• 한국생산제조학회지
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• 제22권5호
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• pp.852-858
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• 2013

In numerical control (NC) machining, a machining error in equipment generally occurs for a variety of reasons. If there is a change in direction in the NC code, the characteristics of the automatic acceleration or deceleration function cause an overlap of each axis of the acceleration and deceleration zones, which in turn causes a shift in the actual processing path. Many studies have been conducted for error calibration of the edge as caused by automatic acceleration or deceleration in NC machining. This paper describes a geometric interpretation of the shape and processing characteristics of the operating NC device. The paper then describes a way to determine a feedrate that achieves the desired tolerance by using linear and parabolic profiles. Experiments were conducted by the validate equations using a three-axis NC machine. The results show that the machining errors were smaller than the machine resolution. The results also clearly demonstrate that the NC machine with the developed system can successfully predict machining errors induced with a change in direction.

• Structural Engineering and Mechanics
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• 제73권2호
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• pp.109-121
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• 2020

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

• Steel and Composite Structures
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• 재36권6호
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• pp.643-656
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• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

• Smart Structures and Systems
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• 제20권4호
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• pp.509-524
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• 2017

In this article, a free vibration analysis of functionally graded (FG) plates resting on elastic foundations is presented using a quasi-3D hybrid-type higher order shear deformation theory. Undetermined integral terms are employed in the proposed displacement field and modeled based on a hybrid-type (sinusoidal and parabolic) quasi-3D HSDT with five unknowns in which the stretching effect is taken into account. Thus, it can be said that the significant feature of this theory is that it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameter) mathematical model. Equations of motion are obtained via the Hamilton's principles and solved using Navier's method. Accuracy of the proposed theory is confirmed by comparing the results of numerical examples with the ones available in literature.

• 대한치과교정학회지
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• 제19권1호
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• pp.95-106
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• 1989

이 연구는 bracket이 붙여지는 위치에서의 이상적인 협측 및 설측 치열궁 형태를 그려내기 위하여 $17\~26$세까지의 정상교합자 63명의 상하악 모헝을 채득하여 계측점과 설정, 통계처리하여 다음과 같은 결과를 얻었다. 치열궁 형태를 나타내는 선계측 항목에서 Bicanine width, Bipremolar width, Bimolar width에서 남자가 여자보다 더 크게 나타났다. NEC 9801 V-M computer를 이용한 graphic 입력을 분석하여 협설측 치열궁 형태를 구하였다. 협측 및 설측 치열궁 형태를 나타내는 포물선식의 상수와 결정계수를 구하였다.

• 소음진동
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• 제10권2호
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• pp.353-360
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• 2000

Numerical methods are developed for calculating the natural frequencies and mode shapes of the tapered cantilever arches with variable curvature. The differential equations governing the free vibrations of such arches are derived and solved numerically, in which the effect of rotatory inertia is included. The parabolic shape is chosen as the arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch. Comparisons the natural jfrequencies between this study and finite element method SAP 90 seve to validate the numerical method developed herein. The lowest four natural frequencies are reported as a function of four non-dimensional system parameters. The effects of both the rotatory inertia and cross-sectional shape are reported. Also, the typical mode shapes of stress resultants as well as the displacements are reported.

• Steel and Composite Structures
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• 제15권4호
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• pp.399-423
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• 2013

In the present study, the thermal buckling behavior of functionally graded sandwich plates is studied using a new hyperbolic displacement model. Unlike any other theory, the theory is variationally consistent and gives four governing equations. Number of unknown functions involved in displacement field is only four, as against five in case of other shear deformation theories. This present model takes into account the parabolic distribution of transverse shear stresses and satisfies the condition of zero shear stresses on the top and bottom surfaces without using shear correction factor. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates.

• Steel and Composite Structures
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• 제26권4호
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• pp.387-405
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• 2018

A novel higher shear deformation theory (HSDT) is proposed for the bending, buckling and free vibration investigations of isotropic and functionally graded (FG) sandwich plates. It contains only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The model accounts for a parabolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral terms. Equations of motion determined in this work are applied for three types of FG structures: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Analytical solutions are given to predict the transverse displacements, stresses, critical buckling forces and natural frequencies of simply supported plates and a comparison study is carried out to demonstrate the accuracy of the proposed model.

• Smart Structures and Systems
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• 제22권1호
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• pp.121-132
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• 2018

This research investigates the free vibration analysis of advanced composite plates such as functionally graded plates (FGPs) resting on a two-parameter elastic foundations using a hybrid quasi-3D (trigonometric as well as polynomial) higher-order shear deformation theory (HSDT). This present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by a sinusoidal and parabolic variation of all displacements across the thickness. Governing equations of motion for FGM plates are derived from Hamilton's principle. The closed form solutions are obtained by using Navier technique, and natural frequencies are found, for simply supported plates, by solving the results of eigenvalue problems. The accuracy of the present method is verified by comparing the obtained results with First-order shear deformation theory, and other predicted by quasi-3D higher-order shear deformation theories. It can be concluded that the proposed theory is efficient and simple in predicting the natural frequencies of functionally graded plates on elastic foundations.

• International Journal of Aeronautical and Space Sciences
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• 제18권2호
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.