• Steel and Composite Structures
• /
• 제33권1호
• /
• pp.133-142
• /
• 2019

In the present study, microstructure-dependent static stability analysis of inhomogeneous tapered micro-columns is performed. It is considered that the micro column is made of functionally graded materials and has a variable cross-section. The material and geometrical properties of micro column vary continuously throughout the axial direction. Euler-Bernoulli beam and modified couple stress theories are used to model the nonhomogeneous micro column with variable cross section. Rayleigh-Ritz solution method is implemented to obtain the critical buckling loads for various parameters. A detailed parametric study is performed to examine the influences of taper ratio, material gradation, length scale parameter, and boundary conditions. The validity of the present results is demonstrated by comparing them with some related results available in the literature. It can be emphasized that the size-dependency on the critical buckling loads is more prominent for bigger length scale parameter-to-thickness ratio and changes in the material gradation and taper ratio affect significantly the values of critical buckling loads.

• Steel and Composite Structures
• /
• 제47권6호
• /
• pp.795-811
• /
• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• 한국환경과학회지
• /
• 제18권2호
• /
• pp.221-230
• /
• 2009

In this study, a river basin with a lot of measured data such as water level, flow rate, current speed, and sediment rate from the past to now was selected and geometrical shape of a pier was re-analyzed, in order to study the effects of the flow around the pier area as well as the riverbed alternation characteristics. A finite element mesh of the entire river was prepared, and via parameter revision, the section that the pier has influence on was decided, to analyze the shape of the pier using RMA-2 and SED2D-WES models. With regards to the section that the pier has influence on, analysis was done on the four pier shapes, namely circle, square, rectangle, and octagon. The results showed that the shape with the least influence around the pier around is the octagon, followed by circle, rectangle, and square, showing the different geometrical effects that the shapes have on the pier. Furthermore, it was shown that the distribution of sediment concentration had effect from about (+) 110 m of the upstream to about (-) 130 m of the downstream, from the pier installation point. Also, it was shown after analyzing drag forces for different sediment particle distributions that the shape with the greatest drag is the octagon, followed by circle, square, and rectangle.

• 대한기계학회논문집A
• /
• 제33권11호
• /
• pp.1202-1208
• /
• 2009

An inverse finite element (FE) model parameter estimation algorithm can be used to characterize mechanical properties of biological tissues. Using this algorithm, we can consider the influence of material nonlinearity, contact mechanics, complex boundary conditions, and geometrical constraints in the modeling. In this study, biomechanical experiments on macro and micro samples are conducted and characterized with the developed algorithm. Macro scale experiments were performed to measure the force response of porcine livers against mechanical loadings using one-dimensional indentation device. The force response of the human liver cancer cells was also measured by the atomic force microscope (AFM). The mechanical behavior of porcine livers (macro) and human liver cancer cells (micro) were characterized with the algorithm via hyperelastic and linear viscoelastic models. The developed models are suitable for computing accurate reaction force on tools and deformation of biomechanical tissues.

• Structural Engineering and Mechanics
• /
• 제52권4호
• /
• pp.663-686
• /
• 2014

This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 2005년도 추계학술대회 논문집
• /
• pp.87-90
• /
• 2005

The drawbead is used to control the material flow into the die and increase the forming quality during the binder wrap process and the stamping process in the sheet metal forming. Drawbead restraining force (DBRF) is controlled by geometrical parameters and influenced by process parameters such as friction coefficient and blank thickness. In order to inspect the effect of process parameters, parameter studies are performed with the variation of parameters using finite element model of drawbead which is utilized reliably for the calculation of the drawbead restraining force. Drawbead analysis is carried out with 2-D plane-strain element and 3-D shell element. After the verification of the accuracy of the drawbead model with 3-D shell element, it is utilized to the prediction and the investigation of the effect of process parameters. The result of parameter studies can be utilized to the die design in the tryout stage.

• Steel and Composite Structures
• /
• 제24권6호
• /
• pp.711-726
• /
• 2017

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.

• Steel and Composite Structures
• /
• 제33권2호
• /
• pp.307-318
• /
• 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.

• Advances in nano research
• /
• 제16권2호
• /
• pp.187-200
• /
• 2024

This study focuses on wave propagation analysis in the curved nanobeam exposed to different thermal loadings based on the Nonlocal Strain Gradient Theory (NSGT). Mechanical properties of the constitutive materials are assumed to be temperature-dependent and functionally graded. For modeling, the governing equations are derived using Hamilton's principle. Using the proposed model, the effects of small-scale, geometrical, and thermo-mechanical parameters on the dynamic behavior of the curved nanobeam are studied. A small-scale parameter, Z, is taken into account that collectively represents the strain gradient and the nonlocal parameters. When Z<1 or Z>1, the phase velocity decreases/increases, and the stiffness-softening/hardening phenomenon occurs in the curved nanobeam. Accordingly, the phase velocity depends more on the strain gradient parameter rather than the nonlocal parameter. As the arc angle increases, more variations in the phase velocity emerge in small wavenumbers. Furthermore, an increase of ∆T causes a decrease in the phase velocity, mostly in the case of uniform temperature rise rather than heat conduction. For verification, the results are compared with those available for the straight nanobeam in the previous studies. It is believed that the findings will be helpful for different applications of curved nanostructures used in nano-devices.

• Structural Engineering and Mechanics
• /
• 제48권6호
• /
• pp.849-878
• /
• 2013

This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.