A scaled boundary polygon formulation for elasto-plastic analyses

This study presents a novel scaled boundary polygon formulation to model elasto-plastic material responses in structures. The polygons have flexible mesh generation capabilities and are more accurate than standard finite elements, especially for problems with cracks and notches. Shape functions of arbitrary n-sided polygons are constructed using the scaled boundary finite element method. These shape functions are conforming and linearly complete. When modeling a crack, strain singularities are analytically modeled without enrichment. Standard finite element procedures are used to formulate the stiffness matrix and residual load vector. The nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function. The stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present. Standard nonlinear equation solvers e.g. the modified Newton–Raphson algorithm are used to obtain the nonlinear response of the structure. The proposed formulation is validated using several numerical benchmarks

Bef analogy for axisymmetrically loaded cylindrical shells

A simple finite element analysis based on an analogy with the theory of beams on elastic foundation is developed for closed circular cylindrical shells with arbitrarily varying wall thickness subjected to axisymmetric radial loading which may vary in the longitudinal direction. The foundation modulus and the beam flexural rigidity are replaced by appropriate parameters pertaining to the shell under consideration. By using the proposed technique, the resulting number of stiffness equations is relatively quite small, and this makes it attractive for implementation on microcomputers.</p

Crack propagation modeling with scaled boundary polygons

Crack propagation is modelled using scaled boundary polygons. The polygons discretise the computational domain and can be of any number of sides, leading to more flexible mesh generation. The scaled boundary finite element method is used to construct shape functions of the polygon elements. These shape functions form a partition of unity and are linearly complete. They can accurately model any kind of stress singularity without local mesh refinement or asymptotic enrichment functions. The scaled boundary shape functions enable the method to be further developed to model the response of heterogeneous and nonlinear materials. As the polygons can be of any number of sides, simple re-meshing algorithms can be devised to model crack propagation. Two numerical benchmarks are modeled to illustrate the salient features of the scaled boundary polygons

Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons

In this paper, the recently developed scaled boundary polygons formulation for the evaluation of stress intensity factors in functionally graded materials is extended to elasto-dynamics. In this approach, the domain is discretized using polygons with arbitrary number of sides. Within each polygon, the scaled boundary polygon shape functions are used to interpolate the displacement field. For uncracked polygons, these shape functions are linearly complete. In a cracked polygon, the shape functions analytically model the stress singularity at the crack tip. Therefore, accurate dynamic stress intensity factors can be computed directly from their definitions. Only a single polygon is necessary to accurately compute the stress intensity factors. To model the material heterogeneity in functionally graded materials, the material gradients are approximated locally in each polygon using polynomial functions. This leads to semi-analytical expressions for both the stiffness and the mass matrices, which can be integrated straightforwardly. The versatility of the developed formulation is demonstrated by modeling five numerical examples involving cracked functionally graded specimens subjected to dynamic loads. © 2014 Elsevier Ltd

Polygon scaled boundary finite elements for crack propagation modelling

An automatic crack propagation modelling technique using polygon elements is presented. A simple algorithm to generate a polygon mesh from a Delaunay triangulated mesh is implemented. The polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are computed directly from their definitions without any nodal enrichment functions. An automatic remeshing algorithm capable of handling any n-sided polygon is developed to accommodate crack propagation. The algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths. The efficiency of the polygon SBFEM in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack. Four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features. The predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature. © 2012 John Wiley & Sons, Ltd

Crack propagation modelling in functionally graded materials using scaled boundary polygons

A recently developed scaled boundary finite element formulation that can model the response of functionally graded materials is further developed to model crack propagation in two-dimensions. This formulation can accurately model the stress singularity at the crack tip in heterogeneous materials. The asymptotic behaviour at the crack tip is analytically represented in the scaled boundary shape functions of a cracked polygon. This enables accurate stress intensity factors to be computed directly from their definitions. Neither local mesh refinement nor asymptotic enrichment functions are required. This novel formulation can be implemented on polygons with an arbitrary number of sides. When modelling crack propagation, the remeshing process is more flexible and leads to only minimal changes to the global mesh structure. Six numerical examples involving crack propagation in functionally graded materials are modelled to demonstrate the salient features of the developed method

Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique

An efficient methodology for automatic dynamic crack propagation simulations using polygon elements is developed in this study. The polygon mesh is automatically generated from a Delaunay triangulated mesh. The formulation of an arbitrary n-sided polygon element is based on the scaled boundary finite element method (SBFEM). All kind of singular stress fields can be described by the matrix power function solution of a cracked polygon. Generalised dynamic stress intensity factors are evaluated using standard finite element stress recovery procedures. This technique does not require local mesh refinement around the crack tip, special purpose elements or nodal enrichment functions. An automatic local remeshing algorithm that can be applied to any polygon mesh is developed in this study to accommodate crack propagation. Each remeshing operation involves only a small patch of polygons around the crack tip, resulting in only minimal change to the global mesh structure. The increase of the number of degrees-of-freedom caused by crack propagation is moderate. The method is validated using four dynamic crack propagation benchmarks. The predicted dynamic fracture parameters show good agreement with experiment observations and numerical simulations reported in the literature. © 2013 Elsevier Ltd

Automatic dynamic crack propagation modeling using polygon scaled boundary finite elements

This study develops a simple and efficient methodology for automatic dynamic crack propagation modeling in structures. It uses high order, arbitrary n-sided polygon elements that are constructed within the scaled boundary finite element framework. Each polygon is treated as a scaled boundary finite element subdomain and their governing equations of equilibrium are assembled using standard finite element procedures. Polygon meshes are automatically generated from a Delaunay triangulated mesh. This method inherits all the positive characteristics of the scaled boundary finite element method. Orders of singularities of any kind can be accurately represented in a unified manner by generalized stress intensity factors to evaluate the crack propagation criterion without dense meshes around the crack tip, special purpose elements or nodal enrichment functions. Crack propagation is efficiently modeled using a simple, yet flexible automatic local remeshing algorithm that is linked to the pre-processing module of a commercial finite element package and can be applied to any polygon mesh. Remeshing involves only polygons around the crack and only minimally changes the global mesh structure. Application of the methodology to model dynamic crack propagation problems is demonstrated by two numerical examples. It is found that the predicted dynamic fracture parameters e.g. dynamic stress intensity factor histories, crack velocity histories, crack length histories and crack paths show good agreement with experiment observations and numerical simulations reported in the literature. © 2013 Taylor & Francis Group.From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 201