• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.615-632
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• 2018

Mechanical buckling of a rectangular functionally graded plate is obtained in the current paper using a refined higher-order shear and normal deformation theory. The impact of transverse normal strain is considered. The material properties are microscopically inhomogeneous and vary continuously based on a power law form in spatial direction. Navier's procedure is applied to examine the mechanical buckling behavior of a simply supported FG plate. The mechanical critical buckling subjected to uniaxial and biaxial compression loads are determined. The numerical investigation are compared with the numerical results in the literature. The influences of geometric parameters, power law index and different loading conditions on the critical buckling are studied.

• Structural Engineering and Mechanics
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• 제89권3호
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• pp.225-238
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• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• Computers and Concrete
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• 제15권3호
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• pp.337-355
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• 2015

In this scientific work, an improved analytical solution for adhesive stresses in a concrete beam bonded with the FRP plate is developed by including the effect of the adherend shear deformations. The analysis is based on the deformation compatibility approach where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The shear stress distribution is supposed to be parabolic across the depth of the adherends in computing the adhesive shear stress and Timoshenko's beam theory is employed in predicting adhesive normal stress to consider the shear deformation. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of adhesive stress distributions.

• Advances in aircraft and spacecraft science
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• 제10권3호
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• pp.281-302
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• 2023

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.

• Restorative Dentistry and Endodontics
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• 제26권5호
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• pp.418-435
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• 2001

Root canal preparation process is of utmost importance in successful treatment of root canal. Also, one of the most important purpose of the root canal preparation is to enlarge the root canal three dimensionally without changing the curvature of the root canal However as the curvature of the root canal increases, there are many difficulties involved in formation of optimum root canal. Therefore in order to solve the above mentioned problems, new developments in methods of root canal preparation and equipments for such purposes were made. Recently, vigorous studies about newly introduced engine-driven nickel-ti-tanium rotary file are conducted. As shown in research results to dates, it is well established that the use of nickel-titanium file is better suited for curved root canal than stainless steel file in maintaining the curvature or root canal and reducing the deformation of root canal. However it is also acknowledged that there are a few discrepancies in research results according to protocol, due to failure to remove variables in experiments. In addition, although it is recommended by the manufacturer that the GT rotary file should maintain a low rotational speed of 150~350rpm and 'light pressure' as light as not to break the lead of a pencil, academic studies about the vertical force which is not yet standardized are not sufficiently explored. Therefore, this research devised and utilized a special research equipment to standardize the appropriate range of vertical force for GT rotary file through experiments by breaking of the lead of a pencil as expressed by the manufacturer and to accurately measure factors involved through repeating and recreating the environment of root canal preparation. Forming nine experimental groups by varying the vertical forces (150g. 220g, 300g) and rpm (150rpm, 250rpm, 350rpm), the effects of changing vertical forces and rpm on working efficiency were measured in terms of time expended in root canal preparation by crown-down method using a transparent resin block with 35 degree curvature and GT rotary file (z-test). The following research using this special research equipment that involved nine experimental groups and varying the vertical force for root canal preparation from 300g which is within the normal vertical force range to 700g and 1000g which fall outside the normal rpm range. The results were as follows : 1. Analysis of the experiment results revealed that the time spent in root canal preparation decreased as the vertical forces and rpm increased (p<0.05). Also, the effects of rpm were greater than those of the vertical forces within the normal vertical force range ($\beta$-weight test). 2. Observation of the deformation of GT rotary file revealed that deformation increases in a direct correlation with the vertical force increase and in a reverse correlation with the rpm decrease. In the case of the vertical forces close to the normal range, the probability of GT rotary file deformation were quite different depending on the rpm changes. In the case of greater vertical forces, the occurrences of deformation of the file were more frequent regardless of the rpm changes. 3. Deformation and breakage of file were also commonly observed in the expended time measurement experiments and GT rotary file deformation experiments in which low speed rpm (150rpm) was used and at the curved portion of the resin block.

• Tunnel and Underground Space
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• 제4권3호
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• pp.274-286
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• 1994

Direct shear tests were on ducted in a laboratory setting in order to investigate the shear strength and deformation behavior of rock joints. Also, the characteristics of acoustic emissions (AE) during shearing of rock joints were studied. The artificial rock joints were created by splitting the intact blocks of Hwangdeung granites and Iksan marbles. Joint roughness profiles were measured by a profile gage and then digitized by Image analyzer. Roughness profile indices(Rp) of the joints were calculated with these digitized data. Peak shear strength, residual shear strength, shear stiffness and maximum acoustic emission(AE) rate were investigated with joint roughness. The peak shear strenght, the residual shear strength and the shear stiffness were increased as roughness popfile index or normal stress increased in the shear tests of granites. In the tests of marble samples, the shear deformation characteristics were not directly affected by joint roughness. As the result of two directional shear tests, the shear characteristics were varied with shear direction. AE count rates were measured during the shear deformation and the AE signals in several stages of the deformation were analyzed in a frequency domain. The AE rate peaks coincided with the stress drops during the shear deformation of joint. The dominant frequencies of the AE signals were in the vicinity of 100 kHz fo rgranite sample and 900 kHz for marble samples. The distribution of amplitude was dispersed with increasing normal stress.

• Journal of the Computational Structural Engineering Institute of Korea
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• 제25권6호
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• pp.505-512
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• 2012

In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.

• Steel and Composite Structures
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• 제34권5호
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• pp.657-670
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• 2020

In this paper, vibration analysis of functionally graded nanoshell is studied based on the sinusoidal higher-order shear and normal deformation theory to account thickness stretching effect. To account size-dependency, Eringen nonlocal elasticity theory is used. For more accurate modeling the problem and corresponding numerical results, sinusoidal higher-order shear and normal deformation theory including out of plane normal strain is employed in this paper. The radial displacement is decomposed into three terms to show variation along the thickness direction. Governing differential equations of motion are derived using Hamilton's principle. It is assumed that the cylindrical shell is made of an arbitrary composition of metal and ceramic in which the local material properties are measured based on power law distribution. To justify trueness and necessity of this work, a comprehensive comparison with some lower order and lower dimension works and also some 3D works is presented. After presentation of comparative study, full numerical results are presented in terms of significant parameters of the problem such as small scale parameter, length to radius ratio, thickness to radius ratio, and number of modes.

• Transactions of the Korean Society of Automotive Engineers
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• 제8권2호
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• pp.110-119
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• 2000

In this study, we considered the method evaluation the flexibility of joint area including member with circular section. We regarded the flexibility of joint area as translational and rotational springs for the purpose of expressing local deformation. We verified this method by the use of normal mode analysis. We also calculated this joint area occurring in penetration so as to apply this method to other cases. Compare with the shell element model. we can the considerably approximate values.

• Steel and Composite Structures
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• 제4권1호
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• pp.1-8
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• 2004

Tests on steel tubular columns of square, rectangular and circular section filled with normal and lightweight aggregate concrete were conducted to investigate the failure modes of such composite columns. Thirty-six full scale columns filled with lightweight and normal weight aggregate concrete, eighteen specimens for each, were tested under axial loads. Nine hollow steel sections of similar specimens were also tested and results were compared to those of filled sections. The test results were illustrated by a number of load-deflection and axial deformation curves. The results showed that both types of filled columns failed due to overall buckling, while hollow steel columns failed due to bulging at their ends (local buckling). According to the above-mentioned results, and due to low specific gravity and thermal conductivity of the lightweight concrete the further interest should be concentrated in replacing the normal concrete by the lightweight aggregate concrete.