ON THE INFLUENCE OF MATERIAL COUPLINGS ON THE LINEAR AND BUCKLING BEHAVIOR OF I-SECTION COMPOSITE COLUMNS

2007 ◽  
Vol 07 (02) ◽  
pp. 243-272 ◽  
Author(s):  
N. FREITAS SILVA ◽  
N. SILVESTRE
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Plane Deformation ◽  
Beam Theory ◽  
Laminated Plates ◽  
Element Formulation ◽  
Equilibrium Equations ◽  
Composite Columns ◽  
Buckling Behavior ◽  
Section Analysis

This paper presents the incorporation of shear deformation effects into a Generalized Beam Theory (GBT) developed to analyze the structural behavior of composite thin-walled columns made of laminated plates and displaying arbitrary orthotropy. Unlike other existing beam theories, the present GBT formulation incorporates in a unified fashion (i) elastic coupling effects, (ii) warping effects, (iii) cross-section in-plane deformation and (iv) shear deformation. The main concepts and procedures involved in the available GBT are adapted/modified to account for the specific aspects related to the member shear deformation. In particular, the GBT fundamental equilibrium equations are presented and their terms are physically interpreted. An I-section is used to illustrate the performance of GBT cross-section analysis and the mechanical properties are explained in detail. With the purpose of solving the GBT system of differential equilibrium equations, a finite element formulation is briefly presented. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, the linear (first-order) and stability behavior of three composite I-section members displaying non-aligned orthotropy are analyzed and the results obtained are thoroughly discussed and compared with estimates available in the literature.

Surface Effects on the Buckling of Piezoelectric Nanobeams

2012 ◽  
Vol 486 ◽  
pp. 519-523 ◽  
Author(s):  
Kai Fa Wang ◽  
Bao Lin Wang
Keyword(s):  
Shear Deformation ◽  
Electric Potential ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Residual Surface Stress ◽  
Buckling Behavior ◽  
Stress Surface ◽  
Piezoelectric Nanobeam

In this paper, we analyze the influence of surface effects including residual surface stress, surface piezoelectric and surface elasticity on the buckling behavior of piezoelectric nanobeams by using the Timoshenko beam theory and surface piezoelectricity model. The critical electric potential for buckling of piezoelectric nanobeams with different boundary condition is obtained analytically. From the results, it is found that the surface piezoelectric reduces the critical electric potential. However, a positive residual surface stress increases the critical electric potential. In addition, the shear deformation reduces the critical electric potential, and the influence of shear deformation become more significant for a stubby piezoelectric nanobeam.

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^

Buckling Behavior of Pultruded Monosymmetric Members

2005 ◽  
Vol 297-300 ◽  
pp. 1259-1264
Author(s):  
Seung Sik Lee ◽  
Soon Jong Yoon ◽  
S.K. Cho ◽  
Jong Myen Park
Keyword(s):  
Cross Section ◽  
Ritz Method ◽  
Beam Theory ◽  
Fiber Reinforced Polymer ◽  
Structural Members ◽  
Uniform Compression ◽  
Torsional Mode ◽  
Axial Forces ◽  
Reinforced Polymer ◽  
Buckling Behavior

Pultruded fiber reinforced polymer (FRP) structural members have been used in various civil engineering applications. T-shapes are commonly used for chord members in trusses and for bracing members. In these cases, T-shapes are mainly subjected to axial forces, and stability of a member is one of the major concerns in the design. Due to the monosymmetry existing in the cross-section of T-shapes, T-shapes are likely to buckle in a flexural-torsional mode. An energy solution, using the Ritz method, to the buckling problem of a pulturuded T-shape under uniform compression is derived based on a composite thin-walled beam theory developed by Bauld and Tzeng. The solution accounts for the bending-twisting and bending-extension coupling effects. The derived energy solutions are compared to the experimental results of buckling tests conducted on seventeen pultruded T-shapes. It is found that the ratios of the experimental to analytical results are in the range of 1.00 to 1.32.

On a Finite Element Formulation of Dynamical Torsion of Beams Including Warping Inertia and Shear Deformation Due to Nonuniform Warping

1983 ◽  
Vol 105 (4) ◽  
pp. 476-483
Author(s):  
A. Potiron ◽  
D. Gay
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Cross Section ◽  
Experimental Results ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Secondary Effects ◽  
Mass Matrices ◽  
Warping Displacement ◽  
Thin Walled

We start from the energetical expressions of dynamical torsion of beams in terms of angular and warping displacement and velocity. We derive the stiffness and two mass matrices including both secondary effects for torsion: the shear deformation due to nonuniform warping and the warping inertia. The suitability of these matrices for evaluation modified torsional frequencies is investigated in the case of thick, as well as thin-walled, cross section beams by comparison with analytical and experimental results.

scholarly journals Shear deformable hybrid finite element formulation for buckling analysis of composite columns

2018 ◽  
Vol 45 (4) ◽  
pp. 279-288
Author(s):  
Vida Niki ◽  
R. Emre Erkmen
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Shear Deformation ◽  
Cross Sections ◽  
Buckling Analysis ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Composite Columns ◽  
Hybrid Finite Element ◽  
Shear Deformable

The objective of this study is to develop a shear deformable hybrid finite element formulation for the flexural buckling analysis of fiber-reinforced laminate composite columns with doubly symmetric cross sections. The hybrid finite element formulation is developed by using the Hellinger-Reissner functional which is obtained by introducing the conditions of compatibility as auxiliary conditions to the potential energy functional. The shear deformation effects due to bending are included by equilibrating shear stress. In comparison to the displacement-based formulations the current hybrid formulation has the advantage of incorporating the shear deformation effects easily by using the strain energy of the shear stress field without modifying the basic kinematic assumptions of the beam theory. The agreement with Engesser formulation for flexural buckling analysis of columns with shear-weak cross sections shows the applicability and accuracy of the current hybrid finite element method for composite structural elements. The applicability of the developed method herein to sandwich and built-up columns are also illustrated.

A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain

1988 ◽  
Vol 55 (1) ◽  
pp. 179-184 ◽  
Author(s):  
D. A. Danielson ◽  
D. H. Hodges
Keyword(s):  
Cross Section ◽  
Variational Principles ◽  
Beam Theory ◽  
Small Strain ◽  
General Context ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Local Rotation ◽  
Material Points

Kinematical relations are derived to account for the finite cross-sectional warping occurring in a beam undergoing large deflections and rotations due to deformation. The total rotation at any point in the beam is represented as a large global rotation of the reference triad (a frame which moves nominally with the reference cross section material points), a small rotation that is constant over the cross section and is due to shear, and a local rotation whose magnitude may be small to moderate and which varies over a given cross section. Appropriate variational principles, equilibrium equations, boundary conditions, and constitutive laws are obtained. Two versions are offered: an intrinsic theory without reference to displacements, and an explicit theory with global rotation characterized by a Rodrigues vector. Most of the formulas herein have been published, but we reproduce them here in a new concise notation and a more general context. As an example, the theory is shown to predict behavior that agrees with published theoretical and experimental results for extension and torsion of a pretwisted strip. The example also helps to clarify the role of local rotation in the kinematics.

Vibration Analysis of Thick Arbitrarily Laminated Plates of Various Shapes and Edge Conditions

2011 ◽  
Vol 471-472 ◽  
pp. 1177-1183
Author(s):  
Tasneem Pervez ◽  
F.K.S. Al-Jahwari ◽  
Abdennour Seibi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Laminated Plates ◽  
Vibration Response ◽  
Element Formulation ◽  
Edge Conditions ◽  
Shear Deformation Theories ◽  
Free Vibration Response

Free vibration analysis of arbitrarily laminated plates of quad, penta and hexagonal shapes, which have combinations of clamped, simply supported and free edge conditions is performed. The finite element formulation is based on first and higher order shear deformation theories to study the free vibration response of thick laminated composite plates. A finite element code is developed incorporating shear deformation theories using an 8-noded serendipity element. The effect of plate shape, arbitrary lamination and different edge conditions on natural frequencies and mode shapes are investigated. A systematic study is carried out to determine the influence of material orthotropy and aspect ratio on free vibration response. For various cases, the comparisons of results from present study showed good agreement with those published in the literature.

Nonlinear Beam-Column Element Under Consistent Deformation

2015 ◽  
Vol 15 (05) ◽  
pp. 1450068 ◽  
Author(s):  
Yi Qun Tang ◽  
Zhi Hua Zhou ◽  
Siu Lai Chan
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Displacement Function ◽  
Shear Locking ◽  
Bernoulli Beam ◽  
Equilibrium Equations ◽  
Nonlinear Beam ◽  
Euler Bernoulli Beam ◽  
Column Element ◽  
Force Equilibrium

A new nonlinear beam-column element capable of considering the shear deformation is proposed under the concept of consistent deformation. For the traditional displacement interpolation function, the beam-column element produces membrane locking under large deformation and shear locking when the element becomes slender. To eliminate the membrane and shear locking, force equilibrium equations are employed to derive the displacement function. Numerical examples herein show that membrane locking in the traditional nonlinear beam-column element could cause a considerable error. Comparison of the present improved formulae based on the Timoshenko beam theory with that based on the Euler–Bernoulli beam theory indicates that the present approach requires several additional parameters to consider shear deformation and it is suitable for computer analysis readily for incorporation into the frames analysis software using the co-rotational approach for large translations and rotations. The examples confirm that the proposed element has higher accuracy and numerical efficiency.

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