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.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

scholarly journals Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

2020 ◽  
Author(s):  
E. Carrera ◽  
◽  
A. Pagani ◽  
R. Augello
Keyword(s):  
Finite Elements ◽  
Large Deflection ◽  
Nonlinear Problems ◽  
Structural Domain ◽  
Fe Model ◽  
Efficient Manner ◽  
Cross Sectional ◽  
Thin Walled Structures ◽  
Post Buckling ◽  
Thin Walled

AbstractIn the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.

Twisting and Bending of Thin-Walled Prismatic Beams of Open Cross-Sectional Profile

1970 ◽  
Vol 12 (2) ◽  
pp. 130-134 ◽  
Author(s):  
T. Harrison
Keyword(s):  
Cross Sections ◽  
Virtual Work ◽  
Cross Sectional ◽  
Transverse Bending ◽  
Prismatic Beam ◽  
Loading System ◽  
Cross Sectional Profile ◽  
Thin Walled ◽  
Sectional Profile ◽  
Principle Of Virtual Displacements

Previous studies of the behaviour, in generalized co-ordinates, of thin-walled, prismatic beams of open cross-sectional profile have included, explicitly, only the effects of distributed transverse forces, q x and q y, distributed longitudinal forces, q z, and distributed torsional couples, m z. Using the principle of virtual displacements, the work of previous investigators is extended to include, quite generally, the effects of the hitherto neglected distributed couples, m x and m y. The derivation of the differential equation relating to the twisting of an open-section prismatic beam is presented fully whilst those relating to transverse and axial displacements of cross-sections are merely stated. The kinematic and static boundary conditions for a cantilever are also established from the virtual work equations. These show that the free-end shear boundary condition associated with transverse bending which is usually adopted in engineering calculations is inadequate for such a generalized loading system.

Buckling Behavior of Well Tubing: The Packer Effect

1982 ◽  
Vol 22 (05) ◽  
pp. 616-624 ◽  
Author(s):  
R.F. Mitchell
Keyword(s):  
Virtual Work ◽  
Beam Theory ◽  
Bending Moment ◽  
Radial Clearance ◽  
Bending Moments ◽  
Principle Of Virtual Work ◽  
Equilibrium Equations ◽  
Conventional Model ◽  
Shear Loads ◽  
Buckling Behavior

Abstract The equilibrium equations for a helically buckled tubing are developed and solved directly. The results show that the packer has a strong influence on the pitch of the helix, and that the pitch developed by the helix is different from the pitch calculated by conventional methods. In addition, the solution providesshear loads and bending moments at the packer andconstraining force exerted on the tubing by the exterior casing. This last result can be used to estimate friction effects on tubing buckling. Introduction The buckling behavior of well tuning and its effect on packer selection and installation have received much attention in the industry. The most well-known analysis of this problem is by Lubinski et al. Later analyses. such as by Hammerlindl, have extended and refined these results. There were two major contributions of this analysis:to clarity the roles of pressures, temperatures, fluid flow, pretension, and packer design in the buckling problem andto present a mechanical model of well buckling behavior that predicted the buckled well configuration as a function of applied loads. The principal results from this model were the motion of the tubing at the packer and the stresses developed in the tubing as a result of buckling. The major features of the conventional model of buckling behavior are summarized as follows.Slender beam theory is used to relate bending moment to curvature.The tubing is assumed to buckle into a helical shape.The principle of virtual work is used to relate applied buckling load to pitch of the helix.Friction between the buckled tubing and restraining casing is neglected. The geometry of the helix is described by three equations: (1) (2) and (3) where u1, u2, and u3 are tubing centerline locations in the x, y, and z coordinate directions, respectively; Theta is the angular coordinate (Fig. 1); r is the tubing-casing radial clearance: and P is pitch of the helix. The principle of virtual work relates P to the buckling force, F, through the following formula. (4) Several questions are not addressed by this analysis:What is the shape of the tubing from packer to fully developed helix?What are the resulting shear loads and moments at the packer caused by buckling?What are the forces exerted on the helically buckled tubing by the restraining casing? Solutions to Questions 2 and 3 would be particularly useful for evaluating friction effects on the tubing and the effect of induced loads on the packer elements. This information would allow better estimates of tubing movement and provide detailed load reactions at the packer for improved packer design. The solution to Question 1 could be particularly interesting because of its effect on results obtained by virtual work methods. SPEJ P. 616^

scholarly journals The Impact of 3D Printing Parameters on the Post-Buckling Behavior of Thin-Walled Structures

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4742
Author(s):  
Tomasz Kopecki ◽  
Przemysław Mazurek ◽  
Łukasz Święch
Keyword(s):  
3D Printing ◽  
Numerical Solutions ◽  
Structure Mapping ◽  
Thin Walled Structures ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled ◽  
The Impact ◽  
Printing Direction ◽  
Bearing Structure

This study presents the results of experimental research and numerical calculations regarding models of a typical torsion box fragment, which is a common thin-walled load-bearing structure used in aviation technology. A fragment of this structure corresponding to the spar wall was made using 3D printing. The examined system was subjected to twisting and underwent post-critical deformation. The research was aimed at determining the influence of the printing direction of the structure’s individual layers on the system stiffness. The experimental phase was supplemented by nonlinear numerical analyses of the models of the studied systems, taking into account the details of the structure mapping using the laminate concept. The purpose of the calculations was to determine the usefulness of the adopted method for modeling the examined structures by assessing the compliance of numerical solutions with the results of the experiment.

scholarly journals A Spinning Finite Beam Element of General Orientation Analyzed With Rayleigh/Timoshenko/Saint-Venant Theory

1994 ◽  
Author(s):  
Thomas J. S. Abrahamsson ◽  
Jan Henrik Sällström
Keyword(s):  
Stiffness Matrix ◽  
Axial Load ◽  
Angular Speed ◽  
Beam Element ◽  
Shape Functions ◽  
Geometric Stiffness ◽  
General Orientation ◽  
Linear Vibrations ◽  
Fixed Axis ◽  
And Performance

Linear vibrations are studied for a straight uniform finite beam element of general orientation spinning at a constant angular speed about a fixed axis in the inertial space. The gyroscopic and circulatory matrices and also the geometric stiffness matrix of the beam element are presented. The effect of the centrifugal static axial load on the bending and torsional dynamic stiffnesses is thereby accounted for. The Rayleigh/Timoshenko/Saint-Venant theory is applied, and polynomial shape functions are used in the construction of the deformation fields. Non-zero off-diagonal elements in the gyroscopic and circulatory matrices indicate coupled bending/shearing/torsional/tensional free and forced modes of a generally oriented spinning beam. Two numerical examples demonstrate the use and performance of the beam element.

scholarly journals Stability analysis of steel frames with semirigid connections and semirigid connections with rigidzones

2001 ◽  
Vol 23 (3) ◽  
pp. 134-148 ◽  
Author(s):  
Vu Quoc Anh
Keyword(s):  
Stiffness Matrix ◽  
Axial Load ◽  
Steel Frames ◽  
Beam Element ◽  
Force Distribution ◽  
Joint Flexibility ◽  
Geometric Stiffness ◽  
Semirigid Connections ◽  
Plane Frames ◽  
Insight Into

To obtain an accurate insight into the behavior of most realistic steel frames, joint flexibility should be allowed for in the analysis since connection flexibility affects both force distribution and deformation in beams and columns of the frames. This paper proposes a method to establish the geometric stiffness matrix and stiffness matrix for semirigid beam element and semirigid beam element with rigidzones. The proposed method can also applied to analyse frame stability with rigid, semirigid and simple connections with rigidzones or without rigidzones. In addition, an approach that evaluates the effective lengthμ factor, thecritical axial load of column in plane frames with rigid, semirigid, and simple connections is also presented.

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