Exact solution for infinite multilayer pipe bonded by viscoelastic adhesive under non-uniform load

An analytical solution is presented for an infinite multilayer pipe bonded by viscoelastic interlayer subjected to racial loads non-uniformly distributed along the circumferential direction in order to investigate its time-dependent behavior. The elasticity equations in the polar coordinate are used to describe the stresses and displacements in each pipe layer. The viscoelastic property of the interlayer is modeled by the standard linear solid model considering the strain memory effect. By means of the Fourier series expansion method, the general solution of stresses and displacements is derived out with unknown coefficients, which are further determined by using the analytical Laplace transformation method. The present solution obtained can be used as the benchmark to validate other solutions such as finite element solution for the same problem. The comparison study shows a trend of the finite element solution converging to the present one as the mesh becomes refined; however, such a finite element model is time-consuming. The influences of load distribution, geometry and material parameters on the time-dependent stress and displacement fields in the pipe are discussed detailedly.