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.

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.

A thin-walled box beam finite element for curved bridge analysis

1984 ◽  
Vol 18 (6) ◽  
pp. 1035-1046 ◽  
Author(s):  
S.H. Zhang ◽  
L.P.R. Lyons
Keyword(s):  
Finite Element ◽  
Curved Bridge ◽  
Box Beam ◽  
Thin Walled

Exact Matching Condition at a Joint of Thin-Walled Box Beams Under Out-of-Plane Bending and Torsion

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Soomin Choi ◽  
Gang-Won Jang ◽  
Yoon Young Kim
Keyword(s):  
Beam Theory ◽  
Matching Condition ◽  
Higher Order ◽  
Transformation Matrix ◽  
Exact Matching ◽  
Box Beam ◽  
Out Of Plane ◽  
Box Beams ◽  
Thin Walled ◽  
Plane Bending

To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5×5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

A Finite Element Formulation for the Analysis of Horizontally-Curved Thin-Walled Beams

2015 ◽  
Author(s):  
Ashkan Afnani ◽  
Vida Niki ◽  
R. Emre Erkmen
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Curved Beams ◽  
Equilibrium Equations ◽  
Rotation Tensor ◽  
Initial Curvature ◽  
Horizontally Curved ◽  
Thin Walled

In this study, a finite element formulation is developed for the elastic analysis of thin-walled curved beams. Using a second-order rotation tensor, the strains of the deformed configuration are calculated in terms of the displacement values and the initial curvature. The principle of virtual work is then used to obtain the nonlinear equilibrium equations, based on which a finite element beam formulation is developed. The accuracy of the method is confirmed through comparisons with test results and shell-type finite element formulations and other curved beam formulations from the literature. It is also shown that the results of the developed formulation are very accurate for cases where initial curvature is very large.

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