Identification of the variable characteristics of a functionally graded elastic pipe with voids

Using the Cowin-Nunziato model, a coefficient inverse problem for inhomogeneous poroelastic bodies is formulated, and operator equations of the 1st kind for its solution are derived. As an example, an inverse problem for a functionally graded elastic pipe with voids is considered using additional information measured in the domain of transient loading. To solve the direct transient problem, a combined method is used: transition to the Laplace transform space, followed by solution of the boundary value problem using the shooting method and inversion using an expansion in shifted Legendre polynomials. The solution to the direct problem was verified by comparing it with the solution obtained in the finite element package FlexPDE for a homogeneous pipe. The influence of the heterogeneity laws of the Lamé moduli, coupling modulus, pore diffusion modulus, density, and pore stiffness modulus on the radial displacement was investigated. For reconstruction of physical and mechanical characteristics the iteration approach is applied. Two methods discretization of operator equations (a collocation method and a projection method) are proposed. The initial approximation is defined among the constants as the average of the maximum and minimum values of the material properties. Refinement of physical and mechanical characteristics in projection method was carried out in stages: (1) among constants; (2) linear functions; (3) quadratic functions. Computational experiments were conducted to reconstruct variable properties both at internal points of the pipe and in the class of power functions. A comparative analysis of the effectiveness of the proposed discretization schemes is performed.