• Structural Engineering and Mechanics
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• 제52권6호
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• pp.1069-1084
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• 2014

The long-term performance of plates resting on viscoelastic foundations is a major concern in the analysis of soil-structure interaction. As a powerful mathematical tool, fractional calculus may address these plate-on-foundation problems. In this paper, a fractionalized Zener model is proposed to study the time-dependent behavior of a uniformly loaded rectangular thin foundation plate. By use of the viscoelastic-elastic correspondence principle and the Laplace transforms, the analytical solutions were obtained in terms of the Mittag-Leffler function. Through the analysis of a numerical example, the calculated plate deflection, bending moment and foundation reaction were compared to those from ideal elastic and standard viscoelastic models. It is found that the upper and lower bound solutions of the plate response estimated by the proposed model can be determined using the elastic model. Based on a parametric study, the impacts of model parameters on the long-term performance of a foundation plate were systematically investigated. The results show that the two spring stiffnesses govern the upper and lower bound solutions of the plate response. By varying the values of the fractional differential order and the coefficient of viscosity, the time-dependent behavior of a foundation plate can be accurately captured. The fractional differential order seems to be dependent on the mechanical properties of the ground soil. A sandy foundation will have a small fractional differential order while in order to simulate the creeping of clay foundation, a larger fractional differential order value is needed. The fractionalized Zener model is capable of accounting for the primary and secondary consolidation processes of the foundation soil and can be used to predict the plate performance over many decades of time.

• Structural Engineering and Mechanics
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• 제70권6호
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• pp.661-669
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• 2019

Buckling analysis of shape memory alloy (SMA) rectangular plates subjected to uniform and linearly distributed inplane loads is the main objective in the present paper. Brinson's model is developed to express the constitutive characteristics of SMA plate. Using the classical plate theory and variational approach, stability equations are derived. In addition to external inplane mechanical loads, the plate is subjected to the pre-stresses caused by the recovery stresses that are generated during martensitic phase transformation. Ritz method is used for solving the governing stability equations. Finally, the effects of conditions on the edges, thickness, aspect ratio, temperature and pre-strains on the critical buckling loads of SMA plate are investigated in details.

• International Journal of Safety
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• 제1권1호
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• pp.13-17
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• 2002

A new system of equations governing the nonlinear thin laminated plates with large deflections using von Karman equations is derived. The effects of transverse shear in the thin interlayer are included as part of the analysis. The finite difference method is used to perform the geometrically nonlinear behavior of the plate. The resultant equations permit the analysis of the effect of transverse shear stress deformation on the overall behavior of the interlayer using the load incremental method. For the purpose of feasibility and validity of this present method, the numerical results are compared with other available solutions for accuracy as well as efficiency. The solution techniques have been implemented and the numerical results of example problem are discussed and evaluated.

• 대한기계학회논문집
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• 제18권6호
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• pp.1520-1534
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• 1994

A new analytical method for the prediction of the buckling behavior of laminated plates consisting of layers having different properties in tension and compression, so called bimodulus, is proposed in this paper. Buckling analysis of bimodular composite laminated paltes are performed with the results reduced from plate bending analysis. The governing equations of bimodular plates are based on the first shear deformation theory. As a case study, bending and buckling of simply supported, multilayered, symmetric, antisymmtric, and specially orthotropic laminates under uniformly distributed lateral load for bending analysis and in-plane load for buckling are considered. The results of the bending analysis are compared with the previous papers. Then, the fundamental critical buckling loads and buckling modes are calculated for the various bimodular composite rectangular thin plates.

• Structural Engineering and Mechanics
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• 제63권1호
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• pp.103-113
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• 2017

Free vibration analysis of plates is necessary for the field of structural engineering because of its wide applications in practical life. Free vibration of plates is largely dependent on its thickness, aspect ratios, and boundary conditions. Here we investigate the natural frequencies of simply supported tapered isotropic rectangular plates with internal cutouts using a nine node isoparametric element. The effect of rotary inertia on Eigenfrequencies was demonstrated by calculating with- and without rotary inertia. We found that rotary inertia has a significant effect on thick plates, while rotary inertia term can be ignored in thin plates. Based on comparison with literature data, we propose that the present formulation is capable of yielding highly accurate results. Internal cutouts at various positions in tapered rectangular simply supported plates were also studied. Novel data are also reported for skew taper plates.

• Steel and Composite Structures
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• 제47권2호
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• pp.297-313
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• 2023

This study aims to extend the application of the spectral element method (SEM) to wave propagation and free vibration analysis of functionally graded (FG) plates integrated with thin piezoelectric layers, plates with tapered thickness and structure on elastic foundations. Also, the dynamic response of the smart FG plate under impact and moving loads is presented. In this paper, the dynamic stiffness matrix of the smart rectangular FG plate is determined by using the exact dynamic shape functions based on Mindlin plate assumptions. The low computational time and results' independence with the number of elements are two significant features of the SEM. Also, to prove the accuracy and efficiency of the SEM, results are compared with Abaqus simulations and those reported in references. Furthermore, the effects of boundary conditions, power-law index, piezoelectric layers thickness, and type of loading on the results are studied.

• Structural Engineering and Mechanics
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• 제44권4호
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• 대한조선학회논문집
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• 제33권3호
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• pp.66-80
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• 1996

최근 고장력강(高張力鋼)이 구조물에 폭넓게 사용되고 있어서 판두께가 얇아지고 있다. 판두께가 얇아지므로해서 좌굴(座屈)이 발생하기 쉽다. 그러므로 좌굴(座屈)발생후 판의 거동(擧動)을 정확하게 파악하는 것은 중요하다. 좌굴(座屈) 발생후 2차좌굴(次座屈)이라고 하는 하중하(荷重下)에서는 판(板)의 처짐모드가 갑자기 변한다. 전체구조물의 붕괴강도(崩壞强度)를 고려할 때 2차좌굴(次座屈)은 매우 중요하다. 이런 관점에서 본 연구에서는 면내압축하중(面內壓縮荷重)을 받는 판(板)의 2차좌굴거동(次座屈擧動)에 관하여 연구하였다. 초기처짐을 갖는 판(板)을 대상으로 하여 탄성대변형해석(彈性大變形解析)을 실시하여, 2차좌굴(次座屈)의 영향을 검토하였다. 그 결과로서 다음과 같은 결론(結論)을 얻었다. 즉, 정사각형판은 대칭의 처짐성분은 영향이 있으나 비대칭의 처짐성분은 영향이 전혀 없다. 또한, 종횡비(縱橫比)를 갖는 판(板)은 모든 처짐성분의 영향이 있으며 초기좌굴(初期座屈)후 면내강성(面內剛性)이 계속적으로 감소한다.

• Structural Engineering and Mechanics
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• 제40권6호
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• pp.783-800
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• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• 한국정밀공학회지
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• 제18권12호
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• pp.54-59
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• 2001

The stability of a thin plate structure is very crucial problem which results buckling. Because the buckling strength of thin plates is lower than the yield strength of the material, reinforcement plate must be used to increase the buckling strength. And, in this case, spot welding is commonly used, however, the spot welded joints are practically designed by experimental decisions, so it is Inefficient and has the risks of buckling demolition. In this study, two parameters, such as the area ratio and the distance ratio of spot welding which have influence on the buckling strength, should be chosen. Under compressive and shearing load, the effect of two parameters on the critical stress is discussed.