Some considerations on dynamic biem—II (original) (raw)

Engineering Fracture Mechanics, 1984

Ahstraet-In Part I of this rePott, the theoretical and numerical fund~en~ls of BIEM techniques in real transformed dynamic are presented. Interesting remarks on how the numerical integrations have been done, are pointed out in the method. In Part II, to be published in a detailed paper, numerical results for impact problems obtained by BIE Method, through a dynamic program of general application, will be shown.

Iterative coupling of BEM and FEM for nonlinear dynamic analyses

Computational Mechanics, 2004

The present work deals with the iterative coupling of boundary element and finite element methods. First, the domain of the original problem is subdivided into two subdomains, which are separately modeled by the FEM and BEM. Thus the special features and advantages of the two methodologies can be taken into account. Then, prescribing arbitrary transient boundary conditions, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local nonlinearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the nonlinear system. The procedure turns out to be very efficient. Moreover, a special formulation allows taking into account different durations of the time steps in each subdomain.

A Boundary-only BEM For Linear And Nonlinear Problems

WIT transactions on modelling and simulation, 1998

In this paper a boundary-only BEM is developed for solving nonlinear problems or linear ones, for which the fundamental solution can not be established The presented method is based on the analog equation method (AEM). According to this method the governing equation is replaced by an equivalent nonhomogeneous linear one with known fundamental solution. The solution of the substitute equation is obtained as a sum of the homogeneous solution and a particular one of the nonhomogeneous. The nonhomogeneous term, which is an unknown fictitious domain source distribution, is approximated by a truncated series of radial base functions. Then, using BEM the field function and its derivatives involved in the governing equation are expressed in terms of the unknown series coefficients, which are established by collocating the equation at discrete points in the interior of the domain. Thus, the presented method becomes a boundary-only method in the sense that only boundary discretization is required. The additional collocation points inside the domain do not spoil the pure BEM character of the method. Numerical results for certain linear and nonlinear problems are presented, which validate the effectiveness and the accuracy of the proposed method.

Numerical modelling in BIM 3 . 1 . Overview

2019

BIM is applied as modern database for civil engineering. Its recent development allows to preserve both structure geometrical and analytical information. The analytical model described in the paper is derived directly from BIM model of a structure automatically but in most cases it requires manual improvements before being sent to FEM software. Dynamo visual programming language was used to handle the analytical data. Authors developed a program which corrects faulty analytical model obtained from BIM geometry, thus providing better automation for preparing FEM model. Program logic is explained and test

An overview of approaches for the stable computation of hybrid BiCG methods

Applied Numerical Mathematics, 1995

It is well known that BiCG can be adapted so that the operations with A T can be avoided, and hybrid methods with computational complexity almost similar to BiCG can be constructed in a further attempt to improve the convergence behavior. Examples of this are CGS, Bi-CGSTAB, and BiCGstab(l). In many applications, the speed of convergence of these methods is very dependent on the incorporated BiCG process. The accuracy of the iteration coefficients of BiCG depends on the particular choice of the hybrid method. We will discuss the accuracy of these coefficients and how this affects the speed of convergence. We will show that hybrid methods exist which have better accuracy properties. This may lead to faster convergence and more accurate approximations. We also discuss look-ahead strategies for the determination of appropriate values for l in BiCGstab(l). These strategies are easily applied for the hybrid part, in contrast to similar techniques for the BiCG part (but of course they do not solve the breakdown problems of the BiCG part).

Blended implicit methods for the numerical solution of DAE problems

Journal of Computational and Applied Mathematics, 2006

Recently, a new approach for solving the discrete problems, generated by the application of block implicit methods for the numerical solution of initial value problems for ODEs, has been devised [L. Brugnano, Blended block BVMs (B 3 VMs): a family of economical implicit methods for ODEs, J. Comput. Appl. Math. 116 (2000) 41-62; L. Brugnano, C. Magherini, Blended implementation of block implicit methods for ODEs, Appl. Numer. Math. 42 (2002) 29-45; L. Brugnano, D. Trigiante, Block implicit methods for ODEs, in: D. Trigiante (Ed.), Recent Trends in Numerical Analysis, Nova Science Publishers, NewYork, 2001, pp. 81-105]. This approach is based on the so-called blended implementation of the methods, giving corresponding blended implicit methods. The latter have been implemented in the computational code BiM [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164-165 (2004) 145-158]. Blended implicit methods are here extended to handle the numerical solution of DAE problems, resulting in a straightforward generalization of the basic approach.

Solution methods for dynamic and non-linear finite element analysis

1981

The solution of large generalized eigenvalue problems arising in dynamic and in buckling analysis of discrete parameter structural systems has attracted much attention during the last few years (1,3,4,14). The most important eigenvalue problem arising in dynamic analysis is the calculation of the lowest eigenvalues

Evaluation of non-singular BEM algorithms for potential problems

Journal of The Brazilian Society of Mechanical Sciences and Engineering, 2009

Two non-singular boundary element method (BEM) algorithms for two-dimensional potential problems have been implemented using isoparametric quadratic, cubic and quartic elements. The first one is based on the self-regular potential boundary integral equation (BIE) and the second on the self-regular flux-BIE. The flux-BIE requires the C1,α continuity of the density functions, which is not satisfied by the standard isoparametric elements. This requirement is remedied by adopting the relaxed continuity strategy. The self-regular flux-BIE has presented some poor and oscillatory results, mainly with continuous quadratic elements. This odd behavior has completely disappeared when discontinuous elements, which satisfy the continuity requirement, were applied, and this suggests that the 'relaxed continuity hypothesis' seems to be the main cause of numerical errors in the implementation of the self-regular flux-BIE. On the other side, the potential algorithm has shown very reliable solutions.