فهرست مقالات Two-Dimensional elasticity

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  1 - Two-Dimensional Elasticity Solution for Arbitrarily Supported Axially Functionally Graded Beams
  A Singh P Kumari
  First time, an analytical two-dimensional (2D) elasticity solution for arbitrarily supported axially functionally graded (FG) beam is developed. Linear gradation of the material property along the axis of the beam is considered. Using the strain displacement and constit چکیده کامل

  First time, an analytical two-dimensional (2D) elasticity solution for arbitrarily supported axially functionally graded (FG) beam is developed. Linear gradation of the material property along the axis of the beam is considered. Using the strain displacement and constitutive relations, governing partial differential equations (PDEs) is obtained by employing Ressiner mixed variational principle. Then PDEs are reduced to two set of ordinary differential equations (ODEs) by using recently developed extended Kantorovich method. The set of 4n ODEs along the z-direction has constant coefficients. But, the set of 4n nonhomogeneous ODEs along x-direction has variable coefficients which is solved using modified power series method. Efficacy and accuracy of the present methodology are verified thoroughly with existing literature and 2D finite element solution. Effect of axial gradation, boundary conditions and configuration lay-ups are investigated. It is found that axial gradation influence vary with boundary conditions. These benchmark results can be used for assessing 1D beam theories and further present formulation can be extended to develop solutions for 2D micro or Nanobeams. پرونده مقاله
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  2 - Vibration Analysis of Thick Functionally Graded Beam under Axial Load Based on Two-Dimensional Elasticity Theory and Generalized Differential Quadrature
  حسین فراهانی فرزان براتی محمد نجاتی حمید باتمانی
  In this paper, vibration analysis of thick functionally graded beam with simply supported boundary condition under constant axial load is studied. The beam has a uniform cross-sectional area and the mechanical properties of the fungtionally graded beam are assumed to be چکیده کامل

  In this paper, vibration analysis of thick functionally graded beam with simply supported boundary condition under constant axial load is studied. The beam has a uniform cross-sectional area and the mechanical properties of the fungtionally graded beam are assumed to be vary through the thickness of the beam. Fundamental relations, the equilibrium and stability equations based on the displacement components are derived using the two-dimensional elasticity theory and hamilton's principle. Generalized differential quadrature (GDQ) method is used to solve the system of coupled differential equations at equilibrium and moving condition. In this paper, the influences of axial loads, dimensionless geometric parameter, functionally graded index and ratio of thickness to length on the vibration of beam is presented. To study the accuracy of the present analysis, a compression is carried out between the present results and published results and also results obtained from ABAQUSE program. Results showed that the generalized differential quadrature method is quite good. Based on the results obtained by increasing the volume fraction of fibers in the functional graded beam, the natural frequency of the beam increases and for high volume fraction, it is not possible to see much change in the natural frequency. Also, by increasing the ratio of thickness to length in the absence of the critical load the natural frequency decreased. پرونده مقاله