• Steel and Composite Structures
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• v.26 no.4
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• pp.513-531
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• 2018

In this article, static, buckling and free vibration analyses of a sinusoidal micro composite beam reinforced by single-walled carbon nanotubes (SWCNTs) with considering temperature-dependent material properties embedded in an elastic medium in the presence of magnetic field under transverse uniform load are presented. This system is used at micro or sub micro scales to enhance the stiffness of micro composite structures such as bar, beam, plate and shell. In the present work, the size dependent effects based on surface stress effect and modified strain gradient theory (MSGT) are considered. The generalized rule of mixture is employed to predict temperature-dependent mechanical and thermal properties of micro composite beam. Then, the governing equations of motions are derived using Hamilton's principle and energy method. Numerical results are presented to investigate the influences of material length scale parameters, elastic foundation, composite fiber angle, magnetic intensity, temperature changes and carbon nanotubes volume fraction on the bending, buckling and free vibration behaviors of micro composite beam. There is a good agreement between the obtained results by this research and the literature results. The obtained results of this study demonstrate that the magnetic intensity, temperature changes, and two parameters elastic foundations have important effects on micro composite stiffness, while the magnetic field has greater effects on the bending, buckling and free vibration responses of micro composite beams. Moreover, it is shown that the effects of surface layers are important, and observed that the changes of carbon nanotubes volume fraction, beam length-to-thickness ratio and material length scale parameter have noticeable effects on the maximum deflection, critical buckling load and natural frequencies of micro composite beams.

• Earthquakes and Structures
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• v.6 no.4
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• pp.335-350
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• 2014

Historical masonry mosques are the most important structures of Islamic societies. To estimate the static and dynamic behavior of these historical structures, an examination of their restoration studies is very important. In this study, Kara Mustafa Pasha Mosque, which was built as a domed mosque by Kara Mustafa Pasha between 1666-1667 in Amasya, Turkey, has been analyzed. This study investigates the structural behavior and architectural features of the mosque. In order to determine specific mechanical properties, compression and three-point bending tests were conducted on materials, which have similar age and show similar properties as the examined mosque. Additionally, a three-dimensional finite element model of the mosque was developed and the structural responses were investigated through static and dynamic analyses. The results of the analyses were focused on the stresses and displacements. The experimental test results indicate that the construction materials have greatly retained their mechanical properties over the centuries. The obtained maximum compression and tensile stresses from the analyses have been determined as smaller than the materials' strengths. However, the stresses calculated from dynamic analysis might cause structural problems in terms of tensile stresses.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.111-130
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• 2016

Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

• Advances in Computational Design
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• v.3 no.2
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• pp.165-190
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• 2018

In this article, the static behavior of non-prismatic sandwich beams composed of functionally graded (FG) materials is investigated for the first time. Two types of beams in which the variation of elastic modulus follows a power-law form are studied. The principle of minimum total potential energy is applied along with the Ritz method to derive and solve the governing equations. Considering conventional boundary conditions, Chebyshev polynomials of the first kind are used as auxiliary shape functions. The formulation is developed within the framework of well-known Timoshenko and Reddy beam theories (TBT, RBT). Since the beams are simultaneously tapered and functionally graded, bending and shear stress pushover curves are presented to get a profound insight into the variation of stresses along the beam. The proposed formulations and solution scheme are verified through benchmark problems. In this context, excellent agreement is observed. Numerical results are included considering beams with various cross sectional types to inspect the effects of taper ratio and gradient index on deflections and stresses. It is observed that the boundary conditions, taper ratio, gradient index value and core to the thickness ratio significantly influence the stress and deflection responses.

• Nuclear Engineering and Technology
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• v.52 no.12
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• pp.2939-2948
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• 2020

This paper presents an analytic solution procedure of the rotationally restrained hinged-hinged beam subjected to transverse motions at supports based on EBT (Euler-Bernoulli beam theory). The EBT solutions are compared with the solutions based on TBT (Timoshenko beam theory) for a wide range of the rotational restraint parameter (kL/EI) of slender beams whose slenderness ratio is greater than 100. The comparison shows the followings. The internal loads such as bending moment and shearing force of an extremely thin beam obtained by EBT show a good agreement with those obtained by TBT. But the discrepancy between two solutions of internal loads tends to increase as the slenderness ratio decreases. A careful examination shows that the discrepancy of the internal loads originates from their dynamic components whereas their static components show a little difference between EBT and TBT. This result suggests that TBT should be employed even for slender beams to consider the rotational effect and the shear deformation effect on dynamic components of the internal loads. The influence of the parameter on boundary conditions is examined by manipulating the spring stiffness from zero to a sufficiently large value.

• Geomechanics and Engineering
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• v.34 no.3
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• pp.233-250
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• 2023

This paper investigates the flexural analysis of isotropic, transversely isotropic, and laminated composite plates using a new higher-order normal and shear deformation theory. In the present theory, only five unknown functions are involved compared to six or more unknowns used in the other similar theories. The developed theory does not need a shear correction factor. It can satisfy the zero traction boundary conditions on the top and the bottom surfaces of the plate as well as account for sufficient distribution of the transverse shear strains. The thickness stretching effect is considered in the computation. A simply supported was considered on all edges of the plate. The plate is subjected to uniform and sinusoidal distributed load in the static analysis. Laminated composite, isotropic, and transversely isotropic plates are considered. The governing equations are obtained utilizing the virtual work principle. The differential equations are solved via Navier's procedure. The results obtained from the developed theory are compared with other higher-order theories considered in the previous studies and 3D elasticity solutions. The results showed that the proposed theory accurately and effectively predicts the bidirectional bending responses of laminated composite plates. Several parametric studies are presented to illustrate the various parameters influencing the static response of the laminated composite plates.

• Geomechanics and Engineering
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• v.21 no.3
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• pp.269-277
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• 2020

In this study, numerical analyses were conducted to investigate the load transfer mechanisms and dynamic responses between the vertical shaft and the surrounding soil using a dynamic analysis method and a pseudo-static method (called response displacement method, RDM). Numerical solutions were verified against data from the literature. A series of parametric studies was performed with three different transient motions and various surrounding soils. The results showed that the soil stratigraphy and excitation motions significantly influenced the dynamic behavior of the vertical shaft. Maximum values of the shear force and bending moment occurred near an interface between the soil layers. In addition, deformations and load distributions of the vertical shaft were highly influenced by the amplified seismic waves on the vertical shaft constructed in multi-layered soils. Throughout the comparison results between the dynamic analysis method and the RDM, the results from the dynamic analyses showed good agreement with those from the RDM calculated by a double-cosine method.

• Structural Engineering and Mechanics
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• v.11 no.6
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• pp.605-616
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• 2001

The purpose of this study is to investigate the effect of the shear wall location in rigid frames on the dynamic behavior of a roof structure due to vertical and horizontal earthquake motions. The study deals with a gabled long span beam supported by two story rigid frames with shear walls. The earthquake response analysis is carried out to study the responses of the roof: vibration mode, natural period, bending moment and horizontal shear force of the bearings. The study results in the following conclusions: First, a large horizontal stiffness difference between the side frames is caused by the shear wall location, which results in a large vertical vibration of the roof and a large shear force at the side bearings. Second, in this case, the seismic design method for ordinary buildings is not useful in determining the distribution of the static equivalent loads for the seismic design of this kind of long span structures.

• Steel and Composite Structures
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• v.26 no.1
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• pp.89-102
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• 2018

This work investigates a novel plate formulation and a modified couple stress theory that introduces a variable length scale parameter is presented to discuss the static and dynamic of functionally graded (FG) micro-plates. A new type of third-order shear deformation theory of Reddy that use only 4 unknowns by including undetermined integral variables is proposed in this study. The equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for a simply supported micro-plate. Numerical examples are presented to examine the effect of the length scale parameter on the responses of micro-plates. The obtained results are compared with the previously published results to demonstrate the correctness of the present formulation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.188-193
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• 2013

The large mass method for dynamic analysis of statically determinate beams subjected to in-phase support motions is justified by showing that the equation of motion of the beams under consideration is equivalent to that of large mass model of the beam when an appropriate large mass ratio is employed. The accuracy of the stress responses based on the beam large mass method is investigated through careful numerical tests. The numerical results are compared to analytic solutions and the comparison shows that the large mass method yields not only the time history of motion but also the distributions of bending moment and shear force accurately.