A polytree-based adaptive approach to limit analysis of cracked structures

• Published in: Computer methods in applied mechanics and engineering Vol. 313; pp. 1006 - 1039
• Main Authors: Nguyen-Xuan, H., Nguyen-Hoang, Son, Rabczuk, T., Hackl, K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2017; Elsevier BV
• Subjects: Accuracy; Adaptivity; Alloys; Bubbles; Cost analysis; Cost engineering; Finite element method; Fracture; Incompressibility; Limit analysis; Locking; Mathematical analysis; Plasticity; Polytree; Solid mechanics; Adaptivity; Fracture; Limit analysis; Incompressibility; Polytree; Plasticity
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.09.016

We in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures. The key idea is to develop a general refinement algorithm based on a so-called polytree mesh structure. The method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones, which are considered as special cases. Also, polytree meshes are conforming and can be regarded as a generalization of quadtree meshes. For the aim of this paper, we restrict our main interest in plane-strain limit analysis to von Mises-type materials, yet its extension to a wide class of other solid mechanics problems and materials is completely possible. To avoid volumetric locking, we propose an approximate velocity field enriched with bubble functions using Wachspress coordinates on a primal-mesh and design carefully strain rates on a dual-mesh level. An adaptive mesh refinement process is guided by an L2-norm-based indicator of strain rates. Through numerical validations, we show that the present method reaches high accuracy with low computational cost. This allows us to perform large-scale limit analysis problems favorably. •We propose a novel adaptive scheme for limit analysis of cracked structures.•The method relies on a volumetric locking-free polygonal finite element formulation.•An adaptive strategy is guided by the L2-norm-based indicator of strain rates.•A novel polytree date structure over polygons is addressed.•The present approach reaches high accuracy with low computational cost.