• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.263-278
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• 2006

Starting with the geometrically non-linear formulation and the subsequent linearization, this paper presents a consistent formulation of the exact mechanical analysis of geometrically and materially linear three-layer continuous planar beams. Each layer of the beam is described by the geometrically linear beam theory. Constitutive laws of layer materials and relationships between interlayer slips and shear stresses at the interface are assumed to be linear elastic. The formulation is first applied in the analysis of a three-layer simply supported beam. The results are compared to those of Goodman and Popov (1968) and to those obtained from the formulation of the European code for timber structures, Eurocode 5 (1993). Comparisons show that the present and the Goodman and Popov (1968) results agree completely, while the Eurocode 5 (1993) results differ to a certain degree. Next, the analytical solution is used in formulating a general procedure for the analysis of layered continuous beams. The applications show the qualitative and quantitative effects of the layer and the interlayer slip stiffnesses on internal forces, stresses and deflections of composite continuous beams.

• Advances in nano research
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• v.8 no.1
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• pp.25-36
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• 2020

Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.323-349
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• 2014

In this paper, linear buckling analysis of a curved sandwich beam with a flexible core is investigated. Derivation of equations for face sheets is accomplished via the classical theory of curved beam, whereas for the flexible core, the elasticity equations in polar coordinates are implemented. Employing the von-Karman type geometrical non-linearity in strain-displacement relations, nonlinear governing equations are resulted. Linear pre-buckling analysis is performed neglecting the rotation effects in pre-buckling state. Stability equations are concluded based on the adjacent equilibrium criterion. Considering the movable simply supported type of boundary conditions, suitable trigonometric solutions are adopted which satisfy the assumed edge conditions. The critical uniform load of the beam is obtained as a closed-form expression. Numerical results cover the effects of various parameters on the critical buckling load of the curved beam. It is shown that, face thickness, core thickness, core module, fiber angle of faces, stacking sequence of faces and openin angle of the beam all affect greatly on the buckling pressure of the beam and its buckled shape.

• Coupled systems mechanics
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• v.2 no.4
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• pp.349-374
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• 2013

In this work we propose a novel procedure for direct computation of buckling loads for extreme mechanical or thermomechanical conditions. The procedure efficiency is built upon the von Karmann strain measure providing the special format of the tangent stiffness matrix, leading to a general linear eigenvalue problem for critical load multiplier estimates. The proposal is illustrated on a number of validation examples, along with more complex examples of interest for practical applications. The comparison is also made against a more complex computational procedure based upon the finite strain elasticity, as well as against a more refined model using the frame elements. All these results confirm a very satisfying performance of the proposed methodology.

• Structural Engineering and Mechanics
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• v.13 no.1
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• pp.103-116
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• 2002

A solution based on the linear three-dimensional theory of elasticity is developed for vibration and elastostatic problems of hollow toroids. The theory is developed for transversely isotropic toroids of arbitrary thickness, and has the potential to validate some vehicle and aircraft tire models in the linear range. In the semi-analytical method that is adopted Fourier series are written in the circumferential direction, forming a set of two-dimensional problems. These problems are solved using the differential quadrature method. A commercial finite element program is used to determine alternative solutions. For validation both problems of vibration and elastostatics are considered. Finally results are determined for local surface loading problems, and conclusions are drawn.

• Structural Engineering and Mechanics
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• v.26 no.2
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• pp.151-162
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• 2007

Rigorous analytical solutions are obtained for the plane stress problem of a rectangular plate subjected to non-linearly distributed bending loads on two opposite edges. They are then used in a Galerkin type solution to obtain the corresponding convergent buckling loads. It is shown that the critical bending moment depends significantly on the actual edge load distribution and further the number of nodal lines of the buckled configuration can also be different from that corresponding to a linear antisymmetric distribution of the bending stresses. Results are tabulated for future use while judging approximate numerical solutions.

• Advances in aircraft and spacecraft science
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• v.5 no.5
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• pp.515-531
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• 2018

In this manuscript, buckling response of the functionally graded material (FGM) nanoplate is investigated. Two opposite edges of nanoplate is under linear and nonlinear varying normal stresses. The small-scale effect is considered by Eringen's nonlocal theory. Governing equation are derived by nonlocal theory and Hamilton's principle. Navier's method is used to solve governing equation in simply boundary conditions. The obtained results exactly match the available results in the literature. The results of this research show the important role of nonlocal effect in buckling and stability behavior of nanoplates. In order to study the FG-index effect and different loading condition effects on buckling of rectangular nanoplate, Navier's method is applied and results are presented in various figures and tables.

• Steel and Composite Structures
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• v.18 no.5
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• pp.1161-1176
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• 2015

The connection between a column and a beam is of particular importance to ensure the safety of civil engineering structures, such as high-rise buildings and bridges. While the connector must bear sufficient force for load transmission, increase of its ductility, toughness and damping may greatly enhance the overall safety of the structures. In this work, a composite beam-column connector is proposed and analyzed with the finite element method, including effects of elasticity, linear viscoelasticity, plasticity, as well as geometric nonlinearity. The composite connector consists of three parts: (1) soft steel; (2) polymer; and (3) conventional steel to be connected to beam and column. It is found that even in the linear range, the energy dissipation capacity of the composite connector is largely enhanced by the polymer material. Since the soft steel exhibits low yield stress and high ductility, hence under large deformation the soft steel has the plastic deformation to give rise to unique energy dissipation. With suitable geometric design, the connector may be tuned to exhibit different strengths and energy dissipation capabilities for real-world applications.

• Proceedings of the Korean Geotechical Society Conference
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• 2002.03a
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• pp.41-48
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• 2002

The fact that nonlinearity and anisotropy of soil should be considered for the proper estimation of soil deformation has been recongnized for a long time. In this study, a new stiffness model which can reflect both nonlinearity and anisotropy is proposed. Nonlinearity is simulated by Ramberg-Osgood model and anisotropy is modeled with the cross-anisotropic elasticity. Analysis results with the developed model compared with those from analyses using linear isotropic model, linear anisotropic model, and nonlinear isotropic model. In the triaxial compression like condition, the effects of nonlinearity on the vertical strain are significant, but soil anisotropy does not affect the vertical strain. In 1-dimensional deformation condition, however, both nonlinearity and anisotropy of soil influence the final magnitude of the vertical strain. Also the increase of poisson's ratio magnifies the effect of anisotropy on the vertical strain in this condition.

• Structural Engineering and Mechanics
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• v.22 no.1
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• pp.107-130
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• 2006

The paper deals with the numerical solution of the dynamic problem of masonry structures. Masonry is modelled as a non-linear elastic material with zero tensile strength and infinite compressive strength. Due to the non-linearity of the adopted constitutive equation, the equations of the motion must be integrated directly. In particular, we apply the Newmark or the Hilber-Hughes-Taylor methods implemented in code NOSA to perform the time integration of the system of ordinary differential equations obtained from discretising the structure into finite elements. Moreover, with the aim of evaluating the effectiveness of these two methods, some dynamic problems, whose explicit solutions are known, have been solved numerically. Comparisons between the exact solutions and the corresponding approximate solutions obtained via the Newmark and Hilber-Hughes-Taylor methods show that in the cases under consideration both numerical methods yield satisfactory results.