Some considerations on dynamic biem—II (original) (raw)
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Iterative coupling of BEM and FEM for nonlinear dynamic analyses
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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
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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
A BEM formulation for transient dynamic elastoplastic analysis via particular integrals
This paper presents the particular integral formulation for two (2D) and three (3D) dimensional transient dynamic elas- toplastic analyses. The elastostatic equation is used for the complementary solution. The particular integrals for displace- ment, traction and stress rates are obtained by introducing the concept of a global shape function to approximate acceleration and initial stress rate terms of the inhomogeneous equation. The Houbolt time integration scheme is used for the time-marching process. The Newton–Raphson algorithm for plastic multiplier is used to solve the system equation. The developed program is integrated with the pre- and post-processor. Numerical results for four example problems aregiven to demonstrate the validity and accuracy of the present formulation.
Engineering Analysis with Boundary Elements, 2016
A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is presented. Such strategy is based on a decomposition of the strain increment variation vector in two parts: one associated to the cumulative external loads and another associated to the current unbalanced vector, obtained from the difference of the first part and the calculated internal strain field distribution, during the iterative process. This approach makes the algorithm generic enough to deal with different control methods that governs the progression of the non-linear analysis. Also, a unified constitutive modelling framework for a single loading function is used to provide the material constitutive informations required by the solution strategy, which permits the implementation of a very comprehensive series of models in an independent way. However, only local models were treated. To demonstrate the efficiency and versatility of the methodology, some numerical examples are presented.
Adaptive and Dynamic Analysis Using the Boundary Element Method
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Inelastic transient dynamic analysis of three-dimensional problems by BEM
International Journal for Numerical Methods in Engineering, 1990
A direct Boundary Element formulation and its numerical implementation for inelastic transient dynamic analysis of three-dimensional solids is presented. The formulation is based on an initial stress approach and is the first ever of its kind in the field of the Boundary Element Method. This formulation employs the Navier–Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution and the Divergence theorem, together with Kinematical and Constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity. The boundary integral equations are cast in an incremental form, in which elastoplastic relations of the incremental type are used for the material description. These equations are then solved using a time-stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations. Higher order shape functions are used to approximate the field quantities in space as well as in time. Finally, the applicability of this methodology is demonstrated by presenting a few example problems.
A NUMERICAL CONVERGENCE STUDY OF THE RELAXED CONTINUITY APPROACH FOR SELF-REGULAR TRACTION-BIE
Self-regular BEM algorithm avoids Cauchy principal value or Hadamard finite part evaluations as regularization is applied prior to discretization. Smoothness requirement for traction BIE is more stringent (C 1,α for displacement). Boundary discretization into standard continuous elements leads to a loss of the smoothness required. Relaxation of the smoothness requirement has been proposed using C 0 continuous elements with collocation points at the intersection between elements. Some researchers claim that this procedure cannot be theoretically justified. Interpolation of displacement tangential derivative an 'relaxed continuity' hypothesis are pointed out as possible sources of error introduced on the discretization of self-regular traction-BIE. Discontinous elements are implemented in order to verify the possible sources of error. Such elements allow the split of these sources of error. Numerical results show that the 'relaxed continuity' hyphotesis seems to be the dominant source of error. Apparently the smoothness requirement for the self-regular traction-BIE must be preserved to guarantee converge.