A Finite Element Modeling Framework for Planar Curved Beam Dynamics Considering Nonlinearities and Contacts

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Tianheng Feng ◽  
Soovadeep Bakshi ◽  
Qifan Gu ◽  
Dongmei Chen
Keyword(s):  
Finite Element ◽  
Beam Dynamics ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Modeling Framework ◽  
External Wall ◽  
Beam Elements ◽  
High Compression ◽  
Assumed Strain

Motivated by modeling directional drilling dynamics where planar curved beams undergo small displacements, withstand high compression forces, and are in contact with an external wall, this paper presents an finite element method (FEM) modeling framework to describe planar curved beam dynamics under loading. The shape functions of the planar curved beam are obtained using the assumed strain field method. Based on the shape functions, the stiffness and mass matrices of a planar curved beam element are derived using the Euler–Lagrange equations, and the nonlinearities of the beam strain are modeled through a geometric stiffness matrix. The contact effects between curved beams and the external wall are also modeled, and corresponding numerical methods are discussed. Simulations are carried out using the developed element to analyze the dynamics and statics of planar curved structures under small displacements. The numerical simulation converges to the analytical solution as the number of elements increases. Modeling using curved beam elements achieves higher accuracy in both static and dynamic analyses compared to the approximation made by using straight beam elements. To show the utility of the developed FEM framework, the post-buckling condition of a directional drill string is analyzed. The drill pipe undergoes spiral buckling under high compression forces, which agrees with experiments and field observations.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

Structural Analysis of Arches in Plane with a Family of Simple and Accurate Curved Beam Elements Based on Mindlin-Reissner Model

2011 ◽  
Vol 27 (1) ◽  
pp. 129-138 ◽  
Author(s):  
N. Tayşi ◽  
M. T. Göĝüş ◽  
M. Özakça
Keyword(s):  
Finite Element ◽  
Structural Analysis ◽  
Numerical Methods ◽  
Variable Thickness ◽  
Element Formulation ◽  
Curved Beam ◽  
Rotatory Inertia ◽  
Inertia Effects ◽  
Beam Elements ◽  
Arch Structures

ABSTRACTIn this paper, the basic finite element formulation of a newly developed family of variable thickness, curved,C(0) continuity Mindlin-Reissner model curved beam elements which include shear deformation and rotatory inertia effects is presented. The accuracy, convergence and efficiency of these newly developed curved beam elements are explored through a series of analyses of arch structures and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements.

scholarly journals Theoretical and Experimental Analysis of Thin-Walled Curved Rectangular Box Beam under In-Plane Bending

Scanning ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Long Yanze ◽  
Zhang Ke ◽  
Shi Huaitao ◽  
Li Songhua ◽  
Zhang Xiaochen
Keyword(s):  
Finite Element ◽  
Test Theory ◽  
Theoretical Formula ◽  
Curved Beams ◽  
Beam Structures ◽  
Box Beam ◽  
Assumed Strain ◽  
Thin Walled ◽  
Plane Bending ◽  
Deformation Modes

Thin-walled curved box beam structures especially rectangular members are widely used in mechanical and architectural structures and other engineering fields because of their high strength-to-weight ratios. In this paper, we present experimental and theoretical analysis methods for the static analysis of thin-walled curved rectangular-box beams under in-plane bending based on 11 feature deformation modes. As to the numerical investigations, we explored the convergence and accuracy analysis by normal finite element analysis, higher-order assumed strain plane element, deep collocation method element, and inverse finite element method, respectively. The out-of-plane and in-plane characteristic deformation vector modes derived by the theoretical formula are superimposed by transforming the axial, tangential, and the normal deformation values into scalar tensile and compression amounts. A one-dimensional deformation experimental test theory is first proposed, formulating the specific contributions of various deformation modes. In this way, the magnitude and trend of the influence of each low-order deformation mode on the distortion and warping in the actual deformation are determined, and the significance of distortion and warping in the actual curved beams subjected to the in-plane loads is verified. This study strengthens the deformation theory of rectangular box-type thin-walled curved beams under in-plane bending, thus providing a reference for analyzing the mechanical properties of curved-beam structures.

In Plane Radial Vibration of Uncracked and Cracked Circular Curved Beams Subjected to Moving Loads

2021 ◽  
pp. 2150146
Author(s):  
Jatin Poojary ◽  
Sankar Kumar Roy
Keyword(s):  
Dynamic Response ◽  
Moving Load ◽  
Real Life ◽  
Beam Theory ◽  
Point Of View ◽  
Curved Beam ◽  
Moving Loads ◽  
Curved Beams ◽  
Beam Elements ◽  
Curved Beam Element

The dynamic response of structures subjected to moving load is a subject of great importance from a practical point of view. In this work, the in-plane dynamic response of a cracked isotropic circular curved beam subjected to moving loads is investigated using the finite element method. The curved beam is modeled using curved beam elements, which is developed based on the Timoshenko beam theory. Furthermore, a cracked curved beam element is developed to incorporate the presence of cracks in the structure. The effect of moving load speed, depth, and the location of the crack on the dynamic response of the beam is investigated. The outcome of the work can be useful in the study of real-life moving load problems like bridges and railways and also in the field of condition monitoring using moving loads.

General curved beam elements based on the assumed strain fields

1995 ◽  
Vol 55 (3) ◽  
pp. 379-386 ◽  
Author(s):  
Jong-keun Choit ◽  
Jang-keun Lim
Keyword(s):  
Curved Beam ◽  
Strain Fields ◽  
Beam Elements ◽  
Assumed Strain

scholarly journals The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhibo Yang ◽  
Xuefeng Chen ◽  
Yumin He ◽  
Zhengjia He ◽  
Jie Zhang
Keyword(s):  
Finite Element ◽  
Polynomial Interpolation ◽  
Physical Space ◽  
Curved Beam ◽  
Approximation Properties ◽  
Curved Beams ◽  
Spline Wavelet ◽  
B Spline ◽  
Wavelet Space ◽  
Interval Finite Element Method

A B-spline wavelet on interval (BSWI) finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch) are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.

Vibrations of Planar Curved Beams, Rings, and Arches

1993 ◽  
Vol 46 (9) ◽  
pp. 467-483 ◽  
Author(s):  
P. Chidamparam ◽  
A. W. Leissa
Keyword(s):  
Finite Element ◽  
Static Loading ◽  
Arbitrary Shape ◽  
Nonlinear Vibrations ◽  
Curved Beam ◽  
Curved Beams ◽  
Vibratory Motion ◽  
Out Of Plane ◽  
Vibration Problems ◽  
Beam Theories

This work attempts to organize and summarize the extensive published literature on the vibrations of curved bars, beams, rings and arches of arbitrary shape which lie in a plane. In-plane, out-of-plane and coupled vibrations are considered. Various theories that have been developed to model curved beam vibration problems are examined. An overview is presented of the types of problems which are addressed in the literature. Particular attention is given to the effects of initial static loading, nonlinear vibrations and the application of finite element techniques. The significantly different frequencies arising from curved beam theories which either allow or prevent extension of the centerline during vibratory motion are shown. An extensive bibliography of 407 relevant references is included.

Design Analysis of a Single-Column Pressframe

1984 ◽  
Vol 106 (4) ◽  
pp. 508-516 ◽  
Author(s):  
U. P. Singh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Curved Beam ◽  
Thin Wall ◽  
The Finite Element Method ◽  
Beam Elements ◽  
Single Column ◽  
Deformed State ◽  
Strength And Stiffness ◽  
Theoretical Results

It is observed in practice that the classic (conventional) method as well as the finite element method, when using beam elements, to evaluate the strength and stiffness of a pressframe, gives results differing substantially from actual values. This discrepancy between experimental and theoretical results can be considerably narrowed if the stress-deformed state of the corner zone is separately considered in the computation of the overall strength and stiffness of the pressframe. By means of the application of the theory of thin-wall curved beam with large curvature it is economically possible to analyze the stress-deformed behavior of the pressform in general and the corner zone element in particular with fair reliability. In the present paper this method is applied to a mechanical C-frame press.

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