Equilibrated patch recovery for accurate evaluation of upper error bounds in quantities of interest

in ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference (2012)

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result ... [more ▼]

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result relevant for design purposes (e.g. the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems,⋯). In general, residual-based error estimators have been used to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this work, we propose a novel a posteriori recovery technique to obtain an upper error bound of the QoI. We use a recovery procedure based on the superconvergent patch recovery (SPR) technique to obtain nearly statically admissible recovered stress fields for the primal and dual problems. This recovery technique was previously used to obtain upper bounds of the error in energy norm and has been used in this paper to obtain a computable version of the upper bound for the quantity of interest. [less ▲]

Equilibrium in capacitated network models with queueing delays, queue-storage, blocking back and control

in Procedia Social and Behavioral Sciences (2013), 80

This paper considers a steady-state, link-based, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queuing delays and explicit bounds on queue ... [more ▼]

This paper considers a steady-state, link-based, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queuing delays and explicit bounds on queue storage capacities. The (spatial queueing) model at the heart of this equilibrium model takes account of the space taken up by queues both when there is no blocking back and also when there is blocking back. The paper shows in theorem 1 that a feasible traffic assignment model has an equilibrium solution provided prices are used to impose capacity restrictions and utilises this result to show that there is an equilibrium with the spatial queueing model, provided queue-storage capacities are sufficiently large. Other results are obtained by changing the variables and sets in theorem 1 suitably. These results include: (1) existence of equilibrium results (in both a steady state and a dynamic context) which allow signal green-times to respond to prices and (2) an existence of equilibrium result which allow signal green-times to respond to spatial queues; provided this response follows the P0 control policy in Smith (1979, 1987). These results show that under certain conditions the P0 control policy maximises network capacity. The spatial queueing model is illustrated on a simple network. Finally the paper includes elastic demand; this is necessary for long-run evaluations. Each of the steady state models here may be thought of as a stationary solution to the dynamic assignment problem either with or without blocking back. [less ▲]

Equilibrium models in multimodal container transport systems

in Flexible Services and Manufacturing Journal (2017), 29

Ermüdungseigenschaften des Wabenkerns von sandwichpaneelen aus Aluminium

Doctoral thesis (2013)

In comparison to their weight, honeycomb composite structures have a high bending stiffness, which makes them very suited for every application where little weight is important, like airplanes, railway ... [more ▼]

In comparison to their weight, honeycomb composite structures have a high bending stiffness, which makes them very suited for every application where little weight is important, like airplanes, railway-cars and vehicles. These structures are subjected to cyclic loading. The sandwich panels consist of two thin and stiff aluminium face sheets, which are bonded to a thick and lightweight aluminium honeycomb core. The shear stresses in the core of these structures depend strongly on the angle of the load application, because the core is not homogeneous. The distribution and the level of the shear stresses are investigated using analytical calculations. The load direction which induces highest stresses in the honeycomb core is derived. This direction is not the W-direction, which is the most compliant one. In literature, there are few fatigue properties of the honeycomb core described. The fatigue properties of the core are investigated in this work using the finite element method and experiments. The experimental investigations consist of three-point bending tests, pulsating roller tests, Food-Cart Roller tests and several tests on real components. Depending on the load application, the honeycomb core fails either through core indentation or shear failure. Several fatigue tests were carried out at constant load amplitude and the failure mode is investigated. The sandwich structures were modeled with the ANSYS finite element software. The number of elements is reduced by replacing the honeycomb core with a homogeneous core with orthotropic properties. In order to get the stresses in the honeycomb core at the critical location, a submodel was created. In this work, some equations are derived in order to calculate the real shear stresses from the shear stresses of the homogeneous core. In addition, imperfections are included in the model. Furthermore, buckling analyses were used to examine core indentation failure. Based on these simulations, both failure modes described above can be explained. Core indentation occurs, when the honeycomb cells are buckling due to the load application. The buckling of the cells can be avoided by using a smoother load application. In this case, the core fails in the three-point bending test by shear failure. The fatigue life of the examined specimens is successfully approximated in this manuscript, with the lifetime analysis being based on the FKM-guideline. Every simulation is validated by experimental results. [less ▲]

Error estimation and error bounding in energy norm based on a displacement recovery technique

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that ... [more ▼]

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that, one can also obtain a recovered displacement field from the FE displacements. Herein, we describe a superconvergent patch recovery of the displacement field which considers the local fulfilment of boundary and internal equilibrium equations, Dirichlet constraints and, for singular problems, the splitting of the displacement and stress fields into singular and smooth parts. Numerical tests using problems with known analytical solution have been carried out to validate the proposed technique for error estimation and error bounding in energy norm and quantities of interest. [less ▲]

Error estimation and space-time adaptivity for the isogeometric analysis of transient structural dynamics

Scientific Conference (2016, April 01)

This paper presents a new adaptive scheme for the error-controlled simulation of transient dynamics problem. We rely on spline bases for the higher-order spatial description of our kinematic fields. Local ... [more ▼]

This paper presents a new adaptive scheme for the error-controlled simulation of transient dynamics problem. We rely on spline bases for the higher-order spatial description of our kinematic fields. Local adaptivity is performed by employing a hierarchical T-mesh technology, in combination with geometry independent field approximation. The Newmark algorithm is chosen to solve the semidiscrete equation of motion. We will present some simple local error estimates to drive the adaptivity, and show how we can ensure that the mechanical energy of conservative systems is preserved during the refinement process. [less ▲]

Error estimation in quantities of interest for XFEM using recovery techniques

in Yang, Z J (Ed.) 20th UK National Conference of the Association for Computational Mechanics in Engineering (ACME) (2012)

Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation

in Computer Methods in Applied Mechanics and Engineering (2017), 318

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique ... [more ▼]

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique (Duflot and Bordas, 2008) is used to quantify the interpolation error. Based on this error distribution, four strategies relying on two different mesh optimality criteria are compared. The first aims at homogenizing the error distribution. The second minimizes the total number of elements given a target global error level. We study the behaviour of these criteria in the context of cracks treated by an X-FE approach. In particular, we investigate the convergence rates at the element-level depending its enrichment type. We conclude on the most suitable refinement criterion and propose and verify a strategy for mesh adaptation on 3D damage tolerance assessment problems. [less ▲]

Estimación precisa del error en magnitudes de interés mediante técnicas de recovery con equilibrio local

in Congress on Numerical Methods in Engineering (2011)

Estimating fibres' material parameter distributions from limited data with the help of Bayesian inference

in European Journal of Mechanics. A, Solids (2019), 75

Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect ... [more ▼]

Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect the structural behaviours of these discrete structures: geometrical randomness and material randomness. Identifying the material randomness is an experimentally demanding task, because many small fibres, yarns or struts need to be tested, which are not easy to handle. To avoid the testing of hundreds of constituents, this contribution proposes an identification approach that only requires a few dozen of constituents to be tested (we use twenty to be exact). The identification approach is applied to articially generated measurements, so that the identified values can be compared to the true values. Another question this contribution aims to answer is how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks. We therefore also study the effect of the identified material randomness to that of the actual material randomness for three types of structures; each with an increasing level of geometrical randomness. [less ▲]