The Pre-Twisted Thin-Walled Beam Element Stiffness Matrix Considering the Saint-Venant Warping Deformation

2013 ◽  
Vol 871 ◽  
pp. 129-134
Author(s):  
Chang Hong Chen ◽  
Ying Huang
Keyword(s):  
Finite Element ◽  
Mechanical Model ◽  
Stiffness Matrix ◽  
Three Dimensional ◽  
Beam Element ◽  
Systematic Analysis ◽  
Element Stiffness Matrix ◽  
Straight Beam ◽  
Elliptical Section ◽  
Thin Walled

Based on the traditional mechanical model of thin-walled straight beam, the paper makes a systematic analysis and research on the pre-twisted thin-walled beam finite element numerical model. Firstly, based on the geometric deformation differential relationship, the paper deduces the pre-twisted thin-walled beam Saint-Venant warping strain. According to traditional thin-walled straight beam finite element mechanical model, the paper establishes its finite element stiffness matrix considering the Saint-Venant warping deformations. Finally, by calculating the pre-twisted elliptical section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted thin-walled beam element stiffness matrix considering Saint-Venant warping deformation has good accuracy.

The Finite Element Model Study of the Pre-Twisted Timoshenko Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3587-3590
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Angular Displacement ◽  
Element Model ◽  
Beam Element ◽  
Element Stiffness Matrix ◽  
Straight Beam ◽  
The Relationship ◽  
Timoshenko Beam Element

The paper studies a new mechanical model of pre-twisted Timoshenko beam. But it is different from the conventional Timoshenko straight beam; the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending displacement and angular displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, more accurate to consider the effects of shear deformation, come up with a new initial reverse Timoshenko beam element stiffness matrix. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element stiffness matrix has good accuracy.

The Finite Element Model Study of the Pre-Twisted Euler Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3615-3618
Author(s):  
Ying Huang ◽  
Chang Hong Chen ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Displacement Function ◽  
Interpolation Function ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Element Stiffness Matrix ◽  
Straight Beam

Based on the traditional mechanical model of straight beam, the paper makes a systematic analysis and research on the pre-twisted Euler beam finite element numerical model. The paper uses two-node model of 12 degrees of freedom, axial displacement interpolation function using 2-node Lagrange interpolation function, beam transverse bending displacements (u and υ) still use the cubic displacement, bending with torsion angle displacement function using cubic polynomial displacement function. Firstly, based on the author previous literature on the flexure strain relationship, the paper deduces the element stiffness matrix of the pre-twisted beam. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Euler beam element stiffness matrix has good accuracy.

scholarly journals Tensile and bending behavior of thin-walled triaxial weave fabric composites

2019 ◽  
Vol 14 ◽  
pp. 155892501989356
Author(s):  
Xiaotao Zhou ◽  
Xiaofei Ma ◽  
Yesen Fan ◽  
Huanxiao Li
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Membrane Structure ◽  
Three Dimensional ◽  
Element Model ◽  
Beam Element ◽  
Shell Membrane ◽  
Weave Fabric ◽  
Fabric Composites ◽  
Thin Walled

The laminate model of thin-walled triaxial weave fabric composites (hereinafter referred to as shell-membrane structure) to calculate the equivalent tensile Young’s modulus and bending stiffness is derived. Three-dimensional beam element finite element model of shell-membrane structure under different loading angles is established, and the tensile and bending properties of shell-membrane structure were simulated, respectively. Both results of laminate model and three-dimensional beam element finite element model verify the “size effect,” indicating that the shell-membrane structure can be equivalent to linear material in the small deformation range. And the shell-membrane structure exhibits an in-plane quasi-isotropic property. These two methods are convenient for the mechanical properties solving in engineering applications.

scholarly journals Three-dimensional nonlinear displacement-based beam element for members with asymmetric thin-walled sections

2020 ◽  
Author(s):  
Xinlong Du ◽  
Jerome Hajjar
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Three Dimensional ◽  
Beam Element ◽  
Truss Structures ◽  
Basic System ◽  
Shear Center ◽  
Torsional Deformation ◽  
Thin Walled ◽  
The Cross

Asymmetric thin-walled sections such as steel angles and tees are widely used in truss structures and transmission towers. To address extreme limit states that these structures encounter due to extreme events such as hurricanes and earthquakes, it is important to capture their response due to large deformations caused by static or dynamic loading. In the nonlinear large deformation regime, these members have coupled axial-flexural-torsional deformation due to the so-called Wagner effect and the noncoincident shear center and centroid. A three-dimensional corotational total Lagrangian beam element is formulated and implemented in the OpenSees corotational framework to account for these coupling effects by invoking Green-Lagrange strains referenced to a basic system. In the basic system, shear forces and torque are defined with respect to the shear center, axial force is referred to the centroid, and flexure is defined around the section principle axes but in the planes containing the shear center. The element tangent stiffness matrix is derived through linearization of the governing equation obtained from the principle of virtual work. Cubic Hermitian functions for the transverse displacements and a linear shape function for the axial and torsional deformation are adopted in the development. Before conducting the corotational transformation, all element end forces and displacements are transformed to act about the shear center. In order to remedy membrane locking in the inextensional bending mode, the high order bending terms in the axial strain are replaced by a constant effective strain. Cyclic material nonlinearity is considered by discretizing the cross section into a grid of fibers, tracking the steel uniaxial stress-strain constitutive at each fiber, and performing numerical integration over the cross section to obtain the section stiffness matrix. The formulation is compared against a set of experimental and numerical results to validate that the element can model geometric and material nonlinearities accurately and efficiently.

The Finite Element Model Research of the Pre-Twisted Beam

2012 ◽  
Vol 188 ◽  
pp. 31-36 ◽  
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Element Model ◽  
Beam Element ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Straight Beam ◽  
The Relationship ◽  
Twisted Beam ◽  
Timoshenko Beam Element

Based on the traditional mechanical model of straight beam element, the paper makes a systematic analysis and research on the pre-twisted beam finite element numerical model. Firstly, the paper proposed the pre-twisted Euler beam element mode, the mode uses 2 node and 12 freedom degrees, the element axial and torsion displacements use 2 nodes Lagrange interpolation function, bending displacement still use the cubic displacement. Secondly, the paper studies a new pre-twisted Timoshenko beam element mode, the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending and rotation displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, which is more accurate to consider the effects of shear deformation. Finally, by calculating the pre-twisted rectangle cantilever beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element mode has good accuracy.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Incorporation of Spinal Flexibility Measurements Into Finite Element Analysis

1990 ◽  
Vol 112 (4) ◽  
pp. 481-483 ◽  
Author(s):  
Mack G. Gardner-Morse ◽  
Jeffrey P. Laible ◽  
Ian A. F. Stokes
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Beam Element ◽  
Technical Note ◽  
Element Analysis ◽  
Spinal Motion ◽  
Spinal Flexibility

This technical note demonstrates two methods of incorporating the experimental stiffness of spinal motion segments into a finite element analysis of the spine. The first method is to incorporate the experimental data directly as a stiffness matrix. The second method approximates the experimental data as a beam element.

UPDATED LAGRANGIAN FORMULATION FOR NONLINEAR STABILITY ANALYSIS OF THIN-WALLED FRAMES WITH SEMI-RIGID CONNECTIONS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250013 ◽  
Author(s):  
GORAN TURKALJ ◽  
JOSIP BRNIC ◽  
DOMAGOJ LANC ◽  
STOJAN KRAVANJA
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Nonlinear Stability ◽  
Plastic Hinge ◽  
Test Problems ◽  
Element Formulation ◽  
Nonlinear Stability Analysis ◽  
Straight Beam ◽  
Thin Walled ◽  
Updated Lagrangian

This paper presents a one-dimensional (1D) finite element formulation for the nonlinear stability analysis of framed structures with semi-rigid (SR) connections. By applying the updated Lagrangian incremental formulation and the nonlinear displacement field of thin-walled cross sections, the equilibrium equations of a straight beam element are first developed. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends. To account for the SR connection behavior, a special transformation procedure is developed. The effectiveness of the numerical algorithm discussed is validated through the test problems.

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