• Geomechanics and Engineering
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• v.14 no.6
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.3
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• pp.21-28
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• 2015

As film products are increasingly used in a wide range of areas, from producing traditional flexible packaging to high-tech electronic products, a higher level of quality is demanded. Most film products are made in the form of rolled finished goods, therefore, various quality issues related to their shape characteristics must be addressed. The thickness of the film products is one of the most common and important critical-to-quality attributes (CTQs). Particularly, the degree of thickness uniformity is more important than other thickness parameters, because it will be potential causes of many secondary thickness-related quality problems, such as wrinkles or faulty windings. To control the degree of thickness uniformity, the fixed bending region is oneof the most important CTQs to manage. Fixed bending regions are special points in the transverse direction of a rolled product with consistent minute variations of the thickness gap. This paper describes the measurement and analysis of thickness uniformity data, which were performed in a real manufacturing field of biaxial oriented polypropylene (BOPP) film. In previous researches, quality function deployment (QFD) or fault tree analysis were used to find the most critical process attributes out to controlthe CTQ of thickness uniformity. Whereas, this paper uses traditional control charts to find the most critical process attributes out in this problem. In addition, the selection of one of the major critical process attributes (CTPs) that is expected to affect the CTQ of thickness uniformity is also described. The selected critical-to-process attributes are the controlled temperatures along the transverse direction. A dramatic improvement in thickness uniformity was observed when the selected CTPs were controlled.

• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed 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, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Steel and Composite Structures
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• v.22 no.2
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• pp.257-276
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• 2016

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Smart Structures and Systems
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• v.26 no.2
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• pp.253-262
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• 2020

In this paper, a new higher order shear deformation model is developed for static analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. The model account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG beam. Based on the present higher-order shear deformation model, the equations of motion are derived by the principle of virtual works. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, and geometry on the bending of imperfect FG beams. It can be concluded that the proposed model is simple and precise for the resolution of the behavior of flexural FGM beams while taking into account the shape of distribution of the porosity.

• Journal of the Korean Society of Safety
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• v.20 no.1 s.69
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• pp.75-80
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• 2005

In this paper, when CF/EPOXY laminates for high efficiency space structure are subjected to FOD(Foreign Object Damage), the effects of temperature change on the impact damages(inter laminar separation and transverse crack) of CF/EPOXY laminates and the relationship between residual life and impact damages ale experimentally investigated. Composite laminates used in this experiment are CF/EPOXY orthotropic laminated plates, which have two-interfaces $[0^{\circ}_6/90^{\circ}_6]S$ and four-interfaces $[0^{\circ}_3/90^{\circ}_6/0^{\circ}_3]S$. CF/EPOXY specimens with impact damages caused by a steel ball launched from the air gun were observed by the scanning acoustic microscope under room and high temperatures. In this experimental results, various relations were experimentally observed including the delamination area vs. temperature change, the bending strength vs. impact energy and the residual bending strength vs. impact damage of CF/EPOXY laminates. And as the temperature of CF/PEEK laminates increases, the delaminaion areas of impact-induced damages decrease linearly. A linear relationship between the impact energy and the delamination areas were observed. As the temperature of CF/PEEK laminates increases, the delamination areas decrease because of higher initial delaminatin damage energy.

• Smart Structures and Systems
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• v.14 no.2
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• pp.71-83
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• 2014

The purpose of this paper is to investigate the flexible structure of parabolic shell using photostrictive actuators. The analysis is made to know its dynamic behavior and light-induced control forces for coupled parabolic shell. The effects of an actuator location as well as membrane and bending components under the control action have been analyzed considering the approximate spherical model. The parabolic membrane shell accuracy is being mathematically approximated and validated comparing the light induced control forces using approximate equivalent spherical shell model. The parabolic shell with kapton smart material and photostrictive actuators has been used to formulate the governing equation in the transverse direction. The Kirchhoff-Love assumptions are used to obtain the governing equation of shell with actuator. The mechanical membrane forces and bending moments for parabolic thin shell with actuator is used to analyze the dynamic effect. The results show that membrane control action is much more significant than bending control action. Photostrictive actuators oriented along circumferential direction (actuator-2) can give better control effect than actuators placed along longitudinal direction (actuator-1). The slight difference is observed between spherical and parabolic shell for a surface with focal length to the diameter ratio of 1.00 or more than unity. Space applications often have the shape of parabolical shells or shell of revolution, due to their required focusing, aiming, or reflecting performance. The present approach is focused that photostrictive actuators can effectively control the vibration of parabolical membrane shell. Also, the actuator's location plays an important role in defining the control force.

• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.439-453
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• 2021

In this work, quasi three-dimensional (quasi-3D) shear deformation theory is presented for bending and dynamic analysis of functionally graded (FG) plates. The effect of varying material properties and volume fraction of the constituent on dynamic and bending behavior of the FG plate is discussed. The benefit of this model over other contributions is that a number of variables is diminished. The developed model considers nonlinear displacements through the thickness and ensures the free boundary conditions at top and bottom faces of the plate without using any shear correction factors. The basic equations that account for the effects of transverse and normal shear stresses are derived from Hamilton's principle. The analytical solutions are determined via the Navier procedure. The accuracy of the proposed formulation is proved by comparisons with the different 2D, 3D and quasi-3D solutions found in the literature.

• Steel and Composite Structures
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• v.43 no.6
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• pp.707-723
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• 2022

This article aims to investigate the size dependent bending behavior of perforated nanobeams incorporating the nonlocal and the microstructure effects based on the nonlocal strain gradient elasticity theory (NSGET). Shear deformation effect due to cutout process is studied by using Timoshenko beams theory. Closed formulas for the equivalent geometrical characteristics of regularly squared cutout shape are derived. The governing equations of motion considering the nonlocal and microstructure effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Analytical solution for the governing equations of motion is derived. The derived non-classical analytical solutions are verified by comparing the obtained results with the available results in the literature and good agreement is observed. Numerical results are obtained and discussed. Parametric studies are conducted to explore effects of perforation characteristics, the nonclassical material parameters, beam slenderness ratio as well as the boundary and loading conditions on the non-classical transverse bending behavior of cutout nanobeams. Results obtained are supportive for the design, analysis and manufacturing of such nanosized structural system.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.233-246
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• 2023

Bending and buckling analysis of multi-directional porous functionally graded sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. The principle of virtual displacements was employed and the solution was obtained using Navier's technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The validation of the present study has been performed with those available in the literature. The composition of metal-ceramic-based FGM changes in longitudinal and transverse directions according to the power law. Different porosity laws, such as uniform distribution, unevenly and logarithmically uneven distributions were used to mimic the imperfections in the functionally graded material that were introduced during the fabrication process. Several sandwich plates schemes were studied based on the plate's symmetry and the thickness of each layer. The effects of grading parameters and porosity laws on the bending and buckling of sandwich plates were examined.