• Coupled systems mechanics
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• v.8 no.5
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• pp.439-457
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• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.

• Structural Engineering and Mechanics
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• v.86 no.2
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• pp.167-180
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• 2023

This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler's and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article's findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

• Steel and Composite Structures
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• v.34 no.6
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• pp.795-802
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• 2020

The subject of the paper is a circular plate with symmetrically thickness-wise varying mechanical properties. The plate is simply supported and carries a concentrated force located in its centre. The axisymmetric bending problem of the plate with consideration of the shear effect is analytically and numerically studied. A nonlinear function of deformation of the straight line normal to the plate neutral surface is assumed. Two differential equations of equilibrium based on the principle of stationary potential energy are obtained. The system of equations is analytically solved and the maximum deflections and shear coefficients for example plates are derived. Moreover, the maximum deflections of the plates are calculated numerically (FEM), for comparison with the analytical results.

• Proceedings of the Korean Geotechical Society Conference
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• 2002.06a
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• pp.43-56
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• 2002

To find a lateral long term behavior of driven H-piles in embankment, inclinometer is installed at pile and measurement is done during a year. When behavior of measured slope angles is in accord with behavior of nonlinear p-y curves(Reese, Murchison and O'Neil, Matlock's p-y analysis), maximum displacement of pile head, maximum stress and maximum bending moment of pile obtained from the numerical analysis are shown. As results, maximum lateral displacement at pile head, maximum stress and maximum bending moment of pile are shown linear behavior, And maximum lateral load, maximum lateral displacement, and maximum bending moment at pile obtained from the numerical analysis are 8∼12.4tonf, 9∼10.1㎜, and 10.39∼12.67tonf-m per pile according to the curves, respectively.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.485-502
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• 2019

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.161-172
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• 2005

This paper presents the section model for analysis of RC circular tower structures based on nonlinear material laws. The governing equations for normal strains due to the bending moment and the normal force are derived in the case when openings are located symmetrically in respect to the bending direction. In this approach the additional reinforcement at openings is also taken into account. The mathematical model is expressed in the form of a set of nonlinear equations which are solved by means of the minimization of the sums of the second powers of the residuals. For minimization the BFGS quasi-Newton and/or Hooke-Jeeves local minimizers suitably modified are applied to take into account the box constraints on variables. The model is verified on the set of data encountered in engineering practice. The numerical examples illustrate the effects of the loading eccentricity and size of the opening on the strains and stresses in concrete and steel in the cross-sections under consideration. Calculated results indicate that the additional reinforcement at the openings increases the resistance capacity of the section by several percent.

• Computers and Concrete
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• v.10 no.5
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• pp.489-505
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• 2012

This paper presents a simplified grid beam model for simulating the nonlinear response of reinforced concrete flat-plate structures. The beam elements are defined with nonlinear behavior for bending moment and torsion. The flexural stiffness and torsional strength of the beam elements are defined based on experimental data to implicitly account for slab two-way bending effects. A failure criterion that considers the interaction between the punching strength and slab flexural behavior is incorporated in the model. The effects of bond-slip of slab reinforcement on connection stiffness are examined. The proposed grid beam model is validated by simulating large-scale tests of slab-column connections subjected to concentric gravity loading and unbalanced moment. This study also determines the critical parameters for a hysteretic model used to simulate flat-plates subjected to cyclic lateral loading.

• Wind and Structures
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• v.23 no.6
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• pp.485-503
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• 2016

To investigate the nonlinear aerostatic stability of the Hutong cable-stayed rail-cum-road bridge with ultra-kilometer main span, a FEM bridge model is established. The tri-component wind loads and geometric nonlinearity are taken into consideration and discussed for the influence of nonlinear parameters and factors on bridge resistant capacity of aerostatic instability. The results show that the effect of initial wind attack-angle is significant for the aerostatic stability analysis of the bridge. The geometric nonlinearities of the bridge are of considerable importance in the analysis, especially the effect of cable sag. The instable mechanism of the Hutong Bridge with a steel truss girder is the spatial combination of vertical bending and torsion with large lateral bending displacement. The design wind velocity is much lower than the static instability wind velocity, and the structural aerostatic resistance capacity can meet the requirement.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.7
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• pp.1119-1124
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• 2001

Nonlinear Vibration of a flexible circular ring is studied in this paper. Based upon the von Karman strain theory, the nonlinear governing equations are derived, in which the in-plane bending and extension displacements as well as the out-of-plane bending displacement are fully coupled. After discretizing the governing equations by the Galerkin approximation method, we obtain the linearlized equation by using the pertubation method. The results from the linearlized equations show that the in-plane displacement has effects on the natural frequencies of the out-of-plane displacement.

• Journal of the Korea Concrete Institute
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• v.11 no.4
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• pp.83-93
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• 1999

This paper presents tension stiffening effect of Reinforced concrete members obtained from experimental results on direct tension and bending. From the direct tension test program, crack patterns were investigated with tension softening behaviors of concrete. Tension stiffening effects and losses of strain energy were, also, analyzed from the load-deflection curve with the main experimental variables such as concrete strength, yielding stress and reinforcement ratio of rebar. Tension stiffening effect of RC members increase linearly until the first crack initiate, decrease inversely with number of cracks, and then decrease rapidly when splitting cracks are happened. The tension stiffening effect is shown to be more important at the member of lower reinforcement than that of higher. Therefore, it necessitates to consider the tension stiffening effects at a nonlinear analysis. From the above analysis, a tension stiffening model of concrete is proposed and verified by applying it to bending members. From the numerical analysis by finite element approach, it is shown that the proposed model evaluates a little higher in analyzing at nonlinear region of high strength concrete, but, perform satisfactorily in general.