• International Journal of Aerospace System Engineering
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• 제3권1호
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• pp.10-16
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• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2003년도 춘계학술발표대회 논문집
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• pp.143-146
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• 2003

A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

• 콘크리트학회논문집
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• 제11권3호
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• pp.3-12
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• 1999

This study presents a suggestion of regulation of skewed slab bridge. In order to find the characteristic behavior of skew bridge, many cases of skew bridges were analyzed with changed angle of skew. The comparison of design methods for cantilever part in pier was also made. It was found that : (1) The lower the skew angle was, the higher the maximum support reaction forces at the end point were. (2) The higher the ratio of L/B was, the higher the maximum support reaction force at the point was. (3) The effect of skew may be neglected for skew angles of $70^{\circ}$or more. (4) If elastic springs are applied to the boundary conditions to simulate the rubber pad bearings, the results will be more reasonable. (5) The shear deformation effect must be considered in the analysis of cantilever part of substructure. (6) Using strut and tie model to design cantilever part of pier, it will be more simple than finite element method with same accuracy and more accurate than using frame element.

• 대한조선학회논문집
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• 제35권3호
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• pp.1-13
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• 1998

본 논문에서는 9절점 라그란지안(Lagrangian) 곡면요소를 바탕으로 한 고차경계요소법(Higher-order Boundary Element Method)을 사용하여 자유수면 아래에서 일정한 속도로 전진하는 3차원 수중익에 대한 유체역학적 특성을 연구하였다. 수치계산법에 있어서 자유수면의 계산결과를 개선하기 위해 겹2차 스플라인(bi-quadratic spline)기법을 도입하였다. 수치기법의 검증에서 잠수된 구와 구형체에 대한 해석해와 수치계산 결과가 잘 일치함을 볼 수 있었다. 수중익 문제에 대한 적용성과 그 타당성을 검증하기 위해서 가로-세로비(aspect ratio; A.R.)가 4인 NACA641A412 단면을 가신 3차원 수중익 주위 유동을 해석하였다. 속도가 일정할 때 받음각(angle of attack)과 잠수깊이 변화에 따른 Wadlin et al.[28]의 양력과 항력 계측 실험결과와 비교하였으며, 각각의 경우에 대해 본 수치계산 결과들이 실험결과와 비교적 잘 일치하는 것을 볼 수 있었다. 가로-세로비 4의 NACA0012단면을 가지는 수중익에 대한 계산결과에서는 수중익에 작용하는 양력과 항력에 미치는 자유수연의 영향을 고찰하였으며, 서로 다른 속도와 잠수깊이에서 수중익에 의해 발생하는 자유수면의 변위변화를 고찰하였다.

• Advances in nano research
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• 제7권2호
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• pp.99-108
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• 2019

Higher-order theories are very important to investigate the mechanical properties and behaviors of nanoscale structures. In this study, a free vibration behavior of SiNW resting on elastic foundation is investigated via Eringen's nonlocal elasticity theory. Silicon Nanowire (SiNW) is modeled as simply supported both ends and clamped-free Euler-Bernoulli beam. Pasternak two-parameter elastic foundation model is used as foundation. Finite element formulation is obtained nonlocal Euler-Bernoulli beam theory. First, shape function of the Euler-Bernoulli beam is gained and then Galerkin weighted residual method is applied to the governing equations to obtain the stiffness and mass matrices including the foundation parameters and small scale parameter. Frequency values of SiNW is examined according to foundation and small scale parameters and the results are given by tables and graphs. The effects of small scale parameter, boundary conditions, foundation parameters on frequencies are investigated.

• 한국전자파학회논문지
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• 제10권3호
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• pp.440-448
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• 1999

본 논문에서는 무한 주기구조로 근사할 수 있는 전파 흡수체의 전파특성을 혼성 유한요소법을 이용하여 해석한 결과를 기술하였다. 가상의 경계면을 설정하여 유한한 영역을 정의하였고, 영역의 각각의 경계면에서 유효한 경계조건을 Floquet 이론으로부터 유도하였다. 고차 Floquet 모드가 사용되었으므로, 본 논문에서의 방법은 파장에 비교할 수 있을 정도로 큰 주기를 가진 구조의 경우에도 적용이 가능하다. 표면적분 계산의 어려움을 줄이기 위해 표면에 수직인 전자계 성분을 표면에 수평인 성분으로 표현하였다. 계산된 결과를 해석적인 해 또는 기존에 발표된 결과와 비교하여 해석의 유효성을 증명하였다.

• Steel and Composite Structures
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• 제24권2호
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• pp.151-176
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• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• 대한조선학회논문집
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• 제37권1호
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• pp.67-81
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• 2000

본 연구에서는 2차원 비선형 방사문제에 대한 정확하고 효과적인 수치기법을 개발하였다. 물체운동에 의해서 생성되는 비선형파계는 이상유체라는 가정에 의하여 기술되고, 라프라스 방정식은 고차경계요소법과 GMRES(Generalized Minimal RESidual) 알고리즘을 이용하여 신속하고 효율적인 풀이가 가능하도록 하였다. 자유표면과 물체면의 교차점에서 발생하는 교차선문제는 불연속 요소를 이용하여 원활하게 해결하였다. 자유표면의 비선형운동을 기술하기 위해서 음해적 사다리꼴 법칙(implicit trapezoidal rule)을 사용하여 시적분하였다. 물체에 의해서 발생한 비선형파가 수직 하류면에서 반사하는 것을 줄이기 위하여 하류면에 수치감쇠항을 도입하였다. 수치계산 결과로부터 본 시적분법 및 수치방사조건이 비선형 방사문제에 매우 적합함을 확인하였다. 시적분 과정에서 자유표면의 격자점들을 재배치함으로써 수치해법의 효율성을 배가하였으며, 교차점근처의 유동 또한 정확하게 기술하였다. 가속도 포텐셜(acceleration potential) 기법을 이용하여 정확하고 안정하게 비선형 방사력을 구하였다. 본 수치계산결과는 다른 수치계산 및 실험결과와 비교하여 볼 때, 좋은 일치를 보인다.

• Structural Engineering and Mechanics
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• 제33권3호
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• pp.373-385
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• 2009

The purpose of this paper is to study shear locking-free parametric earthquake analysis of thick and thin plates using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick and thin plates subjected to earthquake excitations. In the analysis, finite element method is used for spatial integration and the Newmark-${\beta}$ method is used for the time integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the earthquake analysis of thick and thin plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

• Steel and Composite Structures
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• 제24권5호
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• pp.537-548
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• 2017

In this paper presents bending characteristic of single wall carbon nanotube reinforced functionally graded composite (SWCNTRC-FG) plates. The finite element implementation of bending analysis of laminated composite plate via well-established higher order shear deformation theory (HSDT). A seven degree of freedom and $C^0$ continuity finite element model using eight noded isoperimetric elements is developed for precise computation of deflection and stresses of SWCNTRC plate subjected to sinusoidal transverse load. The finite element implementation is carried out through a finite element code developed in MATLAB. The results obtained by present approach are compared with the results available in the literatures. The effective material properties of the laminated SWCNTRC plate are used by Mori-Tanaka method. Numerical results have been obtained with different parameters, width-to-thickness ratio (a/h), stress distribution profile along thickness direction, different SWCNTRC-FG plate, boundary condition, through the thickness (z/h) ratio, volume fraction of SWCNT.