Dynamic relaxation large deflection analysis of non-axisymmetric circular viscoelastic plates

Dynamic relaxation (DR) non-linear shear deformable governing equations for non-axisymmetric circular viscoelastic plates are presented. Combined bending and stretching of the plate are taken into account via the non-linear equilibrium equations together with the effect of transverse shear using higher-order shear deformation theories. Consequently, five equilibrium equations for plate element are obtained. The non-linear strain–displacement equations with third-order displacement fields are used. The constitutive equations are presented for the viscoelastic material which is modeled as the standard linear solid-type material. The limiting process technique is used to eliminate the singularity at the centre. The numerical results are obtained using the DR method together with the finite difference discretization technique. The numerical results are compared with finite element generated results using a first-order shear deformation theory. The correlations are very satisfactory. New dimensionless deflections, stress resultants and stress couples are computed and presented for axisymmetric circular plates. Finally, by decreasing the relaxation time the deflections increase and so does the DR convergence rate.