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Structural Engineering and Mechanics
  Volume 22, Number 3, February20 2006, pages 331-349

Thermal vibration analysis of thick laminated plates
by the moving least squares differential quadrature method
Lanhe Wu

    The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.
Key Words
    differential quadrature method; moving least-squares method; thermal vibration; laminated plate; shear deformation.
Department of Engineering Mechanics, Shijiazhuang Railway Institute, Shijiazhuang 050043, P. R. China

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