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Elements of Plate Bending Theory l
Plates of Various Geometrical Forms
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applied assumed axial axis axisymmetrically bending moments bending stress boundary conditions buckling circular plate coefficients compressive constant coordinates cosh curvature cylinder cylindrical shell d2w d2w deflection surface deformation derived determined differential equation direction displacement dx dy elastic equilibrium Example expression Figure finite difference finite element finite element method force per unit Fourier series given by Eq governing equation Hooke's law hoop stress in-plane isotropic lateral load matrix maximum deflection membrane stresses membrane theory method midplane midsurface Mohr's circle nodal nodes obtained orthotropic plate plane Poisson's ratio polar coordinates potential energy pressure Prob problem radial radius represented respectively Ritz method shear forces shear stress shown in Fig simply supported edges simply supported plate sinh square plate strain energy stress resultants subjected substituting Eqs symmetry Table tanh temperature tensile thickness thin plates tions values wmax yields zero