Circular Viscoelastic Plates Subjected to In-Plane Loads

TLDR: In this article, the general equation for the deflection of a circular viscoelastic plate is derived from the equation of an elastic plate using the well-known correspondence principle.

Abstract: This paper is concerned with circular viscoelastic plates subject to in-plane forces. The plates are assumed to have a small arbitrary initial curvature and the increase in curvature as a function of time is determined. The plate material is assumed to follow a linear viscoelastic stress-strain relation and quasi-static small deflection theory is utilized. The general equation for the deflection of a circular viscoelastic plate is derived from the equation of an elastic plate using the well-known correspondence principle. Special cases are: 1) a circular plate with a fixed edge; 2) a circular plate with a simply supported edge; 3) a circular segment; and 4) an annular plate. Circular symmetry is assumed in cases 1, 2 and 4 but the solution developed in case 3 could readily be applied to the other cases if symmetry did not exist. Numerical examples are given for all cases. The applied load is assumed to be uniformly distributed around the boundary of the plate. For an annular plate the load at the inner boundary may differ from the load at the outer boundary. This leads to a variation of the in-plane forces throughout the plate. The load may vary with time in any arbitrarily prescribed manner. The load is assumed to be compressive but the analysis applies equally well for tensile loads.