• Coupled systems mechanics
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• v.10 no.1
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Geomechanics and Engineering
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• v.11 no.1
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• pp.95-116
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• 2016

A novel higher order shear-deformable beam model, which provides linear variation of transversal normal strain and quadratic variation of shearing strain, is proposed to describe the beam resting on foundation. Then, the traditional two-parameter Pasternak foundation model is modified to capture the effects of the axial deformation of beam. The Masing's friction law is incorporated to deal with nonlinear interaction between the foundation and the beam bottom, and the nonlinear properties of the beam material are also considered. To solve the mathematical problem, a displacement-based finite element is formulated, and the reliability of the proposed model is verified. Finally, numerical examples are presented to study the effects of the interfacial friction between the beam and foundation, and the mechanical behavior due to the tensionless characteristics of the foundation is also examined. Numerical results indicate that the effects of tensionless characteristics of foundation and the interfacial friction have significant influences on the mechanical behavior of the beam-foundation system.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.233-252
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Journal of Korean Society of Steel Construction
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• v.22 no.6
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• pp.543-551
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• 2010

The end-reinforced composite-beam (eco-girder) system was developed that has characteristics of the existing composite beams such as reduced floor height and increased strength. With it, less use of steel is expected. In the eco-girder system, only both ends of the steel-frame beam, which are vulnerable to the ultimate moment, are reinforced with steel plates so that the steel frame beam design will be based on the moment at the beam center. This study used fiber element analysis, which is a simple representation and numerical integration of the principles of the detailed Finite Element Method(FEM), to predict the hysteretic behavior of reinforced composite beams under cyclic loading. The validity of the numerical method was verified by comparing the results of this study with those of previous studies. In addition, the hysteretic behavior of the eco-girder was compared with that of the existing composite beams.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3792-3803
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• 1996

Since the skew beam element has two curvatures which are a curvature and a torsion, spatial behavior of curved beam which cannot be included in one plane can be anlayzed by emploting the skew beam element. The $C^{0}$-continuous skew beam element shows the stiffness locking phenomenon when full integration is employed. The locking phenomenpn is characterized by two typical phenomena ; one is the much smaller displacement thant the exact one and theother is the undelation phenomenon is stress distribution. In this paper, we examine how unmatched coefficient in the constrained energy brings about the locking by Reduced Minimization theory. We perform the numerical ones. These comparisons show that uniformly full integration(UFI), which employs full integration for the constrained energy, entails the locking phenomenon. But the use of uniformly reduced integration(URI) of selectively reduced integration(SRI), which employs reduced integration for constrained energy, does not produce the significant errors of displacements of the undulation phenomenon in stress distribution since they do not entails the locking, Additionally, the error due to the approximated parameters for describing the geometry of skew beam is examined.d.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.3
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• pp.75-86
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• 1982

The degeneration of two classes of thick beam elements has been conducted, one (DB6) based on the conventional Timoshenko beam assumptions whereas the other (DB7) based on the assumed cubic axial displacement profile. While an adjustable shear correction factor is required for the DB 6 element to compensate for the unrealistic distribution of shear strain across the thickness, the DB 7 element assumes the more realistic quadratic profile of shear strain at the outset. With the plane-stress continuum solution as reference, solutions obtained by these two element models are compared with the analytical Timoshenko solution, the analytical thin beam solution and several available solutions of other existing beam elements. The result indicates that the performance of the higher order beam element DB 7 is consistently superior to any others. This is true for the whole range of aspect ratios of beam, in both static and free vibration analyses.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.832-834
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• 2017

In this paper, the finite element models for composite lattice structures were verified through natural frequency test. Finite element models of composite lattice structure were generated using beam, shell and solid element. Natural frequencies were measured using impact test method under free-boundary condition. The natural frequencies of finite element analysis for shell and solid element showed a good agreement with experimental results. But beam element did not show a good agreement with experimental results, because beam element could not consider the degradation of mechanical properties of non-intersection parts for composite lattice structure.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.831-834
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• 2008

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model with variational method for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is the verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.337-346
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• 2018

The purpose of this study is to investigate thermal post-buckling analysis of a laminated composite beam subjected under uniform temperature rising with temperature dependent physical properties. The beam is pinned at both ends and immovable ends. Under temperature rising, thermal buckling and post-buckling phenomena occurs with immovable ends of the beam. In the nonlinear kinematic model of the post-buckling problem, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. Also, material properties of the laminated composite beam are temperature dependent: that is the coefficients of the governing equations are not constant. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The effects of the fibber orientation angles, the stacking sequence of laminates and temperature rising on the post-buckling deflections, configurations and critical buckling temperatures of the composite laminated beam are illustrated and discussed in the numerical results. Also, the differences between temperature dependent and independent physical properties are investigated for post-buckling responses of laminated composite beams.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.11
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• pp.1012-1016
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• 2004

In the present paper, equivalent beam and equivalent bimorph beam models for IPMC(ionic Polymer-Metal Composite) actuators are described. Physical properties of an IPMC, such as Young's modulus and electro-mechanical coupling coefficient. are determined from the rule of mixture, bimorph beam equations, and measured force-displacement data of a cantilevered IPMC actuator. By using a beam equation with estimated physical properties, actuation displacements of a cantilevered IPMC actuator was calculated and a good agreement between the computed tip displacements and the measured data was observed. Finite element analysis(FEA) combined with the estimated physical properties was used to reproduce the force-displacement relationship of an IPMC actuator. Results from the FEA agreed well with the measure data. The proposed models might be used for modeling of IPMC actuators with complicated shapes and boundary conditions.