• Structural Engineering and Mechanics
• /
• v.64 no.4
• /
• pp.403-411
• /
• 2017

In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for EulerBernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.

• Structural Engineering and Mechanics
• /
• v.68 no.6
• /
• pp.713-720
• /
• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.20 no.12
• /
• pp.614-621
• /
• 2019

A generalized laminated composite beam element is presented for the flexural and buckling analysis of laminated composite beams with double and single symmetric cross-sections. Based on shear-deformable beam theory, the present beam model accounts for transverse shear and warping deformations, as well as all coupling terms caused by material anisotropy. The plane stress and plane strain assumptions were used along with the cross-sectional stiffness coefficients obtained from the analytical technique for different cross-sections. Two types of one-dimensional beam elements with seven degrees-of-freedom per node, including warping deformation, i.e., three-node and four-node elements, are proposed to predict the flexural behavior of symmetric or anti-symmetric laminated beams. To alleviate the shear-locking problem, a reduced integration scheme was employed in this study. The buckling load of laminated composite beams under axial compression was then calculated using the derived geometric block stiffness. To demonstrate the accuracy and efficiency of the proposed beam elements, the results based on three-node beam element were compared with those of other researchers and ABAQUS finite elements. The effects of coupling and shear deformation, support conditions, load forms, span-to-height ratio, lamination architecture on the flexural response, and buckling load of composite beams were investigated. The convergence of two different beam elements was also performed.

• Journal of Korean Association for Spatial Structures
• /
• v.10 no.4
• /
• pp.123-132
• /
• 2010

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analyses. For this, the displacement field is expressed by introducing displacement parameters defined at the centroid and shear center axes, respectively. Next the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are rigorously derived by degenerating the energies of the elastic continuum to those of curved beam. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by centroid formulation, previous research and ABAQUS's shell elements.

• Computational Structural Engineering
• /
• v.9 no.3
• /
• pp.135-143
• /
• 1996

The differential equations governing both the free vibrations and buckling loads of tapered beam-columns of circular cross-section with constant volume are derived and solved numerically. The effects of axial load are included in the differential equations. The parabolic equation is chosen as the variable radius of circular cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, clamped-hinged and hinged-hinged end constraints are considered. The variations of the frequency parameters and buckling load parameters with the non-dimensional system parameters are presented in figures and the configurations of strongest columns are obtained.

• Structural Engineering and Mechanics
• /
• v.75 no.6
• /
• pp.737-746
• /
• 2020

This paper attempts to investigate the free vibration of functionally graded material beams with nonuniform width based on the nonlocal elasticity theory. The theoretical formulations are established following the Euler-Bernoulli beam theory, and the governing equations of motion of the system are derived from the minimum total potential energy principle using the nonlocal elasticity theory. In addition, the Differential Quadrature Method (DQM) is applied, along with the Chebyshev-Gauss-Lobatto polynomials, in order to determine the weighting coefficient matrices. Furthermore, the effects of the nonlocal parameter, cross-section area of the functionally graded material (FGM) beam and various boundary conditions on the natural frequencies are examined. It is observed that the nonlocal parameter and boundary conditions significantly influence the natural frequencies of the functionally graded material beam cross-section. The results obtained, using the Differential Quadrature Method (DQM) under various boundary conditions, are found in good agreement with analytical and numerical results available in the literature.

• Journal of the Korean Society of Industry Convergence
• /
• v.23 no.2_2
• /
• pp.289-299
• /
• 2020

The composition of convergence cross-section of the material is a technique that provides reasonable design and construction of structures. It is frequently used in medium-sized bridges and architectural structures. However, the structural behavioral spare capacity enhancement of the structure by the application of the convergence cross-section is still limited by the expandability due to the limiting state of each material. In order to overcome these limitations, this study reasonably analyzed the construction stages before and after the convergence cross-section constructed and developed a technique for forming multi-point boundary conditions using struts, which are compression members. Based on the existing cases, a reasonable construction step for forming the material composite section of the entire structural system of the structure was derived, and a numerical analysis model for a specific part was constructed to analyze the behavior of the strut application. As a result of this study, the effect of reducing the sectional force of 7.40% in beam-column joint and 6.31% in the center of girder was derived, and the deflection, which is a measure of the serviceability of the structure, improved by 54.41% from the installation and dismantling of strut members at each construction stage.

• Composites Research
• /
• v.17 no.4
• /
• pp.25-31
• /
• 2004

In this study, a refined beam analysis model has been developed for multi-celled composite blades with elliptic cross-sections. Reissner's semi-complimentary energy functional is introduced to describe the beam theory and also to deal with the mixed-nature of the formulation. The wail of elliptic sections is discretized into finite number of elements along the contour line and Gauss integration is applied to obtain the section properties. For each cell of the section, a total of four continuity conditions are used to impose proper constraints for the section. The theory is applied to single- and double-celled composite blades with elliptic cross-sections and is validated with detailed finite element analysis results.

• Wind and Structures
• /
• v.23 no.1
• /
• pp.45-57
• /
• 2016

Open-cross-section composite beam (OCB) tends to suffer vortex-induced vibration (VIV) due to its bluff aerodynamic shape. A cable-stayed bridge equipped with typical OCB is taken as an example in this paper to conduct sectional model wind tunnel test. Vortex-induced vibration is observed and maximum vibration amplitudes are obtained. CFD approach is employed to calculate the flow field around original cross sections in service stage and construction stage, as well as sections added with three different countermeasures: splitters, slabs and wind fairings. Results show that flow separate on the upstream edge and cause vortex shedding on original section. Splitters can only smooth the flow field on the upper surface, while slabs cannot smooth flow field on the upper or lower surface too much. Thus, splitters or slabs cannot serve as valid aerodynamic means. Wind tunnel test results show that VIV can only be mitigated when wind fairings are mounted, by which the flow field above and below the bridge deck are accelerated simultaneously.

• Advances in aircraft and spacecraft science
• /
• v.1 no.3
• /
• pp.253-271
• /
• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.