A partitioning reduced order IG-SBFEM to solve elastic/viscoelastic problems with cyclic symmetry

Purpose This research aims to advance the Isogeometric Scaled Boundary Finite Element Method (IG-SBFEM) by introducing a partitioning approach for solving elastic and viscoelastic problems with cyclic symmetry. The study seeks to mitigate the computational burden associated with eigenvalue problems by proving the block-circulant nature of the system matrices. Through partitioning, the solution scale is reduced, and the study further explores the integration of the Lagrange multiplier scheme and temporally adaptive algorithms (TPAA) to handle complex displacement constraints and viscoelastic properties, ensuring efficient computation even in cyclically symmetric structures. Design/methodology/approach The methodology centers on the development of a partitioning algorithm integrated into the Isogeometric Scaled Boundary Finite Element Method (IG-SBFEM). By leveraging the block-circulant nature of matrices under cyclic symmetry, the study reduces the solution scale of both eigenvalue and system equations. Displacement constraints are addressed through a Lagrange multiplier scheme. The approach further applies a temporally piecewise adaptive algorithm (TPAA) to convert viscoelastic problems into elastic problems, allowing efficient numerical analysis and computation for cyclically symmetric structures. Findings This study finds that the partitioning IG-SBFEM efficiently addresses elastic and viscoelastic problems with cyclic symmetry, reducing both the solution scale and computational cost. The block-circulant property of the matrices enables the decomposition of complex equations into smaller sub-problems, improving performance. Additionally, the Lagrange multiplier scheme successfully handles displacement constraints. The temporally piecewise adaptive algorithm (TPAA) further enhances efficiency by transforming viscoelastic problems into elastic equivalents. Numerical results confirm that this approach achieves accurate solutions with reduced computational effort. Originality/value The originality of this research stems from the innovative partitioning algorithm that reduces the computational burden of IG-SBFEM in elastic and viscoelastic problems with cyclic symmetry. By proving the block-circulant nature of the matrices and integrating the Lagrange multiplier scheme and TPAA, the study offers a unique approach to efficiently solve complex problems. The value of this work lies in its ability to provide accurate results with reduced computational effort, making it a valuable contribution to advanced numerical analysis techniques. Highlights (1) The first time to utilize cyclic symmetry in reduced order modelling of IG-SBFEM for elastic and viscoelastic problems. (2) Block-circulant eigenvalue and stiffness Matrices under a symmetry-adapted reference co-ordinate system. (3) Partitioning algorithms to solve eigenvalue and system equations with smaller solution scale and less computational expense. (4) No restriction on distribution of displacement constraints, cyclically symmetric or not. (5) A steady temporal solution accuracy provided by TPAA for viscoelastic problems.