Determining the change of stress concentration with time in a 3-D viscoelastic transverse isotropic plate

Abstract

The 3-D problem of linear viscoelasticity for a transversely isotropic structural member (a 3-D plate with a circular hole) is solved. The constitutive equations in the Boltzmann-Volterra integral form were used. The integrals in the constitutive equations are converted to the incremental form on the time grid. At each time interval, the problem is solved with respect to displacement increments. The relaxation functions of viscoelastic transversally isotropic material modules are described in exponential form. Analytical expressions for the constitutive matrix of the finite element method were constructed for these modules using the principle of elastic–viscoelastic analogy. The changes of stresses in the plane of the plate and transverse stresses with time on the concentration line are illustrated. Numerical examples are constructed for the middle of the stress concentration line and its ends.