484 research outputs found
Discontinuous modelling of strain localisation and failure
No full textThe computational simulation of failure in solids poses many challenges. A proper understanding of how structures respond under loading, both before and past the peak load, is important for safe and economical constructions. This requires numerical models for failure which are both faithful to the physical reality and mathematically well founded. A serious computational issue is that of objectivity with respect to the spatial discretisation of a problem. This requires that upon refinement of the spatial discretisation of a problem, a unique, physically meaningful result is approached. One approach to ensure objectivity with respect to spatial discretisation when simulating failure in solids is to allow displacement discontinuities in the solution. In this work, different techniques, of varying complexity, are developed to simulate displacement discontinuities which are independent of the spatial discretisation using finite elements. The different techniques are then critically evaluated. The first model examined involves adding only the effect of a displacement discontinuity to a finite element as an incompatible strain mode. This allows a traction–separation relationship to be applied at an interface and can be implemented simply in a standard finite element code. It is however shown that this type of model can be cast in an equivalent continuum format, a form which is known to be sensitive to the spatial discretisation. The second approach developed involves the addition of the Heaviside function to the underlying finite element interpolation basis. This method is based on the partition of unity concept, and allows the Heaviside function to be added locally to a finite element mesh to simulate a propagating displacement discontinuity. The approach is formulated for geometrically linear, geometrically nonlinear, quasi-static and dynamic problems. It is shown to be completely independent of the spatial discretisation. The partition of unity-based model is used also to simulate failure using a regularised strain softening model. When a critical level of inelastic deformation is reached, a displacement discontinuity is inserted. This model is better suited to modelling the entire failure process than a continuum or discontinuous model alone. Through numerical examples, it is shown that the inclusion of a displacement discontinuity during the failure process can lead to a different failure mode than for a continuum-only model
Correction to: The ‘can do, do do’ concept in COPD; quadrant interpretation, affiliation and tracking longitudinal changes
No full textFollowing publication of the original article [1], the authors identified a mistake in the author names, as both forename and initials were stated. Initially published author names: A. J. Alex van ’t Hul, E. H. Noortje Koolen, H. W. Jeroen van Hees, B. Bram van den Borst and M. A. Martijn Spruit Correct author names: Alex J. van ‘t Hul, Noortje H. Koolen, Jeroen W. van Hees, Bram van den Borst, Martijn A. Spruit. The original article has been corrected.</p
Human-automation interaction for helicopter flight: Comparing two decision-support systems for navigation tasks
No full textThis paper investigates the effects of different automation design philosophies for a helicopter navigation task. A baseline navigation display is compared with two more advanced systems: an advisory display, which provides a discrete trajectory suggestion; and a constraint-based display, which provides information about the set of possible trajectory solutions. The results of a human-in-the-loop experiment with eight pilot participants show a significant negative impact of the advisory display on pilot trajectory decision-making: out of the 16 encountered off-nominal situations across the experiment, only 6 were solved optimally. The baseline and constraint-based display both lead to better decisions, with 14 out of 16 being optimal. However, pilots still preferred the advisory display, in particular in off-nominal situations. These results highlight that even when a support system is preferred by pilots, it can have strong inadvertent negative effects on their decision-making
Efficient Multigrid based solvers for isogeometric analysis
No full textIntroduced in [1], Isogeometric Analysis (IgA) has become widely accepted in academia and industry. However, solving the resulting linear systems remains a challenging task. For instance, the condition number of the Poisson operator scales quadratically with the mesh width h, but, in contrast to standard Finite Elements, exponentially with the order of the approximation p [2]. The performance of (standard) iterative solvers thus decreases fast for higher values of p. In this talk we propose an efficient solution strategy for IgA discretizations that is based on p- multigrid techniques used both as a solver and as a preconditioner in a Krylov subspace iteration method. The approach makes use of a hierarchy of B-spline based discretizations of different approximation orders, which is in contrast to (geometric) h-multigrid methods, where a hierarchy of coarser and finer meshes is constructed. The `coarse grid' correction is determined at level p = 1, which enables us to use established solution techniques developed for low-order Lagrange finite elements. Prolongation and restriction operators are defined as mappings between arbitrary spline spaces, solely determined by the generating knot vectors, allowing us to combine coarsening in both h and p, leading to a flexible hp-multigrid. Prelimenary numerical results are presented for different two-dimensional benchmark problems on non-trivial geometries. It follows from a Local Fourier Analysis [3], that the coarse grid correction and the smoothing procedure complement each other quite well. Moreover, the obtained convergence rates indicate that p-multigrid methods have the potential to efficiently solve IgA discretizations.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Numerical Analysi
Stationary and Propagative Instabilities in Metals - A Computational Point of View
No full textCivil Engineering and Geoscience
Characterisation of fibre metal laminates under thermomechanical loadings
No full textFibre metal laminates, such as Arall or Glare, can offer improved properties compared to monolithic materials. Glare for example shows improved fatigue, residual strength, burn-through, impact and corrosion properties with respect to aluminium 2024, together with a considerable weight reduction and competitive costs. A large research program has proven the technological readiness of Glare and the fibre metal laminate has seen its application today in the primary structure of the Airbus A380 super jumbo. However, the effect of temperature on the performance of the fibre metal laminates has not been fully characterised. Differences in thermal expansion coefficients cause residual stresses after curing of the laminate. In service the temperature of the aircraft skin can vary between -55 up to 70 C due to solar radiation and convection, which will affect the thermal and mechanical properties of Glare. A detailed understanding of the behaviour of these laminates is necessary for further improvement of their performance and durability. With the increase in complexity of structures and material systems, the need for powerful design tools becomes evident. In this thesis, the thermo-mechanical behaviour of fibre metal laminates has been characterised via experimental testing and numerical modelling. Experimental tests have been performed to determine the temperature-dependent thermal and mechanical behaviour of unidirectional (UD) glass-fibre epoxy. Calculations based on these test results at room temperature and 80 C for the tension and shear stiffness of three different composite laminate lay-ups showed a good agreement with experimental test results. The UD glass-fibre epoxy data is used as input for the finite element model, together with aluminium 2024-T3 data from the literature. Glare laminates with a special lay-up have been experimentally tested to determine the effect of temperature and mechanical loadings on the laminate characteristics. The test results show that the off-axis and temperature effect can give a reduction of 24% in ultimate strength at room temperature due to off-axis loading and a further reduction of 17% at 80 C temperature. For standard Glare from the literature, where tests at elevated temperature have only been performed in fibre direction, the strength and stiffness reductions are at most 12% compared to room temperature. Numerical simulation is a very powerful tool to investigate the behaviour of materials and structures. Therefore, a thermo-mechanical finite element model, based on a solid-like shell element and including thermal expansion and heat transfer, has been developed to capture the behaviour of Glare in a fully three-dimensional state. The through-the-thickness temperature and stress distributions can thereby be determined, which allows for a straight-forward implementation of damage and plasticity models. Moreover, the solid-like shell element is ideal for thin-walled (aerospace) structures since it can have high aspect ratios without showing Poisson thickness locking, which occurs in standard continuum elements, and can have multiple layers in one element. To account for physical nonlinearities, a strain hardening model for the aluminium 2024-T3 and an orthotropic damage model for the UD glass-fibre epoxy layers in Glare are used. The strain hardening behaviour of aluminium has been modelled with a yield function based on an isotropic Von Mises plasticity formulation. An exponentially saturating hardening law has been assumed, which gives a good agreement with the experimental aluminium 2024-T3 stress-strain curve. A return-mapping algorithm is used to project the stress back onto the yield surface when the stress state violates the loading condition. The concept of continuum damage mechanics is used, with a separate damage parameter for fibre and matrix, to describe the appearance of microcracks that lead to ultimate failure. The equivalent strain measure is obtained by rewriting the yield function of the orthotropic Hoffman plasticity model into a strain-based format. The damage parameters are directly implemented into the stiffness matrix to avoid undesirable coupling terms in the damage matrix. The simulations of the shear and tensile test in transverse direction show a good fit with the experimental curves for the UD glass-fibre epoxy. The transient behaviour is captured by taking the heat capacity, inertia forces and damping into account. Park's method is used to solve the dynamic system of equations. The good performance of the thermomechanical solid-like shell element and the transient solver have been demonstrated for a single element under thermo-mechanical loadings and the snap-through of a cylindrical panel subjected to a concentrated load. Via a number of benchmark tests for practical applications the obtained numerical model is compared with the experimental test results. Bluntnotch test simulations have been performed on Glare3-3/2-0.4 and on a special Glare laminate (tested at 0, 45, 67.5, and 90 off-axis angle), which show a good agreement with experimental results. Simulations of off-axis tensile tests on a 0/90 composite, tensile tests on standard Glare laminates, and off-axis tensile tests on special Glare laminates with additional fibre layers in -45 and 45 direction, also showed a good agreement with experimental results. The thermo-mechanical solid-like shell element and the experimentally obtained material data, presented in this thesis, together create a powerful simulation tool for the effective and accurate characterisation of fibre metal laminates under thermo-mechanical loadings.Aerospace Engineerin
Gradient-dependent plasticity in numerical simulation of localization phenomena
No full textArchitectur
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