• Structural Engineering and Mechanics
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• 제33권5호
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• pp.621-633
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• 2009

In this paper we compare the solution of the one-dimensional beam model and the numerical solution of the two-dimensional linearized elasticity problem for rectangular domain of the beam-like form. We first derive the beam model starting from the two-dimensional linearized elasticity, the same way it is derived from the three-dimensional linearized elasticity. Then we present the numerical solution of the two-dimensional problem by finite element method. As expected the difference of two approximations becomes smaller as the thickness of the beam tends to zero. We then analyze the applicability of the one-dimensional model and verify the main properties of the beam modeling for thin beams.

• Structural Engineering and Mechanics
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• 제3권2호
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• pp.121-133
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• 1995

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

• Structural Engineering and Mechanics
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• 제51권6호
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• pp.1067-1089
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• 2014

In this paper, three dimensional static and dynamic analyses of two dimensional functionally graded annular sector plates have been investigated. The material properties vary through both the radial and axial directions continuously. Graded finite element and Newmark direct integration methods have been used to solve the 3D-elasticity equations in time and space domains. The effects of power law exponents and different boundary conditions on the behavior of FGM annular sector plate have been investigated. Results show that using 2D-FGMs and graded elements have superiority over the homogenous elements and 1D-FGMs. The model has been compared with the result of a 1D-FGM annular sector plate and it shows good agreement.

• Structural Engineering and Mechanics
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• 제10권5호
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• pp.441-449
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• 2000

In this study, the state equation for axisymmetric bending of laminated transversely isotropic circular plates on elastic foundation is established on the basis of three-dimensional elasticity. By using the expansions of Bessel functions, an analytical solution of the problem is presented. As a result, all the fundamental equations of three-dimensional elasticity can be satisfied exactly and all the independent elastic constants can be fully taken into account. Furthermore, the continuity conditions at the interfaces of plies can also be satisfied.

• 대한기계학회논문집
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• 제13권3호
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• pp.323-329
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• 1989

본 연구에서는 판이론으로서는 해석이 불가능한 집중하중작용점에서 응력을 해석할 목적으로 3차원탄성이론과 변링포텐셜(POTENTIAL) 이론을 이용하여 유근평판의 집중하중작용점에서의 응력을 해석하는 방법을 제안하고저 한다.

• Structural Engineering and Mechanics
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• 제72권1호
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• pp.131-139
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• 2019

According to the properties of monoclinic materials, the normal and shear stresses are depending on both normal and shear strains. In the current investigation, the static analysis of monoclinic plates based on three dimensional elasticity theory is investigated. New governing equations and boundary conditions are derived for monoclinic plates and the Differential Quadrature Method (DQM) is used to solve the static problem. In our method of solution, no approximation is used and the DQM is adopted in all directions. By showing the differences between our results and the results for especially orthotropic plates, one can find that it is worth to investigate the monoclinic plates to have more accurate results.

• Steel and Composite Structures
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• 제26권5호
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Steel and Composite Structures
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• 제48권1호
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• pp.1-17
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• 2023

The main goal of this paper is to study vibration of damaged core laminated sectorial plates with Functionally graded (FG) face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular sector plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions.

• 한국재난정보학회 논문집
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• 제10권1호
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• pp.1-14
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• 2014

본 연구에서는 탄성이론에 근거하여 3차원 spline 대판법을 이용하여 직교이방성판의 3차원 응력해석을 제시한다. 직교이방성판은 아라고나이트 결정과 시트카 스프러스로 구성되어 있다. 해석에 대한 수렴섬과 정밀도의 정확성을 수치해석 예를 들어 검증하고, 탄성이론에 근거하여 이산화된 수치해석법에 의해 결과을 비교 검토한다. 해석법에 따라 해의 수렴성과 정밀도를 구할 수 있으며, 두께폭 비, 종횡비와 아라고나이트 결정과 시트카 스프러스판의 수직응력분포에 대한 경계조건의 영향을 검토하고, 응력 분포의 특성에 미치는 직교이방성과 강한 이방성의 특징의 차를 비교 검토한다.

• Steel and Composite Structures
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• 제24권5호
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.