Dual Boundary Element Method Approach Research Articles

Mechanical modelling of three-dimensional cracked structural components using the isogeometric dual boundary element method

The mechanical modelling of cracked structural components using Linear Elastic Fracture Mechanics (LEFM) concepts has major importance for structural integrity analysis. In addition, the Isogeometric Analysis (IGA) has recently emerged as a robust approach for analysing structural components directly from Computer-Aided Design (CAD) models. In this context, this study presents an isogeometric Dual Boundary Element Method (DBEM) formulation for the mechanical modelling of cracked three-dimensional structural components. The isogeometric formulation is based on NURBS surfaces. It was implemented regarding any polynomial orders for the basis functions. The strong singular and hypersingular integrals required by the DBEM are evaluated by the Guiggiani method. The C1 continuity is achieved at any collocation point inside the NURBS surfaces, ensuring the existence of hypersingular integrals. Consequently, discontinuous boundary elements are no longer required for the isogeometric DBEM, which enables an important reduction on the amount of collocation points at the crack surfaces. The Stress Intensity Factors (SIF) are evaluated by the displacement correlation technique. The geometrically exact description of the crack front eliminates the approximation errors related to the rotation of the displacement discontinuities with respect to the crack front local coordinate systems. Three applications involving edge and embedded cracks are presented. The isogeometric formulation provided accurate SIF results with less degrees of freedom at the crack surfaces in comparison with the conventional DBEM approach. However, the isogeometric DBEM approach has shown to be more expensive in terms of computational time.

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment 'Wendelstein 7-X'

At the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7-X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non-planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub-modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment ‘Wendelstein 7‐X’

AbstractAt the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7‐X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non‐planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub‐modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.

Three-Dimensional BEM and FEM Submodelling in a Cracked FML Full Scale Aeronautic Panel

This paper concerns the numerical characterization of the fatigue strength of a flat stiffened panel, designed as a fiber metal laminate (FML) and made of Aluminum alloy and Fiber Glass FRP. The panel is full scale and was tested (in a previous work) under fatigue biaxial loads, applied by means of a multi-axial fatigue machine: an initial through the thickness notch was created in the panel and the aforementioned biaxial fatigue load applied, causing a crack initiation and propagation in the Aluminum layers. Moreover, (still in a previous work), the fatigue test was simulated by the Dual Boundary Element Method (DBEM) in a bidimensional approach. Now, in order to validate the assumptions made in the aforementioned DBEM approach and concerning the delamination area size and the fiber integrity during crack propagation, three-dimensional BEM and FEM submodelling analyses are realized. Due to the lack of experimental data on the delamination area size (normally increasing as the crack propagates), such area is calculated by iterative three-dimensional BEM or FEM analyses, considering the inter-laminar stresses and a delamination criterion. Such three-dimensional analyses, but in particular the FEM proposed model, can also provide insights into the fiber rupture problem. These DBEM-BEM or DBEM-FEM approaches aims at providing a general purpose evaluation tool for a better understanding of the fatigue resistance of FML panels, providing a deeper insight into the role of fiber stiffness and of delamination extension on the stress intensity factors.

Thermo-mechanical crack propagation in aircraft engine vane by coupled FEM–DBEM approach

New generation jet engines are subject to severe reduced fuel consumption requirements. This usually leads to thin components in which damage issues such as thermo-mechanical fatigue, creep and crack propagation can be quite important. The combination of mechanical and thermal stresses usually leads to mixed-mode loading. Consequently, a suitable crack propagation tool must be able to predict mixed-mode crack propagation of arbitrarily curved cracks in three-dimensional space. To tackle this problem a procedure has been developed based on a combined FEM (finite element method) - DBEM (dual boundary element method) approach. Starting from a three-dimensional FEM mesh for the uncracked structure a subdomain is identified, in which crack initiation and propagation are simulated by DBEM. Such a subdomain is extracted from the FEM domain and imported, together with its boundary conditions (calculated by a previous thermal-stress FEM analysis), in a DBEM environment, where a linear elastic multiple crack growth analysis is performed. Once the crack propagation direction is determined a new crack increment can be calculated and, for the new crack front, the procedure can be repeated until failure. The proposed procedure also allows the consideration of the spectrum effects and creep effects: both conditions determine residual stresses that the crack will encounters during its propagation. The procedure has been tested on a gas turbine vane, getting sound results, and can be made fully automatic, thanks to in house made routines needed to facilitate the data exchange between the two adopted codes.

An enriched Dual Boundary Element Method for Fracture Mechanics

The direct collocation Boundary Element Method (BEM) has been enriched in the Partition of Unity sense by a set of functions known to describe the displacement field in the immediate vicinity of a crack tip. The Dual BEM approach is adopted to preclude the need for substructuring. The enrichment introduces a small number of additional degrees of freedom, and this therefore requires a corresponding number of auxiliary integral equations. The paper describes the enrichment strategies that may be employed and the results demonstrate that the enrichment provides for approximately one order of magnitude improvement in accuracy in comparison with the conventional, unenriched Dual BEM.

A two-parameter model for crack growth simulation by combined FEM–DBEM approach

This paper describes the application of a two-parameters crack growth model, based on the usage of two threshold material parameters (Δ K th and K max,th) and on the allowance for residual stresses, introduced at the crack tip by a fatigue load spectrum or by material plastic deformations. The coupled usage of finite element method (FEM) and dual boundary element method (DBEM) is proposed in order to take advantage of the main capabilities of the two methods. The procedure is validated by comparison with available experimental results, in order to assess its capability to predict the retardation phenomena, introduced by a variable load spectrum or by a plastic deformation introduced with a tool on the panel (indentation). In particular two different tests are made: the first test involve a CT specimen undergoing a load spectrum and the second one involve a dented panel undergoing a constant amplitude fatigue load. In both cases a satisfactory numerical–experimental correlation will be proved. The main advantages of the aforementioned procedure are: the simplicity of the crack growth law calibration (few constant amplitude tests are sufficient without the need for any non-physical calibration parameters), and the possibility to simulate residual stress effects on crack propagation with a simplified approach, based on linear elastic fracture mechanics.