• Advances in materials Research
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• 제5권3호
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• pp.141-169
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• 2016

In this paper, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The mechanical properties of functionally graded material are assumed to vary according to a power law distribution of the volume fraction of the constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular plates are obtained. Comparison studies are performed to verify the validity of present results. The effects of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are investigated and discussed.

• Composite Materials and Engineering
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• 제3권3호
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• pp.179-199
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• 2021

A simple solution for free vibration of cross-ply and angle-ply laminated composite plates in a thermal environment is investigated using a basic trigonometric shear deformation theory. By application of trigonometric four variable plate theory, the transverse displacement is subdivided into bending and shear components, the present theory's number of unknowns and governing equations is reduced, making it easier to use. Hamilton's Principle is extended to derive the equations of motion of the plates using Navier's double trigonometric series, a closed-form solution is obtained; the primary conclusion is that simple solution is obtained with good results accuracy when compared with previously published results, and the natural frequency will differ depending on, environment temperature, thickness ratio, and lamination angle, as well as the aspect ratio of the plate.

• 한국강구조학회 논문집
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• 제13권1호
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• pp.61-69
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• 2001

본 연구에서는 거더와 가로보로 이루어진 패널을 특별 직교 이방성 판이론을 응용하여 해석하였다. 거더와 가로보는 H 형단면을 사용하였으며, 임의의 단면과 지점을 갖고 임의의 하중을 받는 보다 탑의 진동해석 방법이 발표된 바가 있다. 본 논문에서는 특별 직교 이방성 판이론을 강교량에 응용하였으며, 해석한결과를 제시하였다. 이러한 진동 해석을 위하여 처짐의 영향을 고려한 다양한 방법이 검토되었다. 이러한 목적으로 본 논문에서는 유한차분법을 사용하였다. 고유진동수에 대한 $D_{22}$ 탄성계수의 영향을 철저히 검토하였다. 본 연구에서는 제시한 판이론을 수치해석을 해본 결과 빔이론 보다 강성이 2.43배인 것을 알 수 있었다.

• Structural Engineering and Mechanics
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• 제72권5호
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• pp.653-673
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• 2019

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

• Steel and Composite Structures
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• 제28권1호
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• pp.99-110
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• 2018

In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

• Structural Engineering and Mechanics
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• 제82권6호
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• pp.725-734
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• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• 대한조선학회논문집
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• 제55권4호
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• pp.281-288
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• 2018

Acoustic radiation efficiency is a crucial factor to estimate Underwater Radiated Noise (URN) of ships accurately. This paper describes a numerical method to analyse acoustic radiation efficiency of one side-wetted rectangular Mindlin plate with simply supported boundaries excited by a harmonic point force. Transverse displacements of plate and acoustic radiation pressures are evaluated by the mode superposition method. The acoustic radiation efficiencies analyzed by both Mindlin and thin plate theories show little differences at monopole and corner modes of low frequency regions but relatively large differences at edge and critical modes of high frequency regions. Especially, the critical frequency with the highest acoustic radiation efficiency evaluated by the Mindlin plate theory is higher than that of thin plate theory. In addition, the acoustic loading effect of fluid also increases bending wave-number of plate and its critical frequency. Finally, the acoustic radiation characteristics of plates with different aspect ratios and thicknesses through numerical analyses are investigated and discussed.

• Structural Engineering and Mechanics
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• 제17권5호
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• pp.641-654
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• 2004

This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

• Structural Engineering and Mechanics
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• 제36권5호
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• pp.625-642
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• 2010

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.25-32
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• 2004

In this proposed work new finite element model for multi-delaminated plates is proposed. In the current analysis procedures of multi-delaminated plates, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. The numerical results show that the effect of delaminations on the modal parameters of delaminated composites plates is dependent not only on the size, the location and the number of the delaminations but also on the mode number and boundary conditions. Kirchhoff based model have higher natural frequency than Mindlin based model and natural frequency of the presented model is closed to Mindlin based model.