Bing Tie

Adaptive strategy for transient/coupled problems applications to thermoelasticity and elastodynamics

Abstract The interest in adaptive strategies for the finite element method is growing at a fast pace. Researchers are now fully convinced that this should be part of any numerical modelling and try to incorporate the methodology to their problems. Even the industry begins to require such an approach to increase the quality of the numerical results and to get more effective analyses to increase the ratio between computer costs and target error level. The adaptive strategy has first been applied to linear elliptic problems, e.g. linear infinitesimal elasticity [1,6,17,11]). It is now enlarged to nonlinear and transient problems [12–16,5,10,17]. It is the aim of this paper to illustrate the application of the technique of residuals to adaptive refinement of coupled problems and to elastic wave propagation. There are many other approaches to a posteriori error estimations. Some of them appear to be difficult to extend to coupled and transient problems. It is believed that the residual approach is versatile enough to be easily applied to more complex problems. The two basic ideas used here rely on a space-time Galerkin formulation which provides a variational formulation of the error with respect to the residual, and the adjoint state which gives an upper bound of the error by the norm of the residuals weighted by some power of h and Δ t , extending the ideas of Eriksson et al. [5].

Une approche intégrée pour le calcul adaptatif par éléments finis

Abstract.This paper presents an adaptive finite element approach, which aims to integrate in a single software the a posteriori error estimates, the mesh adaptation and the multi-mesh transfer operators and solvers. The proposed residual method for the error estimates proves to be sufficiently general to treat a large class of mechanical problems. Two techniques of mesh adaptation are considered: the h method which takes advantage of the h hierarchical FEs; the remeshing technique coupled with an exact CAD description of structures. Several numerical examples are presented and emphasise the efficiency of our approach

A combined mesh and model adaptive strategy for the scaling issues in the numerical modelling of the ductile damage in thin panels

Abstract In this paper, a combined model and mesh adaptive computational approach is presented for the numerical modelling of ductile damage in thin panels. The aim of such a strategy is to be able to compute with the finite element techniques, the damage tolerance of large structures, such as a fuselage, in a fully coupled way, taking into account the multiscale character of the problem. In a sole computation, both global structural features at the macroscale level––such as fasteners, stiffeners and joint configuration––and a realistic material damage behaviour at the microscale level are treated in a coherent way.

Adaptive computation for elastic wave propagation in plate/shell structures under moving loads

An adaptive remeshing method tailored to computations for elastic wave propagation is proposed and its application to the elastic wave propagation in plates or shells under moving loads is presented. The method is defined within the framework of the space-time discontinuous Galerkin method, which is particularly suitable for dealing with adaptive meshes that change in time. An a priori theoretical wave propagation analysis is done to determinate an appropriate element size, then the mesh adaption strategy consists of refining finite elements according to this size in zones where local unbalanced residuals are large. The plate/shell structures are modelled with Mindlin kinematics and the dispersive phenomenon of bending waves is considered. The pertinence of the Kirchhoff-Love and Mindlin kinematical models with respect to frequency ranges and plate/shell thickness is discussed. Numerical examples are given to illustrate the interest of the adaptive method.

Unstable and limited crack propagation

We consider in this paper the unstable and limited extension of brittle cracks when they initiate near or in local brittle zones and extend through them towards tougher material zones. Our aim is to predict their arrest and in this case, one observes the so-called “pop-in” phenomenon. We use the cohesive zone models as constitutive law of brittle cracks, which are numerically modelled using interface-type elements. Non-linear solvers including loading step adaptive strategy are developed, that is necessary to overcome convergence difficulties during the pop-in. Some numerical aspects specifically related to the pop-in modelling are discussed. Parametric studies on CT specimens are carried out to point out the influential numerical, plastic and fracture parameters. As an example, the yield strength mismatch between the local brittle zone and the tougher material plays a very important role on the pop-in phenomenon and makes its modelling dependent upon the element size at the crack-tip.

Adaptive time discontinuous Galerkin method for numerical modelling of wave propagation in shell and 3D structures

This paper presents an adaptive time discontinuous Galerkin method tailored to the numerical modelling of the wave propagation phenomena through shell and 3D structures. To achieve a reliable and efficient numerical implementation, several important computational issues concerning adaptive computation are discussed, namely the variable transfer between unmatched adaptively refined finite element meshes and the improvement of the convergence of the implicit dynamic solver by using a frequency dependent relaxation coefficient. Numerical examples of large-sized engineering structures are given to illustrate the interest and efficiency of the presented method.

Wave Propagation in Orthotropic Elastic Shells: Theoretical and Numerical Modeling

Shell type structures are used in a wide variety of industrial components, especially in automotive or aeronautic industries. A full understanding and predictive modeling of elastic waves propagation through those structures can be of great importance at their design stage for several reasons, such as the noise reduction in a vehicle or the control of high energy shock waves triggered by pyrotechnic cut in a space launcher. This paper deals with the theoretical and numerical modeling of elastic wave propagation in shells. The aim is to discuss the relevance of theoretical models and to develop appropriate and efficient numerical tools.