• Title/Summary/Keyword: Elastic plate

Search Result 983, Processing Time 0.033 seconds

Axisymmetric bending of a circular plate with stiff edge on a soft FGM layer

  • Volkov, Sergey S.;Litvinenko, Alexander N.;Aizikovich, Sergey M.;Wang, Yun-Che;Vasiliev, Andrey S.
    • Structural Engineering and Mechanics
    • /
    • v.59 no.2
    • /
    • pp.227-241
    • /
    • 2016
  • A circular plate with constant thickness, finite radius and stiff edge lying on an elastic halfspace is considered. The half-space consists of a soft functionally graded (FGM) layer with arbitrary varying elastic properties and a homogeneous elastic substrate. The plate bends under the action of arbitrary axisymmetric distributed load and response from the elastic half-space. A semi-analytical solution for the problem effective in whole range of geometric (relative layer thickness) and mechanical (elastic properties of coating and substrate, stiffness of the plate) properties is constructed using the bilateral asymptotic method (Aizikovich et al. 2009). Approximated analytical expressions for the contact stresses and deflections of the plate are provided. Numerical results showing the qualitative dependence of the solution from the initial parameters of the problem are obtained with high precision.

Ultrasonic Estimation and FE Analysis of Elastic Modulus of Kelvin Foam

  • Kim, Nohyu;Yang, Seungyong
    • Journal of the Korean Society for Nondestructive Testing
    • /
    • v.36 no.1
    • /
    • pp.9-17
    • /
    • 2016
  • The elastic modulus of a 3D-printed Kelvin foam plate is investigated by measuring the acoustic wave velocity of 1 MHz ultrasound. An isotropic tetrakaidecahedron foam with 3 mm unit cell is designed and printed layer upon layer to fabricate a Kelvin foam plate of 14 mm thickness with a 3D CAD/printer using ABS plastic. The Kelvin foam plate is completely filled with paraffin wax for impedance matching, so that the acoustic wave may propagate through the porous foam plate. The acoustic wave velocity of the foam plate is measured using the time-of-flight (TOF) method and is used to calculate the elastic modulus of the Kelvin foam plate based on acousto-elasticity. Finite element method (FEM) and micromechanics is applied to the Kelvin foam plate to calculate the theoretical elastic modulus using a non-isotropic tetrakaidecahedron model. The predicted elastic modulus of the Kelvin foam plate from FEM and micromechanics model is similar, which is only 3-4% of the bulk material. The experimental value of the elastic modulus from the ultrasonic method is approximately twice as that of the numerical and theoretical methods because of the flexural deformation of the cell edges neglected in the ultrasonic method.

Transient thermo-piezo-elastic responses of a functionally graded piezoelectric plate under thermal shock

  • Xiong, Qi-lin;Tian, Xin
    • Steel and Composite Structures
    • /
    • v.25 no.2
    • /
    • pp.187-196
    • /
    • 2017
  • In this work, transient thermo-piezo-elastic responses of an infinite functionally graded piezoelectric (FGPE) plate whose upper surface suffers time-dependent thermal shock are investigated in the context of different thermo-piezo-elastic theories. The thermal and mechanical properties of functionally graded piezoelectric plate under consideration are expressed as power functions of plate thickness variable. The solution of problem is obtained by solving the corresponding finite element governing equations in time domain directly. Transient thermo-piezo-elastic responses of the FGPE plate, including temperature, stress, displacement, electric intensity and electric potential are presented graphically and analyzed carefully to show multi-field coupling behaviors between them. In addition, the effects of functionally graded parameters on transient thermo-piezo-elastic responses are also investigated to provide a theoretical basis for the application of the FGPE materials.

Wave propagation in a generalized thermo elastic plate embedded in elastic medium

  • Ponnusamy, P.;Selvamani, R.
    • Interaction and multiscale mechanics
    • /
    • v.5 no.1
    • /
    • pp.13-26
    • /
    • 2012
  • In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

Exact solution for transverse bending analysis of embedded laminated Mindlin plate

  • Heydari, Mohammad Mehdi;Kolahchi, Reza;Heydari, Morteza;Abbasi, Ali
    • Structural Engineering and Mechanics
    • /
    • v.49 no.5
    • /
    • pp.661-672
    • /
    • 2014
  • Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

Buckling of an elastic plate due to surface-attached thin films with intrinsic stresses

  • Zhu, J.;Yang, J.S.;Ru, C.Q.
    • Structural Engineering and Mechanics
    • /
    • v.52 no.1
    • /
    • pp.89-95
    • /
    • 2014
  • We analyze the buckling of a thin elastic plate due to intrinsic stresses in thin films attached to the surfaces of the plate. In the case of cylindrical buckling, it is shown that for a plate with clamped edges compressive intrinsic film stresses can cause flexural buckling of the plate, while tensile intrinsic film stresses cannot. For a plate with free edges, film intrinsic stresses, compressive or tensile, cannot cause buckling.

Alternative plate finite elements for the analysis of thick plates on elastic foundations

  • Ozgan, K.;Daloglu, Ayse T.
    • Structural Engineering and Mechanics
    • /
    • v.26 no.1
    • /
    • pp.69-86
    • /
    • 2007
  • A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

The Analysis of Contact Pressure of Plate on Elastic Half-Space Considering Local Separation between Plate and Half-Space (판과 지반의 분리를 고려한 반무한 탄성지반상에 놓인 사각형 평판의 접촉응력 해석)

  • 조현영;정진환;김성철;김호진
    • Proceedings of the Computational Structural Engineering Institute Conference
    • /
    • 1997.10a
    • /
    • pp.73-79
    • /
    • 1997
  • It is one of classical problems in the elastic theory to analyze contact stresses between elastic bodies. Concrete pavements under traffic wheel loads can be considered as one of these typical Problems. In the paper, Mindlin plate theory is used to consider the transverse shear effect, 8-node isoparametric plate bending element is adopted in this study, and an elastic plate resting on tensionless elastic half-space is analyzed by finite element method. The Boussineq's solution of elastic half-space is used to evaluate the flexibility of foundation. To obtain the boundary of contact area, the flexibility matrix of foundation is modified after each cycle of analysis iteratively. A Numerical example is presented by using these method.

  • PDF

A Study on the Load Distribution Factor in the Perforated Square Plate with Elastic Support at Four Corners (彈性支持를 받는 四角多孔板의 荷重分布係數에 관한 연구)

  • 임정식;이영신
    • Transactions of the Korean Society of Mechanical Engineers
    • /
    • v.13 no.4
    • /
    • pp.563-571
    • /
    • 1989
  • The load distribution factor in the perforated square plate under concentrated load acting at arbitrary points through elastic media are calculated. For the calculation the perforated plate was converted into an orthotropic plate using the method suggested by J.B. Mahoney. In the process of the calculation the angle support at each corners was equivalent to a point support having equivalent stiffness. The deflections for the calculation of the load distribution factor were obtained using auxiliary plate extended in both directions of the plate and compared with the results from ANSYS calculations. After showing the validity of the current method, the calculation of the load distribution factor was performed. The result showed that the load distribution factor at the periphery of the plate is larger than that of in the central locations. This load distribution factor could be used for re-distribution of the applied load in more accurate analysis of the plate as well as it can be used in the analysis of the elastic media as the load factor.

Thermal postbuckling of imperfect Reissner-Mindlin plates with two free side edges and resting on elastic foundations

  • Shen, Hui-Shen
    • Structural Engineering and Mechanics
    • /
    • v.6 no.6
    • /
    • pp.643-658
    • /
    • 1998
  • A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to uniform or nonuniform tent-like temperature loading and resting on an elastic foundation. The plate is assumed to be simply supported on its two opposite edges and the two side edges remain free. The initial geometrical imperfection of the plate is taken into account. The formulation are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick plates resting on Pasternak-type or softening nonlinear elastic foundations from which results for Winker elastic foundations follow as a limiting case. Typical results are presented in dimensionless graphical form.