beam element and its convergence rate

In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems and the performance of the proposed element is discussed by comparing with the fully parameterized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with non-incremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared to that of the fully parameterized element and the classical large displacement beam element with incremental solution procedures.

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Inelastic Response of Nuclear Piping Subjected to Rupture Forces

Journal of Pressure Vessel Technology ◽

10.1115/1.3454360 ◽

1976 ◽

Vol 98 (2) ◽

pp. 98-104 ◽

Cited By ~ 1

Author(s):

J. C. Anderson ◽

A. K. Singh

Keyword(s):

Dynamic Response ◽

Numerical Procedure ◽

Beam Element ◽

Piping System ◽

Curved Beam ◽

Blow Down ◽

Curved Beam Element ◽

Piping Systems ◽

Support Element ◽

System 1

A numerical procedure which can be used to evaluate the inelastic dynamic response of piping systems subjected to blow-down forces is described. The following finite elements are used to represent the piping system: (1) bilinear beam element, (2) bilinear curved beam element, and (3) bilinear support element with an initial gap. The method is then used to evaluate the dynamic response of two typical segments of a main steamline.

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Locking Behavior of Isoparametric Curved Beam Finite Elements

Applied Mechanics Reviews ◽

10.1115/1.3005077 ◽

1995 ◽

Vol 48 (11S) ◽

pp. S25-S29 ◽

Cited By ~ 12

Author(s):

Miguel Luiz Bucalem ◽

Klaus-Ju¨rgen Bathe

Keyword(s):

Shell Element ◽

Beam Element ◽

Curved Beam ◽

Shear Locking ◽

Shell Elements ◽

One Dimensional ◽

Curved Beam Element ◽

The One ◽

Insight Into ◽

The Continuum

We present a study of the membrane and shear locking behavior in an isoparametric curved beam element. The objective is to gain insight into the locking phenomenon, specially membrane locking, of continuum based degenerated shell elements. This is possible since the isobeam element is the one-dimensional analogue of the continuum based shell element. In this context, reduced integration and mixed interpolation schemes are briefly examined. Such a study can be a valuable aid when developing new shell elements.

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