Buckling of Shallow Viscoelastic Arches

摘要

A method of solution to the buckling problem for shallow viscoelastic shells is presented. The arches are considered to be pin-ended at rigid supports, of arbitrary initial shape but of uniform cross section, and made of an aribitrary linear viscoelastic material. The lateral loading may be an arbitrary function of both position and time. Specific solutions are given for several arches to point out the influence of the material and of asymmetries in the initial arch shape on the deformation and buckling time of the system. Two types of viscoelastic material, the Maxwell Fluid and the three parameter solid, are included in the examples. The viscoelastic property of the material in the analysis is expressed in integral operator form, which is shown to lead to simple numerical time integrations in determining the arch deflection, as well as maintaining the form of the governing equations that determine stability in the same general form as the equations of an elastic arch. (Author)