• Steel and Composite Structures
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• v.21 no.5
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• pp.999-1016
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• 2016

This study presents free vibration of beam made of porous material. The mechanical properties of the beam is variable in the thickness direction and the beam is investigated in three situations: poro/nonlinear nonsymmetric distribution, poro/nonlinear symmetric distribution, and poro/monotonous distribution. First, the governing equations of porous beam are derived using principle of virtual work based on Euler-Bernoulli theory. Then, the effect of pores compressibility on natural frequencies of the beam is studied by considering clamped-clamped, clamped-free and hinged-hinged boundary conditions. Moreover, the results are compared with homogeneous beam with the same boundary conditions. Finally, the effects of poroelastic parameters such as pores compressibility, coefficients of porosity and mass on natural frequencies has been considered separately and simultaneously.

• Earthquakes and Structures
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• v.13 no.3
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• pp.241-253
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• 2017

In this paper, dynamic response of the horizontal nanofiber reinforced polymer (NFRP) strengthened concrete beam subjected to seismic ground excitation is investigated. The concrete beam is modeled using hyperbolic shear deformation beam theory (HSDBT) and the mathematical formulation is applied to determine the governing equations of the structure. Distribution type and agglomeration effects of carbon nanofibers are considered by Mori-Tanaka model. Using the nonlinear strain-displacement relations, stress-strain relations and Hamilton's principle (virtual work method), the governing equations are derived. To obtain the dynamic response of the structure, harmonic differential quadrature method (HDQM) along with Newmark method is applied. The aim of this study is to investigate the effect of NFRP layer, geometrical parameters of beam, volume fraction and agglomeration of nanofibers and boundary conditions on the dynamic response of the structure. The results indicated that applied NFRP layer decreases the maximum dynamic displacement of the structure up to 91 percent. In addition, using nanofibers as reinforcement leads a 35 percent reduction in the maximum dynamic displacement of the structure.

• Steel and Composite Structures
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• v.11 no.4
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• pp.341-358
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• 2011

This paper presents the effects of thermal environment and temperature-dependence of the material properties on axisymmetric bending of functionally graded (FG) circular and annular plates. The material properties are assumed to be temperature-dependent and graded in the thickness direction. In order to accurately evaluate the effect of thermal environment, the initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Governing equations and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the virtual work principle based on the elasticity theory. The differential quadrature method (DQM) as an efficient and robust numerical tool is used to obtain the initial thermal stresses and response of the plate. Comparison studies with some available results for FG plates are performed. The influences of temperature rise, temperature-dependence of material properties, material graded index and different geometrical parameters are carried out.

• Steel and Composite Structures
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• v.27 no.5
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• pp.599-611
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• 2018

In this article a four unknown quasi-3D shear deformation theory for the bending analysis of functionally graded (FG) plates is developed. The advantage of this theory is that, in addition to introducing the thickness stretching impact (${\varepsilon}_z{\neq}0$), the displacement field is modeled with only four variables, which is even less than the first order shear deformation theory (FSDT). The principle of virtual work is utilized to determine the governing equations. The obtained numerical results from the proposed theory are compared with the CPT, FSDT, and other quasi-3D HSDTs.

• Steel and Composite Structures
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• v.2 no.5
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• pp.315-330
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• 2002

This paper proposes a model for analysing the non-linear behaviour of steel concrete composite beams prestressed by external slipping cables, taking into account the deformability of the interface shear connection. By assuming a suitable admissible displacement field for the composite beam, the balance condition is obtained by the virtual work principle. The solution is numerically achieved by approximating the unknown displacement functions as series of shape functions according to the Ritz method. The model is applied to real cases by showing the consequences of different connection levels between the concrete slab and the steel beam. Particular attention is focused on the limited ductility of the shear connection that may be the cause of premature failure of the composite girder.

• Structural Engineering and Mechanics
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• v.2 no.2
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• pp.185-196
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• 1994

In this paper a spline function solution for the ultimate strength of steel members and member structures is derived based on total Lagrangian formulation. The displacements of members along longitudinal and transverse directions are interpolated by one-order B spline functions and three-order hybrid spline functions respectively. Equilibrium equations are established according to the principle of virtual work. All initial imperfections of members and effects of loading, unloading and reloading of material are taken into account. The influence of the instability of members on structural behavior can be included in analyses. Numerical examples show that the method of this paper can satisfactorily analyze the elasto-plastic large deflection problems of planar steel member and member structures.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.635-640
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• 2000

This paper presents the analysis method of the instantaneous screw axis using line geometry in bump and rebound motion of 5-SS multi-link suspensions. Instantaneous screw axis is based on screw motion, and screw motion of zero pitch can be expressed as $Pl{\ddot{u}}cker$ line coordinates of line geometry instead of screw coordinates. In screw coordinates, twist and wrench are described by components of instantaneous screw axis. For instantaneous motion of wheel assembly, the principle of virtual work with twist and wrench is applied to 5-SS multi-link suspension, and it makes 5 linear equations. Therefore, it is possible to find instantaneous screw axis by solving these equations. This analysis by line geometry demands geometric values only, such as the locations of spherical joints in the case of multi-link suspensions.

• Earthquakes and Structures
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• v.16 no.2
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• pp.177-183
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• 2019

In this paper, a new refined hyperbolic shear deformation beam theory for the bending analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the bending response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equilibrium equations are derived from the principle of virtual work. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG beams.

• Advances in aircraft and spacecraft science
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• v.7 no.1
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• pp.19-40
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• 2020

In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.169-176
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• 1999

An improved formulation for spatial stability md free vibration of thin-walled curved beams with variable curvature and non-symmetric cross sections are presented based on the displacement field considering the second order terms of finite semitangential rotations. By introducing Vlasov's assumptions, the total potential energy is derived from the principle of linearized virtual work for a continuum. In this formulation, all displacement parameters and the warping function are defined at the centroid axis so that the coupled terms of bending and torsion are added to the elastic strain energy. Also, the potential energy due to initial stress resultants is consistently derived corresponding to the semitangential rotation and moment. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. In order to illustrate the accuracy and practical usefulness of this study, . numerical solutions for free vibration of arches are presented and compared with resells of other researchers and solutions analyzed by the ABAQUS's shell element.