• Structural Engineering and Mechanics
• /
• 제74권3호
• /
• pp.365-380
• /
• 2020

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.

• Structural Engineering and Mechanics
• /
• 제69권5호
• /
• pp.511-525
• /
• 2019

This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate.

• Steel and Composite Structures
• /
• 제18권2호
• /
• pp.409-423
• /
• 2015

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

• Steel and Composite Structures
• /
• 제41권6호
• /
• pp.805-820
• /
• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Steel and Composite Structures
• /
• 제18권3호
• /
• pp.793-809
• /
• 2015

In this scientific work, constructing of a novel shear deformation beam model including the stretching effect is of concern for flexural and free vibration responses of functionally graded beams. The particularity of this model is that, in addition to considering the transverse shear deformation and the stretching effect, the zero transverse shear stress condition on the beam surface is assured without introducing the shear correction parameter. By employing the Hamilton's principle together with the concept of the neutral axe's position for such beams, the equations of motion are obtained. Some examples are performed to demonstrate the effects of changing gradients, thickness stretching, and thickness to length ratios on the bending and vibration of functionally graded beams.

• Coupled systems mechanics
• /
• 제13권2호
• /
• pp.171-186
• /
• 2024

In the present paper, thermal buckling characteristics of functionally graded rectangular plates made of porous material that are integrated with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and constant applied actuator voltage are investigated by utilizing a Navier solution method. The uniform temperature rise loading is considered. Thermomechanical material properties of FGM plates are assumed to be temperature independent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of stability for the piezoelectric FGM plate are derived based on higher order shear deformation plate theory. Influences of several important parameters on the critical thermal buckling temperature are investigated and discussed in detail.

• Structural Engineering and Mechanics
• /
• 제66권1호
• /
• pp.61-73
• /
• 2018

In this article, a higher shear deformation theory (HSDT) is improved to consider the influence of thickness stretching in functionally graded (FG) plates. The proposed HSDT has fewer numbers of variables and equations of motion than the first-order shear deformation theory (FSDT), but considers the transverse shear deformation influences without requiring shear correction coefficients. The kinematic of the present improved HSDT is modified by considering undetermined integral terms in in-plane displacements and a parabolic distribution of the vertical displacement within the thickness, and consequently, the thickness stretching influence is taken into account. Analytical solutions of simply supported FG plates are found, and the computed results are compared with 3D solutions and those generated by other HSDTs. Verification examples demonstrate that the developed theory is not only more accurate than the refined plate theory, but also comparable with the HSDTs which use more number of variables.

• Structural Engineering and Mechanics
• /
• 제69권3호
• /
• pp.335-345
• /
• 2019

In present study, a novel refined hyperbolic shear deformation theory is proposed for the buckling analysis of thick isotropic plates. The new displacement field is constructed with only two unknowns, as against three or more in other higher order shear deformation theories. However, the hyperbolic sine function is assigned according to the shearing stress distribution across the plate thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using any shear correction factors. The equations of motion associated with the present theory are obtained using the principle of virtual work. The analytical solution of the buckling of simply supported plates subjected to uniaxial and biaxial loading conditions was obtained using the Navier method. The critical buckling load results for thick isotropic square plates are compared with various available results in the literature given by other theories. From the present analysis, it can be concluded that the proposed theory is accurate and efficient in predicting the buckling response of isotropic plates.

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

• 한국산학기술학회논문지
• /
• 제14권1호
• /
• pp.436-444
• /
• 2013

미세 규모 효과를 고려한 비국소 연속체 이론을 이용한 고차전단변형 나노-스케일 판의 동적응답에 대하여 연구하였다. Eringen의 비국소 연속체 이론은 미소 규모 효과를 고려할 수 있고 고차전단변형이론은 나노 판의 두께방향으로의 전단변형률과 전단응력의 곡선변화 효과를 고려할 수 있다. 비국소 탄성 이론과 고차전단변형이론이 나노-스케일 판의 동적응답에 미치는 비국소 이론의 효과를 제시하였다. 국소 탄성이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 비국소 계수 변화, 형상비, 폭-두께비, 나노-스케일 판의 크기 그리고 하중재하 시간간격 등이 나노-스케일 판의 동적응답 미치는 효과에 대하여 관찰하고 분석하였다. 비국소 변수의 증가는 나노-스케일 판의 주기와 진폭을 증가시켰다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였다. 본 연구에서 제시한 이론적 발전과 수치결과들은 나노-스케일 구조물의 동적해석에 적용하는 비국소 이론들을 위한 참고자료로 활용될 수 있을 것이다.