• Structural Engineering and Mechanics
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• 제59권3호
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• pp.579-599
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• 2016

In this study, static bending of edge cracked micro beams is studied analytically under uniformly distributed transverse loading based on modified couple stress theory. The cracked beam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-beams connected through a massless elastic rotational spring. The deflection curve expressions of the edge cracked microbeam segments separated by the rotational spring are determined by the Integration method. The elastic curve functions of the edge cracked micro beams are obtained in explicit form for cantilever and simply supported beams. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the elastic deflections of the edge cracked micro beams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and some typical boundary conditions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked microbeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• 항공우주시스템공학회지
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• 제11권5호
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• pp.13-19
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• 2017

본 연구에서는 굽힘 하중을 받는 복합재료 적층판의 파손 해석을 위하여 2D 변형률 기반 파손 이론을 적용하였다. 복합재료 적층판의 비선형 기계적 거동을 모사하기 위하여, 선형 증분 접근 방식을 적용하고 단위 길이 적층판에 대한 점진적 파손 해석을 수행하였다. 크로스플라이 및 준등방성 적층 패턴에 대하여 3점 굽힘 시험을 수행하고 해석 결과와 비교 검증하였다.

• Steel and Composite Structures
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• 제21권6호
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• pp.1347-1368
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• 2016

In this article, an exact analytical solution for mechanical buckling analysis of symmetrically cross-ply laminated plates including curvature effects is presented. The equilibrium equations are derived according to the refined nth-order shear deformation theory. The present refined nth-order shear deformation theory is based on assumption that the in-plane and 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 parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Buckling of orthotropic laminates subjected to biaxial inplane is investigated. Using the Navier solution method, the differential equations have been solved analytically and the critical buckling loads presented in closed-form solutions. The sensitivity of critical buckling loads to the effects of curvature terms and other factors has been examined. The analysis is validated by comparing results with those in the literature.

• Advances in nano research
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• 제9권3호
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• pp.183-191
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• 2020

The content of this study focuses on bending of flexoelectric Magneto-Electro-Elastic (MEE) nanobeams inserted within the foundation of Winkler-Pasternak according to nonlocal elasticity theory. Applying Hamilton's principle, the nonlocal nanobeams' governing equations in the framework higher order refined beam theory are attained and resolved through adapting an analytical solution. A parametric research is demonstrated for studying the effects that magneto-electro-mechanical loadings, the nonlocal parameter, flexoelectric, as well as the aspect ratio all have on the deflection properties of nanobeams. A discovery lead to beam geometrical parameters, the boundary conditions, flexoelectricity and nonlocal parameter partake substantial effects on nanoscale beams' dimensionless deflection.

• Advances in nano research
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• 제8권3호
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• pp.203-214
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• 2020

This paper investigated bending of magneto-electro-elastic (MEE) nanobeams under hygro-thermal loading embedded in Winkler-Pasternak foundation based on nonlocal elasticity theory. The governing equations of nonlocal nanobeams in the framework parabolic third order beam theory are obtained using Hamilton's principle and solved implementing an analytical solution. A parametric study is presented to examine the effect of the nonlocal parameter, hygro-thermal-loadings, magneto-electro-mechanical loadings and aspect ratio on the deflection characteristics of nanobeams. It is found that boundary conditions, nonlocal parameter and beam geometrical parameters have significant effects on dimensionless deflection of nanoscale beams.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2000년도 춘계학술대회논문집 - 한국공작기계학회
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• pp.88-94
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• 2000

A winding bend rig for measurement of springback ratio is made. It measures the bending angles before and after release of bending load which bends specimens with keeping a constant curvature. Thus the springback ratio can be obtained by using this bend rig. Analytical explanations for the spring back are tried by employing simple beam theory. For the analytical calculations with the theory, Young's modulus, fracture strain and stress-strain curve are necessary and these data are obtained from a tensile test. Using both of the beam theory and the results of tensile test, the springback ratio is also calculated. Comparisons of the two springback ratios, one is obtained from bending test and the other from tensile test, show a good agreement.

• Smart Structures and Systems
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• 제17권2호
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• pp.257-274
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• 2016

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.105-119
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• 2020

In this work, a novel higher-order shear deformation theory (HSDT) for static and free vibration analysis of functionally graded (FG) plates is proposed. Unlike the conventional HSDTs, the proposed theory has a novel displacement field which includes undetermined integral terms and contains fewer unknowns. Equations of motion are obtained by using Hamilton's principle. Analytical solutions for the bending and dynamic investigation are determined for simply supported FG plates. The computed results are compared with 3D and quasi-3D solutions and those provided by other plate theories. Numerical results demonstrate that the proposed HSDT can achieve the same accuracy of the conventional HSDTs which have more number of variables.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.755-769
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• 2015

In this study, a 2-D finite element formulation in the frame of nonlocal integral elasticity is presented. Subsequently, the bending problem of a nanobeam under different types of loadings and boundary conditions is solved based on classical beam theory and also 3-D elasticity theory using nonlocal finite elements (NL-FEM). The obtained results are compared with the analytical and numerical results of nonlocal differential elasticity. It is concluded that the classical beam theory and the nonlocal differential elasticity can separately lead to significant errors for the problem under consideration as distinct from 3-D elasticity and nonlocal integral elasticity respectively.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.145-153
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• 2019

Modified couple stress formulation and first order shear deformation theory are used for magneto-electro-elastic bending analysis of three-layered curved size-dependent beam subjected to mechanical, magnetic and electrical loads. The governing equations are derived using a displacement field including radial and transverse displacements of middle surface and a rotation component. Size dependency is accounted based on modified couple stress theory by employing a small scale parameter. The numerical results are presented to study the influence of small scale parameter, initial electric and magnetic potentials and opening angle on the magneto-electro-elastic bending results of curved micro beam.