Dynamics of structures

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

This article presents an overview on poroelastodynamic models and some analytical solutions. A brief summary of Biot’s theory and on other poroelastic dynamic governing equations is given. There is a focus on dynamic formulations and the quasi-static case is not considered at all. Some analytical solutions for special problems, fundamental solutions, and Green’s functions are discussed. The numerical realization with two different methodologies, namely the Finite Element Method and the Boundary Element Method, is reviewed. Preprint No 3/2008 Institute of Applied Mechanics

Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods

Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Green's functions, symmetric Galerkin formulations, boundary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for students, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review.

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Recent Advances and Emerging Applications of the Boundary Element Method

Experimental and numerical analyses of vibrations induced by high-speed trains on the Córdoba–Málaga line

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.

Iterative coupling of BEM and FEM for nonlinear dynamic analyses

A novel family of explicit time marching techniques for structural dynamics and wave propagation models

A simple and effective new family of time marching procedures for dynamics

An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid–solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, 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 non-linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non-linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain. Copyright © 2005 John Wiley & Sons, Ltd.

Delfim Soares

Papers

Iterative coupling of BEM and FEM for nonlinear dynamic analyses

A novel family of explicit time marching techniques for structural dynamics and wave propagation models

A simple and effective new family of time marching procedures for dynamics

Efficient non‐linear solid–fluid interaction analysis by an iterative BEM/FEM coupling

Explicit time-domain approaches based on numerical Green's functions computed by finite differences - The ExGA family