• Steel and Composite Structures
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• v.33 no.2
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• pp.307-318
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• 2019

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.888-895
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• 2006

In this study, anisotropically consolidated undrained shear(CAU) test was performed to examine the variation of the shear strength according to the stress history. The specimen having 30% relative density was homogeniously prepared, and 200KPa of back pressure was applied to increase the B value more than 0.95. To make NC specimens, the vertical stress was applied on the specimen by 100KPa, 200KPa and 400KPa, and to make OC specimens, the vertical stress was applied upto 400KPa and was reduced to 200KPa and 100KPa resulting in OCR 2 and 4 respectively. The test result indicates the shear strength for the OC specimens are slightly higher then that of the NC specimens at the same confining pressure. The elastic modulus varies according to the confining stress and considerably affected by preconsolidation stress.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.63-74
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• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.527-544
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• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.607-622
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• 1999

Being a significant mode of deformation, shear effect in addition to the other modes of stretching and bending have been considered to develop two finite element models for the analysis of beams on elastic foundation. The first beam model is developed utilizing the differential-equation approach; in which the complex variables obtained from the solution of the differential equations are used as interpolation functions for the displacement field in this beam element. A single element is sufficient to exactly represent a continuous part of a beam on Winkler foundation for cases involving end-loadings, thus providing a benchmark solution to validate the other model developed. The second beam model is developed utilizing the hybrid-mixed formulation, i.e., Hellinger-Reissner variational principle; in which both displacement and stress fields for the beam as well as the foundation are approxmated separately in order to eliminate the well-known phenomenon of shear locking, as well as the newly-identified problem of "foundation-locking" that can arise in cases involving foundations with extreme rigidities. This latter model is versatile and indented for utilization in general applications; i.e., for thin-thick beams, general loadings, and a wide variation of the underlying foundation rigidity with respect to beam stiffness. A set of numerical examples are given to demonstrate and assess the performance of the developed beam models in practical applications involving shear deformation effect.

• Computational Structural Engineering
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• v.8 no.1
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• pp.137-146
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• 1995

Structural stress under shock or impact load is varied with the lapse of time and the structural stress is called stress wave. Propagating longitudinal stress wave is studied in a 2-dimensional plate. A finite element program for elastic stress wave propagation is developed in order to investigate the shape of stress field at time increment. The longitudinal stress wave is generated by unit step function. According to the finite element analysis results, the longitudinal stress wave propagates to the similar direction of impact load and the front of stress wave propagates with the same speed as analytic solution and the shape of stress field is similar to that of analytic solution. The shear wave is occurred after the longitudinal stress wave and declined at an angle of 45 degrees compared with longitudinal stress wave and the speed of shear wave is about a half of the longitudinal stress wave. The intensity of shear wave is larger than that of longitudinal stress wave.

• Computers and Concrete
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• v.32 no.5
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• pp.439-454
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• 2023

In this article, the surface stress effects on the buckling analysis of the annular sandwich plate is developed. The proposed plate is composed of two face layers made of carbon nanotubes (CNT) reinforced composite with assuming of fully bonded to functionally graded porous core. The generalized rule of the mixture is employed to predict the mechanical properties of the microcomposite sandwich plate. The derived potentials energy based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST) is solved by employing the Ritz method. An exact analytical solution is presented to calculate the critical buckling loads of the annular sandwich plate. The predicted results are validated by carrying out the comparison studies for the buckling analysis of annular plates with those obtained by other analytical and finite element methods. The effects of various parameters such as material length scale parameter, core thickness to total thickness ratio (hc/h), surface elastic constants based on surface stress effect, various boundary condition and porosity distributions, size of the internal pores (e0), Skempton coefficient and elastic foundation on the critical buckling load have been studied. The results can be served as benchmark data for future works and also in the design of materials science, injunction high-pressure micropipe connections, nanotechnology, and smart systems.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.10a
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• pp.295-300
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• 2003

In discontinuous composite mechanics, shear lag theory is one of the most popular model because of its simplicity and accuracy. However, it does not provide sufficiently accurate strengthening predictions in elastic regime when the fiber aspect ratio is small. This is due to its neglect of stress transfer across the fiber ends and the stress concentrations that exist in the matrix regions near the fiber ends. To overcome this shortcoming, a more simplified shear lag model introducing the stress concentration factor which is a major function of modulus ratio is proposed. It is found that the proposed model gives a good agreement with finite element results and has the capability to correctly predict the values of intefacial shear stresses and local stress variations in the small fiber aspect ratio regime.

• Steel and Composite Structures
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• v.47 no.5
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

• Journal of Mechanical Science and Technology
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• v.15 no.1
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• pp.61-65
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• 2001

Using the theory of linear piezoelectricity, the problem of two layered strip with a piezoelectric ceramic bonded to an elastic material containing a finite interface crack is considered. The out-of-plane mechanical and in-plane electrical loadings are simultaneously applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The stress intensity factor is determined, and numerical analyses for several materials are performed and discussed.