• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.3207-3215
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• 2012

In this paper, we study the bending and free vibration analysis of nano plate, using a nonlocal elasticity theory of Eringen with a third-order shear deformation theory. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and vibration of a laminated composite nano plate are presented using this theory to illustrate the effect of nonlocal theory on deflection of the nano plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) nonlocal parameters, (ii) laminate schemes, (iii) directions of the fiber angle and (iv) number of layers on nondimensional deflections are investigated. In order to validate the present solutions, the reference solutions are used and discussed. The results of anisotropic nano plates using the nonlocal theory may be the benchmark test for the bending analysis.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.95-100
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• 2008

A 4-node assumed strain finite element based on higher order shear deformation theory is developed to investigate the behaviours of symmetric and unsymmetric laminated composite plates. The present element is based on Reddy's higher order shear deformation theory so that it can consider the parabolic distribution of shear deformation through plate thickness direction. In particular, assumed strain method is adopted to alleviate the shear locking phenomena inherited plate elements based on higher order shear deformation theory. The present finite element has seven degrees of freedom per node and denoted as HSA4. Numerical examples are carried out for symmetric and unsymmetric laminated composite plate with various thickness values. Numerical results are compared with reference solutions produced by other higher order shear deformation theories.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.481-488
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• 1988

In the analysis of impulsive response of plate, Lagrange's theory, Reissner's theory and Mindlin's theory are generally used. But, in applying these theories the impulsive stresses directly underneath the concentrated impact point cannot be analyzed because the solution fails to converge. In this paper, therefore, an attempt for a supported square plate is made by using three-dimensional dynamic theory of elasticity on the supposition that the uniform distributed load acts on the central part of it. In order to clarify the validity of theoretical analysis, the strain variations are measured experimentally for a square glass plate. Finally it is shown that these theoretical results are in close agreement with the experimental results.

• Journal of Korean Association for Spatial Structures
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• v.5 no.3 s.17
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• pp.65-74
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• 2005

An analytical model was developed to investigate the flexural behavior of a pultruded fiber-reinforced plastic deck of rectangular unit module. The model is based on first-order shea. deformable plate theory (FSDT), and capable of predicting deflection of the deck of arbitrary laminate stacking sequences. To formulate tile problem, two-dimensional plate finite element method is employed. Numerical results are obtained for FRP decks under uniformly-distributed loading, addressing the effects of fiber angle and span-to-height ratio. It is found that the present analytical model is accurate and efficient for solving flexural behavior of FRP decks. Also, as the height of FRP deck plate is higher, the necessity of higher order Shear deformable plate theory(HSDT) is announced, not the FSDT in the plate analysis theory.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.3
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• pp.35-40
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• 2010

The specially orthotropic plate theory is used for analysis of panels made of girders and cross-beams. The cross-sections of both girders and cross-beams are H-types. The results of application of this method to rolled beam bridge by using specially orthotropic plate theory is presented. The result is compared with that of the beam theory. Finite difference method is used for this purpose. The influence of the $D_{22}$ stiffness on the natural frequency is rigorously investigated. According to numerical examination given in this paper, the result by the plate theory is 2.43 times stiffer than that of beam theory.

• Proceedings of the Korean Society of Disaster Information Conference
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• 2015.11a
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• pp.150-151
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• 2015

본 연구에서는 충격 문제를 거론하며 Mindlin 판 이론을 확장한 1차 전단 변형 이론에 근거하여 충격 하중을 받는 임의의 형상 라미네이트 응답 특성의 해명을 목적으로 아이소파라메트릭요소에 의한 정식화를 시도한다.

• Journal of the Society of Disaster Information
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• v.12 no.1
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• pp.62-68
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• 2016

In this study, the impact problems are brought up and the formulation by isoparametric element is attempted for the purpose of analyzing the response characteristics of laminated plate receiving impact load based on the first-order shear deformation theory expanded from the Mindlin plate theory. The result of static analysis and dynamic analysis is drawn through the numerical analysis rectangular and circular plates of antisymmetric Angle-Ply laminated plate using the finite element method and the analysis on each displacement is compared.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.105-111
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• 2002

A post-tensioned slab bridge is analyzed by the specially orthotropic laminates theory. Both the geometry and the material of the cross section of the slab are considered symmetrical with respect to the mid-surface so that the bending extension coupling stiffness, $B_{ij}=0$, and $D_{16}=D_{26}=0$. Each longitudinal and transverse steel layer is regarded as a lamina, and material constants of each lamina is calculated by the use of rule of mixture. This bridge with simple support is under uniformly distributed vertical and axial loads. In this paper, the finite difference method and the beam theory are used for analysis. The result of beam analysis is modified to obtain the solution of the plate analysis. The result of this paper can be used for post-tensioned slab bridge analysis by the engineers with undergraduate study in near future.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.1
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• pp.436-444
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• 2013

This article presents the dynamic response of nano-scale plates using the nonlocal continuum theory and higher-order shear deformation theory. The nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Also, the effects of nonlocal parameters, aspect ratio, side-to-thickness ratio, size of nano-scale plate and time step on dynamic response are investigated and discussed. The amplitude and cycle increase when nonlocal parameter increase. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the transient dynamic analysis of nano-scale structures.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.06c
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• pp.319.1-321
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• 1998

판 구조물의 전달 손실은 효과적인 차음 설계를 위한 필수적인 지표 중 하나이다. 특히, 흡/차음재 부착등 적층에 의한 차음 성능의 변화 예측이 중요하다. 실제의 차음 구조물은 유한한 크기를 갖게 마련인데, 현재까지는무한 판 이론에 제한각이나 경계 손실등을 적용하여 그 값을 산출함으로써 판의 유한효과를 고려하였지만, 해석의 임의성으로 인해 일반적인 적용이 어렵다. 이에 본 연구에서는 흡음재가 부착된 유한한 면적을 갖는 적층판의 음향 전달 손실을 임계 주파수 미만의 주파수 대역에 대해 예측하고 흡음재의 부착에 따른 전달 손실의 변화를 관찰하였다. 판은 무한한 강체 배플위에 있다고 가정하였고, 모드 전개법을 응용하여 개개의 판모드들의 거동을 고려하였다. 여기서 흡음재는 공극질 재료로 가정하여 Biot의 이론을 적용하였다. 해석 결과로부터, 흡음재등이 부착된 적층판에 대해서는 일반적인 제한각의 적용이 어렵고, 그 영향을 충분히 고려할 수 있는 새로운 예측 도구의 필요성을 확인하였다.