A. Portela

Dual boundary element incremental analysis of crack propagation

Abstract This paper describes an application of the dual boundary element method to the analysis of mixed-mode crack growth in linear elastic fracture mechanics. Crack-growth processes are simulated with an incremental crack-extension analysis based on the maximum principal stress criterion which is expressed in terms of the stress intensity factors. For each increment of the crack extension, the dual boundary element method is applied to perform a single-region stress analysis of the cracked structure and the J-integral technique is used to compute the stress intensity factors. When the crack extension is modelled with new boundary elements, remeshing is not required because of the single-region analysis, an intrinsic feature of the dual boundary element method. Results of this incremental crack-extension analysis are presented for several geometries. The analysis of fatigue crack-growth is introduced as a post-processing procedure on the crack-extension results and an example is presented.

Trefftz boundary element method applied to fracture mechanics

Abstract The linear elastic problem is solved by means of Trefftz functions which automatically satisfy the elasticity equations in a 2D domain. Using Kolosov–Muskhelishvili’s complex variable representation, complex potentials are expanded in power series. Trial elementary elastic fields are derived from each expansion term. The Galerkin weighted residuals formulation is used to derive the system of equations in which the unknowns are the retained expansion coefficients. For crack problems, special expansions that satisfy the zero traction condition along crack edges are used to obtain the approximating elastic field, which allow the direct determination of the stress intensity factors. Several numerical results, obtained for typical crack problems using Trefftz Boundary Element Method, are presented and compared with those published by other authors. A simple example of multiple site damage with two offset parallel cracks is also analyzed.

Programming Trefftz boundary elements

Abstract This paper is concerned with the numerical implementation of the Trefftz boundary element method, for the analysis of two-dimensional potential problems. The weighted residual formulation of the different techniques of the Trefftz boundary element method is reviewed. The relative advantages of each technique are shown, when compared with the direct Somigliana boundary element method. Computational programs for both the Trefftz techniques of point collocation and Galerkin are presented in this paper. Several examples are analysed with these two techniques. The accuracy and efficiency of the implementations described herein make the Trefftz formulation of the boundary element method ideal for the study of potential problems.

Dual Boundary Element Incremental Analysis of Crack Growth in Rotating Disc

Application of the dual boundary element method (DBEM) to the analysis of mixed-mode crack growth in rotating disc is presented. The crack growth process is simulated with an incremental crack extension based on the maximum principal stress criterion. For each increment of the extension, the DBEM is applied to perform a single region stress analysis of the cracked structure and mixed-mode J-integral is used to compute the stress intensity factors. The domain integrals containing the rotational body force terms are transformed to boundary integrals using the multiple-reciprocity method. Results of this incremental crack-extension analysis are presented for several edge crack in rotating disc.

Fluid Mechanics Applications

The application of the finite element method to fluid mechanics problems is not as advanced as it is in solid mechanics. The main reason seems to be that the finite difference method has proved very successful in solving fluid flow problems. Furthermore, the large investment of time and money made in the development of finite difference software naturally led to a reluctance to consider the application of other methods. This situation is gradually changing and the finite element method is now becoming a standard approximation tool used in the solution of fluid mechanics problems.

Solid Mechanics Applications

Mathematical modelling in Solid Mechanics uses the theory of elasticity as the fundamental generating model which is thus considered a mathematicallyexact model. Based on this exact model and considering simplifying assumptions, asymptotic models, still continuous, can be generated. These continuous asymptotic models are eventually discretized in order to obtain numerical approximate solutions.

Introduction to Maple

Maple is a symbolic computational system. This means that it does not require numerical values for all variables, as numerical systems do, but manipulates information in a symbolic or algebraic manner, maintaining and evaluating the underlying symbols, like words and sentence-like objects, as well as evaluates numerical expressions. As a complement to symbolic operations, Maple provides the user with a large set of graphic routines, numerical algorithms and a comprehensive programming language.

The Finite Element Method

Discretization is an essential engineering tool for the analysis of physical problems. Formal solutions of continuum models, defined in the first step of the mathematical modelling process, are generally not available for practical problems and, consequently discretization must be used in order to obtain an approximate solution.

Theoretical basis of boundary solutions for the linear theory of structures

where U’ is-the exact solution, L, C and D are differential operators and g, h and 1 are prescribed functions. As the set of differential equations (l)-(3) has to be zero at each point of the domain A and its boundary, it follows that: Let A be a domain and S its boundary. Consider a symmetric stress field, ab, which is assumed equilibrated by a system of surface and body forces with densities 0 and f respectively on S and in A. For the sake of simplicity, the stress field u

The dual boundary element method: Effective implementation for crack problems

is assumed to admit first derivatives everywhere in A. Therefore, ub belongs to the class of equilibrated elastic fields and satisfies the equations: