• Structural Engineering and Mechanics
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• 제51권5호
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• pp.867-891
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• 2014

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

• Advances in aircraft and spacecraft science
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• 제3권2호
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• pp.113-148
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• 2016

In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

• Advances in aircraft and spacecraft science
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• 제10권3호
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• pp.281-302
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• 2023

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.

• Geomechanics and Engineering
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• 제11권5호
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• pp.671-690
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• 2016

This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

• 한국전산구조공학회논문집
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• 제25권6호
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• pp.505-512
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• 2012

본 논문에서는 일차전단변형 평판 이론(FSDT)의 개선을 통한 복합재료 적층평판의 효율적 열응력 해석 기법을 제안한다. 횡방향 응력 성분에 대해서만 변분을 취하는 혼합변분이론(Mixed variational theorem)을 이용하여 횡방향 변형에너지를 개선하였다. 가정된 횡방향 전단응력 성분들은 효율적 고차이론으로부터 구하였으며, 면내 변위 성분들은 일차적층평판 이론의 변위장을 사용하였다. 또한, 열응력 해석에 있어서 횡방향 수직 변형을 효과적으로 고려하기 위해서 횡방향 수직 변위를 두께방향에 대하여 포물선으로 가정하였다. 이 과정을 통하여 얻어진 전단변형 에너지를 본 논문에서는 횡방향 수직 변형이 고려된 개선된 일차전단변형이론(EFSDTM_TN)이라고 명명하였다. 제안된 EFSDTM_TN은 복합재료 적층평판의 열탄성 거동을 해석함에 있어서 횡방향 수직 변형이 고려된 일차전단변형 평판 이론(FSDT_TN)과 비슷한 수준의 계산만을 필요로 하며, 동시에 후처리 과정을 통하여 열변형 및 열응력의 두께방향 분포를 정확하게 예측할 수 있도록 개선하였다. 계산된 결과는 FSDT_TN, 3차원 탄성해 등의 결과와 비교하여 검증하였다.

• Advances in aircraft and spacecraft science
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• 제7권1호
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• pp.19-40
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• 2020

In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

• Structural Engineering and Mechanics
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• 제22권5호
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• pp.599-611
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• 2006

The theory with hierarchical warping functions had been used to analyze composite thin-walled structure, laminated beam and had good results. In the present paper, a series of hierarchical warping functions are developed to analyze the cylindrical bending problems of composite lamina. These warping functions which refine through-the-thickness variation of displacements were composed of basic and corrective functions by taking into account of anisotropic, material discontinues, and transverse shear and normal strain. Then the hierarchical finite element method was used to form a numerical algorithm. The distribution of the displacements, in-plane stresses, transverse shear stresses and transverse normal stress for composite laminate were analyzed with the present model. The results show that the present model has precise mechanical response compared with the first deformation transverse theory and the corrective order affects the accuracy of result.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2005년도 춘계학술발표대회 논문집
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• pp.1-4
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• 2005

A higher order zig-zag shell theory is developed to refine accurately predict deformation and stress of smart shell structures under the mechanical, thermal, and electric loading. The displacement fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. Smooth parabolic distribution through the thickness is assumed in the transverse deflection in order to consider transverse normal deformation. The mechanical, thermal, and electric loading is applied in the sinusoidal distribution function in the in-surface direction. Thermal and electric loading is given in the linear variation through the thickness. Especially, in electric loading case, voltage is only applied in piezo-layer. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. In order to obtain accurate transverse shear and normal stresses, integration of equilibrium equation approach is used. The numerical examples of present theory demonstrate the accuracy and efficiency of the proposed theory. The present theory is suitable for the predictions of behaviors of thick smart composite shell under mechanical, thermal, and electric loadings combined.

• Steel and Composite Structures
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• 제19권3호
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• pp.521-546
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• 2015

A new refined hyperbolic shear and normal deformation beam theory is developed to study the free vibration and buckling of functionally graded (FG) sandwich beams under various boundary conditions. The effects of transverse shear strains as well as the transverse normal strain are taken into account. Material properties of the sandwich beam faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending, free vibration and buckling analyses are obtained for simply supported sandwich beams. Illustrative examples are given to show the effects of varying gradients, thickness stretching, boundary conditions, and thickness to length ratios on the bending, free vibration and buckling of functionally graded sandwich beams.

• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.615-632
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• 2018

Mechanical buckling of a rectangular functionally graded plate is obtained in the current paper using a refined higher-order shear and normal deformation theory. The impact of transverse normal strain is considered. The material properties are microscopically inhomogeneous and vary continuously based on a power law form in spatial direction. Navier's procedure is applied to examine the mechanical buckling behavior of a simply supported FG plate. The mechanical critical buckling subjected to uniaxial and biaxial compression loads are determined. The numerical investigation are compared with the numerical results in the literature. The influences of geometric parameters, power law index and different loading conditions on the critical buckling are studied.