• Architectural research
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• v.16 no.2
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• pp.57-65
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• 2014

A study on the static analysis of Timoshenko beams is presented. A beam element is developed by using isogeometric approach based on Timoshenko beam theory which allows the transverse shear deformation. The identification of transverse shear locking is conducted by three refinement schemes such as h-, p- and k-refinement and compared to other reference solutions. From numerical examples, the present beam element does not produce any shear locking in very thin beam situations even with full Gauss integration rule. Finally, the benchmark tests described in this study is provided as future reference solutions for Timoshenko beam problems based on isogeometric approach.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.477-501
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• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.271-276
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• 2004

In this paper. dynamic behavior of the cracked beam under a moving mass is presented using the finite element method (FEM). Model accuracy is improved with the following consideration: (1) FE model with Timoshenko beam element (2) Additional flexibility matrix due to crack presence (3) Interaction forces between the moving mass and supported beam. The Timoshenko bean model with a two-node finite element is constructed based on Guyan condensation that leads to the results of classical formulations. but in a simple and systematic manner. The cracked section is represented by local flexibility matrix connecting two unchanged beam segments and the crack as modeled a massless rotational spring. The inertia force due to the moving mass is also involved with gravity force equivalent to a moving load. The numerical tests for various mass levels. crack sizes. locations and boundary conditions were performed.

• Structural Engineering and Mechanics
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• v.43 no.1
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• pp.15-30
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• 2012

A damped Timoshenko beam element is introduced for the DOF-efficient forced vibration analysis of beam-like structures coated with viscoelastic damping layers. The rotary inertia as well as the shear deformation is considered, and the damping effect of viscoelastic layers is modeled as an imaginary loss factor in the complex shear modulus. A complex composite cross-section of structures is replaced with a homogeneous one by means of the transformed section approach in order to construct an equivalent single-layer finite element model capable of employing the standard $C^{0}$-continuity basis functions. The numerical reliability and the DOF-efficiency are explored through the comparative numerical experiments.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.17-24
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• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.183-195
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• 2003

In this study, the method of the finite element modeling for free vibration control of beam-type smart structures with bonded plate-type piezoelectric sensors and actuators is proposed. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered. By using the variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. Therefore, by analyzing beam-type smart structures with smart beam finite elements, it is possible to simulate the control of the structural behavior by applying voltages to piezoelectric actuators and monitoring of the structural behavior by sensing voltages of piezoelectric sensors. By using the smart beam finite element and constant-gain feed back control scheme, the formulation of the free nitration control for the beam structures with bonded plate-tyPe Piezoelectric sensors and actuators is proposed.

• Steel and Composite Structures
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• v.26 no.6
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• pp.733-743
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• 2018

This paper presents post-buckling responses of a simply supported laminated composite beam subjected to a non-follower axially compression loads. In the nonlinear kinematic model of the laminated beam, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The distinctive feature of this study is post-buckling analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. The effects of the fibber orientation angles and the stacking sequence of laminates on the post-buckling deflections, configurations and stresses of the composite laminated beam are illustrated and discussed in the numerical results. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the laminated composite beams.

• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.347-371
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• 2011

This paper focuses on post-buckling analysis of Timoshenko beams with various boundary conditions subjected to a non-uniform thermal loading by using the total Lagrangian Timoshenko beam element approximation. Six types of support conditions for the beams are considered. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of Timoshenko beams under uniform and non-uniform thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, the relationships between deflections, end rotational angles, end constraint forces, thermal buckling configuration, stress distributions through the thickness of the beams and temperature rising are illustrated in detail in post-buckling case.

• Journal of Korean Society of Steel Construction
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• v.13 no.1
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• pp.91-100
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• 2001

This paper is to analyze the stability of Timoshenko beam-column on Pasternak foundation, with the extensional and the rotational spring at center point of span by Finite Element Method. To verify this Finite Element Method, the results by the proposed method are compared with the existing solutionsof Timoshenko beam-column without the extensional and the rotational spring and the shear foundation. The dynamic stability regions are decided by the dynamic stability analysis of Timoshenko beam-column on Pasternak foundation with the extensional and the rotation spring at center point of span.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.389-400
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• 2018

An exact solution for the title problem was obtained in closed-form fashion considering general boundary conditions. The expressions of moment, shear and shear coefficient (or shear factor) of cross section under the effect of arbitrary temperature distribution were first derived. In view of these relationships, the differential equations of Timoshenko beam under the effect of temperature were obtained and solved. Second, the characteristic equations of Timoshenko beam carrying several spring-mass systems under the effect of temperature were derived based on the continuity and force equilibrium conditions at attaching points. Then, the correctness of proposed method was demonstrated by a Timoshenko laboratory beam and several finite element models. Finally, the influence law of different temperature distribution modes and parameters of spring-mass system on the modal characteristics of Timoshenko beam had been studied, respectively.