• Structural Engineering and Mechanics
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• 제62권2호
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• pp.247-258
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• 2017

Beam-like structures such as bridge, high building and tower, pipes, flexible connecting rods and some robotic manipulators are often excited by support motions. These structures are important in machines and structures. So, this study proposes an analytic method to accurately predict the dynamic behaviors of the structures during support motions or an earthquake. Using Timoshenko beam theory which is valid even for non-slender beams and for high-frequency responses, the analytic responses of fixed-fixed beams subjected to a real seismic motions at supports are illustrated to show the principled approach to the proposed method. The responses of a slender beam obtained by using Timoshenko beam theory are compared with the solutions based on Euler-Bernoulli beam theory to validate the correctness of the proposed method. The dynamic analysis for the fixed-fixed beam subjected to support motions gives useful information to develop an understanding of the structural behavior of the beam. The bending moment and the shear force of a slender beam are governed by dynamic components while those of a stocky beam are governed by static components. Especially, the maximal magnitudes of the bending moment and the shear force of the thick beam are proportional to the difference of support displacements and they are influenced by the seismic wave velocity.

• 한국정밀공학회지
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• 제15권12호
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• pp.202-211
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• 1998

The present paper proposes a modal analysis procedure to obtain exact modal parameters (natural frequencies, damping ratios, eigenvectors) for general, non-uniform beam-like structures. The proposed method includes a derivation of the system dynamic matrix for a Timoshenko beam element. The proposed method provides not only exact modal parameters but also exact frequency response functions (FRFs) for general beam structures. A time domain analysis method is also proposed. Two examples are provided for validating and illustrating the proposed method. The first numerical example compares the proposed method with FEM. The second example deals with a non-uniform beam structure supported in joints with damping property. The numerical study proves that the proposed method is useful for the dynamic analysis of continuous systems consisting of beam-like structures.

• Structural Engineering and Mechanics
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• 제43권1호
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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.

• Steel and Composite Structures
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• 제29권4호
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• pp.483-491
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• 2018

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the nonuniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution for the elasticity field is then employed to introduce two shear correction factors consistent with the Cowper's and energy approaches. The mathematical form of the proposed shear correction factors are then simplified and compared with the results available in the literature over an extended range of Poisson's and aspect ratios. The proposed shear correction factors do not exhibit implausible issue of negative values and do not result in numerical instabilities too. Based on the comprehensive discussion on the shear correction factors, a piecewise definition of shear correction factor is introduced for rectangular cross-sections having excellent agreement with the numerical results in the literature for both shallow and deep cross-sections.

• 한국태양에너지학회 논문집
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• 제36권3호
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Advances in nano research
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• 제13권4호
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• pp.351-368
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• 2022

Recently, promising structural technologies like multi-function, ultra-load bearing capacity and tailored structures have been put up for discussions. Finite Element (FE) modelling is probably the best-known option capable of treating these superior properties and multi-domain behavior structures. However, advanced materials such as Functionally Graded Material (FGM) and nanocomposites suffer from problems resulting from variable material properties, reinforcement aggregation and mesh generation. Motivated by these factors, this research proposes a unified shape function for FGM, nanocomposites, graded nanocomposites, in addition to traditional isotropic and orthotropic structural materials. It depends not only on element length but also on the beam's material properties and geometric characteristics. The systematic mathematical theory and FE formulations are based on the Timoshenko beam theory for beam structure. Furthermore, the introduced element achieves C1 degree of continuity. The model is proved to be convergent and free-off shear locking. Moreover, numerical results for static and free vibration analysis support the model accuracy and capabilities by validation with different references. The proposed technique overcomes the issue of continuous properties modelling of these promising materials without discarding older ones. Therefore, introduced benchmark improvements on the FE old concept could be extended to help the development of new software features to confront the rapid progress of structural materials.

• 대한조선학회논문집
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• 제41권4호
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• pp.45-52
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• 2004

Exact solution on the anti-symmetric response of ships having uniform sectional properties in waves is derived. Boundary value problem consisted of Timoshenko beam equation and free-free end condition is solved analytically. The responses are assumed as linear and wave loads are calculated by using strip method. Horizontal bending moment, shear force and torsional moment are calculated. The developed analysis model is used for the benchmark test of the numerical codes in this problem. Also the application on the preliminary design of barge-like ships and VLFS (Very Large Floating Structure) is expected

• 대한조선학회논문집
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• 제41권2호
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• pp.47-54
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• 2004

Exact solution on the vertical responses of ships having uniform sectional properties in waves is derived. Boundary value problem consisted of Timoshenko beam equation and free-free end condition is solved analytically. The responses are assumed as linear and wave loads are calculated by using strip method. Vertical bending moment, shear force and deflection are calculated. The developed analysis model is used for the benchmark test of the numerical codes in this problem. Also the application on the preliminary design of barge-like ships and VLFS (Very Large Floating Structure) is expected.

• 동력기계공학회지
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• 제19권3호
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• pp.55-62
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• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Smart Structures and Systems
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• 제17권5호
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• pp.837-857
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• 2016

In the present study, for first time the size dependent vibration behavior of a rotating functionally graded (FG) Timoshenko nanobeam based on Eringen's nonlocal theory is investigated. It is assumed that the physical and mechanical properties of the FG nanobeam are varying along the thickness based on a power law equation. The governing equations are determined using Hamilton's principle and the generalized differential quadrature method (GDQM) is used to obtain the results for cantilever boundary conditions. The accuracy and validity of the results are shown through several numerical examples. In order to display the influence of size effect on first three natural frequencies due to change of some important nanobeam parameters such as material length scale, angular velocity and gradient index of FG material, several diagrams and tables are presented. The results of this article can be used in designing and optimizing elastic and rotary type nano-electro-mechanical systems (NEMS) like nano-motors and nano-robots including rotating parts.