A gradient based numerical algorithm to solve inverse dynamic viscoelastic problems of multi-variable identification. (June 2023)

• Record Type: Journal Article
• Authors: Yu, Yang; He, Yiqian; Wang, Chongshuai; Yang, Haitian
• Is Part Of: Engineering analysis with boundary elements. Volume 151(2023)
• Page Start: 686
• Page End: 706
• Publication Date: 2023-06
• Subjects: Viscoelasticity -- Inverse dynamic problem -- Multi-variable identification -- Scaled boundary finite element method (SBFEM) -- Sensitivity analysis -- Adaptive computing -- Third kind boundary condition; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2023.03.023
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: A gradient based numerical model is presented to solve inverse dynamic viscoelastic problems of multi-variable identification for the constitutive and TKBC related parameters. A recursive adaptive algorithm is developed to gain the derivatives with an accurate and stable temporal solution accuracy for different step sizes. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. A reliable platform is provided by TPAA-SBFEM to gain the solution of forward problems repeatedly required in the inverse solution process. The advantages of SBFEM in the structural analysis make the solution process of some inverse problems more efficient, such as the problem with stress singularity. Abstract: A gradient based numerical method is put forward to solve the inverse dynamic viscoelastic problem with multi-variable identification for the constitutive and TKBC (third kind boundary conditions) related parameters. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of forward problems, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the sensitivity analysis, which is able to provide a stable temporal solution accuracy for different step sizes. SBFEM (Scaled Boundary Finite Element Method) is stressed in the structural analysis with its own advantages, such as the efficient and convenient treatment of stress singularity problem and flexibility of mesh generation with polygonal elements and image based quadtree gridding. The inverse problem of identification is solved by the Levenberg-Marquardt method, and the regional inhomogeneity, crack, initial guess, location/number of measurement points, material contrast ratios, and noisy data are taken into account. Numerical examples are provided to verify the proposed approach, and the satisfactory results are achieved.