Speaker
Description
In structural modeling, adaptive techniques based on a posteriori error estimation are well accepted to simulate finite element discretizations of partial differential equations. Based on a goal-oriented a posteriori error estimation, the quality of computational results is evaluated according to the physical significance of a specific quantity. In this contribution, several new methods of error representation are presented using the errors of the primal and dual solutions to improve the accuracy and efficiency in a proposed adaptive framework of goal-oriented a posteriori estimation. These error representations are derived from different adjoint-based error models for the governing equations of an elasto-plastic primal problem and related variational local and global forms. The framework generates a balanced mesh consisting of fine, medium and coarse elements for accurate results, avoiding a numerically expensive simulation with only fine elements. The effectiveness of the different proposed error representations is illustrated by numerical examples of a perforated sheet and a CT specimen for adaptive mesh refinement, leading to an effective reduction in computational effort. Furthermore, the results obtained from the new error representations are compared with the results obtained from error representation methods in the literature.
References
[1] A. T. Simeu and R. Mahnken: Error representations for goal-oriented aposteriori error estimation in elasto-plasticity with applications to mesh adaptivity, Engineering Computations, EC-12-2023-0975.R1, (2024).
[2] R. Mahnken and A. T. Simeu: Downwind and upwind approximations for primal and dual problems of elasto-plasticity with Prandtl–Reuss typematerial laws, Computer Methods in Applied Mechanics and Engineering,Vol. 432, 117277, (2024).
