scholarly journals Buckling analysis of steel fiber column with different cross-section and boundary conditions using Euler-Bernoulli beam theory

2019 ◽  
Vol 11 (1) ◽  
pp. 330-344
Author(s):  
Mahmut tunahan Özdemir ◽  
Veysel Kobya ◽  
Mustafa özgür Yaylı ◽  
Ali Mardani Aghabaglou
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Steel Fiber ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

Advanced Beam Theory for Multibody Dynamics

2013 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Three Dimensional ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Bernoulli Beam Theory ◽  
The Cross ◽  
Euler Bernoulli Beam

In flexible multibody systems, many components are often approximated as beams or shells. More often that not, classical beam theories, such as Euler-Bernoulli beam theory, form the basis of the analytical development for beam dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the beam’s section is assumed to remain plane and its displacement field is fully defined by three displacement and three rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from Saint-Venant’s theory for torsion that the cross-section will warp under torque, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, sectional stiffnesses are computed based on sophisticated mechanics of material theories that evaluate the complete state of deformation. These sectional stiffnesses are then used within the framework of an Euler-Bernoulli beam theory based on far simpler kinematic assumptions. While this approach works well for simple cross-sections made of homogeneous material, very inaccurate predictions result for realistic sections, specially for thin-walled beams, or beams made of anisotropic materials. This paper presents a different approach to the problem. Based on a finite element discretization of the cross-section, an exact solution of the theory of three-dimensional elasticity is developed. The only approximation is that inherent to the finite element discretization. The proposed approach is based on the Hamiltonian formalism and leads to an expansion of the solution in terms of extremity and central solutions, as expected from Saint-Venant’s principle.

Three-Dimensional Beam Theory for Flexible Multibody Dynamics

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Three Dimensional ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Bernoulli Beam Theory ◽  
The Cross ◽  
Euler Bernoulli Beam

In multibody systems, it is common practice to approximate flexible components as beams or shells. More often than not, classical beam theories, such as the Euler–Bernoulli beam theory, form the basis of the analytical development for beam dynamics. The advantage of this approach is that it leads to simple kinematic representations of the problem: the beam's section is assumed to remain plane and its displacement field is fully defined by three displacement and three rotation components. While such an approach is capable of accurately capturing the kinetic energy of the system, it cannot adequately represent the strain energy. For instance, it is well known from Saint-Venant's theory for torsion that the cross-section will warp under torque, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, sectional stiffnesses are computed based on sophisticated mechanics of material theories that evaluate the complete state of deformation. These sectional stiffnesses are then used within the framework of a Euler–Bernoulli beam theory based on far simpler kinematic assumptions. While this approach works well for simple cross-sections made of homogeneous material, inaccurate predictions may result for realistic configurations, such as thin-walled sections, or sections comprising anisotropic materials. This paper presents a different approach to the problem. Based on a finite element discretization of the cross-section, an exact solution of the theory of three-dimensional elasticity is developed. The only approximation is that inherent to the finite element discretization. The proposed approach is based on the Hamiltonian formalism and leads to an expansion of the solution in terms of extremity and central solutions, as expected from Saint-Venant's principle.

Matrix Method for Buckling Analysis of Frames Based on Hencky Bar-Chain Model

2019 ◽  
Vol 19 (08) ◽  
pp. 1950093 ◽  
Author(s):  
W. H. Pan ◽  
C. M. Wang ◽  
H. Zhang
Keyword(s):  
Matrix Method ◽  
Structural Changes ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Chain Model ◽  
Bernoulli Beam ◽  
Various Boundary Conditions ◽  
End Restraint ◽  
Euler Bernoulli Beam ◽  
General Frames

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

Exact solutions for the bending of Timoshenko beams using Eringen’s two-phase nonlocal model

2018 ◽  
Vol 24 (3) ◽  
pp. 559-572 ◽  
Author(s):  
Yuanbin Wang ◽  
Kai Huang ◽  
Xiaowu Zhu ◽  
Zhimei Lou
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Model ◽  
Bernoulli Beam ◽  
Two Phase ◽  
Differential Model ◽  
Euler Bernoulli Beam

Eringen’s nonlocal differential model has been widely used in the literature to predict the size effect in nanostructures. However, this model often gives rise to paradoxes, such as the cantilever beam under end-point loading. Recent studies of the nonlocal integral models based on Euler–Bernoulli beam theory overcome the aforementioned inconsistency. In this paper, we carry out an analytical study of the bending problem based on Eringen’s two-phase nonlocal model and Timoshenko beam theory, which accounts for a better representation of the bending behavior of short, stubby nanobeams where the nonlocal effect and transverse shear deformation are significant. The governing equations are established by the principal of virtual work, which turns out to be a system of integro-differential equations. With the help of a reduction method, the complicated system is reduced to a system of differential equations with mixed boundary conditions. After some detailed calculations, exact analytical solutions are obtained explicitly for four types of boundary conditions. Asymptotic analysis of the exact solutions reveals clearly that the nonlocal parameter has the effect of increasing the deflections. In addition, as compared with nonlocal Euler–Bernoulli beam, the shear effect is evident, and an additional scale effect is captured, indicating the importance of applying higher-order beam theories in the analysis of nanostructures.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

2012 ◽  
Vol 24 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Harvesters ◽  
Bernoulli Beam Theory ◽  
Spectral Finite Element ◽  
Euler Bernoulli Beam ◽  
Element Method

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).

Case Study of the Effect of Combined Axial and Lateral Loadings on the Critical Buckling Capacity of Piping Supports

2020 ◽  
Author(s):  
Phillip Wiseman ◽  
Alex Mayes ◽  
Shreeya Karnik
Keyword(s):  
Large Deformation ◽  
Axial Loading ◽  
Beam Theory ◽  
Second Order ◽  
Lateral Acceleration ◽  
Bernoulli Beam ◽  
Deformation Method ◽  
Closed Form Solutions ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

Abstract Snubbers are used in industry to restrain piping in dynamic events which can see significant axial loading as well as lateral acceleration. Snubbers are often employed with an extension when required to bridge gaps between the piping and building structure. As a result, they are susceptible to buckling instability issues. The pipe support and restraint design by analysis buckling criteria for supports given within the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 1, Subsection NF is investigated to determine the behavior of snubber assemblies under combined axial and lateral loadings. Four types of analyses are performed on the assemblies under the action of axial loading to demonstrate finite element and closed form solutions. These include the following: linear Eigen buckling, nonlinear second order large deformation method, energy method and Euler Bernoulli beam theory. In addition, a variety of snubber assembly sizes are subjected to combined axial and lateral loading in the form of multiple magnitudes of lateral acceleration. The behavior was analyzed by the Euler Bernoulli beam theory and nonlinear second order large deformation method. The techniques of each method are compared providing explanations of the assumptions taken, relevant limitations and recommended applications.

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