• Steel and Composite Structures
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• 제29권1호
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Structural Engineering and Mechanics
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• 제55권2호
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• Steel and Composite Structures
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• 제29권3호
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• pp.349-362
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• 2018

Thermal buckling behavior of porous functionally graded nanobeam integrated with piezoelectric sensor and actuator based on the nonlocal higher-order shear deformation beam theory is investigated for the first time. Its material properties are assumed to be temperature-dependent and varying along the thickness direction according to the modified power-law rule. Note that the porosity with even type is considered herein. The equations of motion are obtained through Hamilton's principle. The influences of several parameters (such as type of temperature distribution, external electric voltage, material composition, porosity, small-scale effect, Ker foundation parameters, and beam thickness) on the thermal buckling of FG nanobeam are investigated in detail.

• 대한기계학회논문집
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• 제15권3호
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• pp.735-750
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• 1991

본 연구에서는 적층 복합판의 충격 해석을 위하여 Reddy의 고차 전단 변형 이 론에 기초를 두고, 정적 압입 실험에 의한 접촉 법칙을 고려한 동적 유한 요소 해석 (dynamic finite element analysis)을 행하여 충격 실험에 의한 결과와 1차 전단변형 이론에 의한 해와 비교 검토하므로서, 그 유용성과 우수성을 입증하고, 적층 복합재의 충격 응력 및 응력파 전파 특성에 대하여 연구하고자 한다.

• 한국전산구조공학회논문집
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• 제12권1호
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• pp.37-44
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• 1999

비등방성으로 적층된 복합판 및 쉘구조물에서 온도와 습도의 급격한 변화는 구조물의 강도와 성능을 저하시키는 중요한 원인이 된다. 더욱이 하중에 의한 역학적 변위와 조합될 때에는 좌굴, 대변형 혹은 고응력 상태를 유발하게 된다. 본 연구에서는 이중 퓨리에급수를 이용하여 3차의 전단변형함수로 가정된 평형방정석을 전개하고 폭-두께비, 형상비의 변화 그리고 재료의 성질에 따른 결과에 대하여 고찰하였다.

• Coupled systems mechanics
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• 제13권2호
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• pp.171-186
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• 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
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• 제73권6호
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• pp.667-684
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• 2020

In this article, the static responses of layered magneto-electro-thermo-elastic (METE) plates in thermal environment have been investigated through FE methods. By using Reddy's third order shear deformation theory (TSDT) in association with the Hamilton's principle, the direct and derived quantities of the coupled system have been obtained. The coupled governing equations of METE plates have been derived through condensation technique. Three layered METE plates composed of piezoelectric and piezomagnetic phases are considered for evaluation. For investigating the correctness and accuracy, the results in this article are validated with previous researches. In addition, a special attention has been paid to evaluate the influence of different electro-magnetic boundary conditions and pyrocoupling on the coupled response of METE plates. Finally, the influence of stacking sequences, magnitude of temperature load and aspect ratio on the coupled static response of METE plates are investigated in detail.

• 한국강구조학회 논문집
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• 제9권3호통권32호
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• pp.333-340
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• 1997

본 연구에서는 복합재료로 구성된 복합적층판 및 쉘에 대하여 3차 전단 변형이론을 이용한 변위를 가정하여 단순지지 경계조건을 만족하는 변위형상함수를 퓨리예급수로 전개하고 동적 평형 방정식을 유도하여 뉴마크의 수치적분법을 사용하여 단면특성계수, 재료의 특성, 층의 배열에 따른 복합적층판 및 쉘의 비감쇄 동적응답특성을 연구하였다.

• International Journal of Aeronautical and Space Sciences
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• 제18권2호
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.