• Advances in aircraft and spacecraft science
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• 제6권5호
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.

• Smart Structures and Systems
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• 제20권3호
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• pp.369-383
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• 2017

In this work, the effects of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is studied by proposing a novel simple trigonometric shear deformation theory. The main advantage of this theory is that, in addition to including the shear deformation influence, the displacement field is modeled with only 2 unknowns as the case of the classical beam theory (CBT) and which is even less than the Timoshenko beam theory (TBT). Three types of environmental condition namely uniform, linear, and sinusoidal hygrothermal loading are studied. Material properties of FG beams are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from Hamilton's principle. Numerical examples are presented to show the validity and accuracy of present shear deformation theories. The effects of hygro-thermal environments, power law index, nonlocality and elastic foundation on the free vibration responses of FG beams under hygro-thermal effect are investigated.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.33-54
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• 2020

The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

• Earthquakes and Structures
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• 제16권5호
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• pp.547-561
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• 2019

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

• 항공우주시스템공학회지
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• 제1권4호
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• pp.28-36
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• 2007

This paper presents critical buckling loads of laminated composites under cylindrical bending. In-plane displacements are assumed to vary exponentially through plate thickness. The accuracy of this theory is examined for symmetric/antisymmetric cross-ply, angle-ply and unsymmetric laminates under cylindrical bending. Analytical solutions are provided to investigate the effect of transverse shear deformation on critical buckling loads of the laminated plates, and the results are compared with those obtained from the first-order shear deformation plate theory and the classical laminated plate theory.

• Steel and Composite Structures
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• 제33권4호
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• pp.551-568
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• 2019

This proposed project presents the bi-axial and uni-axial stability behavior of laminated composite plates based on an original three variable "refined" plate theory. The important "novelty" of this theory is that besides the inclusion of a cubic distribution of transverse shear deformations across the thickness of the structure, it treats only three variables such as conventional plate theory (CPT) instead five as in the well-known theory of "first shear deformation" (FSDT) and theory of "higher order shear deformation" (HSDT). A "shear correction coefficient" is therefore not employed in the current formulation. The computed results are compared with those of the CPT, FSDT and exact 3D elasticity theory. Good agreement is demonstrated and proved for the present results with those of "HSDT" and elasticity theory.

• Steel and Composite Structures
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• 제17권3호
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• pp.321-338
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• 2014

In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.

• Earthquakes and Structures
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• 제26권4호
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• pp.299-309
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• 2024

The present paper develops application of third-order shear deformation theory (TSDT) and modified couple stress theory (MCST) to size-dependent bending analysis of a functionally graded cylindrical micro-shell. The radial and axial displacement components are described based on TSDT for more accurate analysis. The effect of small scales is accounted based on MCST. The principle of virtual work is used for derivation of bending governing equations. The solution is presented for a simply-supported boundary condition to account the influence of various important parameters such as micro length scale parameter, in-homogeneous index and some dimensionless geometric parameters such as length to radius and length to thickness ratios on the bending results. A comparative analysis is presented to examine the effect of order of employed shear deformation theory on the axial and radial displacements.

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.317-328
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• 2018

In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.

• 한국전산구조공학회논문집
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• 제24권3호
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• pp.249-257
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• 2011

본 논문에서는 고전적 고차전단변형이론(HSDT)을 이용한 복합재료 적층평판의 응력해석 개선기법을 소개한다. 횡방향 응력들에 대해서만 변분을 취하는 혼합변분이론(Mixed variational theorem)을 통하여 횡방향 전단 변형에너지를 개선하였다. 가정된 횡방향 전단응력은 면내 변위가 5차 다항식을 갖는 고차 지그재그 이론으로부터 구하였으며, 변위들은 고전적 고차전단변형이론의 변위장을 사용하였다. 이 과정을 통하여 얻어진 변형 에너지를 본 논문에서는 EHSDTM라고 명명하였으며, 이 이론을 통해 복합재 적층평판의 변위와 응력을 계산함에 있어서 HSDT와 비슷한 수준의 계산적 효율을 가지면서, 동시에 최소자승오차법에 따른 후처리 과정을 적용함으로써 변위와 응력의 두께방향 분포를 정확하게 예측할 수 있도록 개선하였다. 계산된 결과는 고전적 HSDT, 3차원 탄성해 등의 여러 결과들과 비교하여 검증하였다.