217 research outputs found
Accurate prediction of melt pool shapes in laser powder bed fusion by the non-linear temperature equation including phase changes - isotropic versus anisotropic conductivity
In this contribution, we validate a physical model based on a transient
temperature equation (including latent heat) w.r.t. the experimental set
AMB2018-02 provided within the additive manufacturing benchmark series,
established at the National Institute of Standards and Technology, USA. We aim
at predicting the following quantities of interest: width, depth, and length of
the melt pool by numerical simulation and report also on the obtainable
numerical results of the cooling rate. We first assume the laser to posses a
double ellipsoidal shape and demonstrate that a well calibrated, purely thermal
model based on isotropic thermal conductivity is able to predict all the
quantities of interest, up to a deviation of maximum 7.3\% from the
experimentally measured values.
However, it is interesting to observe that if we directly introduce, whenever
available, the measured laser profile in the model (instead of the double
ellipsoidal shape) the investigated model returns a deviation of 19.3\% from
the experimental values. This motivates a model update by introducing
anisotropic conductivity, which is intended to be a simplistic model for heat
material convection inside the melt pool. Such an anisotropic model enables the
prediction of all quantities of interest mentioned above with a maximum
deviation from the experimental values of 6.5\%.
We note that, although more predictive, the anisotropic model induces only a
marginal increase in computational complexity
Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes
In the present work we introduce a complete set of algorithms to efficiently
perform adaptive refinement and coarsening by exploiting truncated hierarchical
B-splines (THB-splines) defined on suitably graded isogeometric meshes, that
are called admissible mesh configurations. We apply the proposed algorithms to
two-dimensional linear heat transfer problems with localized moving heat
source, as simplified models for additive manufacturing applications. We first
verify the accuracy of the admissible adaptive scheme with respect to an
overkilled solution, for then comparing our results with similar schemes which
consider different refinement and coarsening algorithms, with or without taking
into account grading parameters. This study shows that the THB-spline
admissible solution delivers an optimal discretization for what concerns not
only the accuracy of the approximation, but also the (reduced) number of
degrees of freedom per time step. In the last example we investigate the
capability of the algorithms to approximate the thermal history of the problem
for a more complicated source path. The comparison with uniform and
non-admissible hierarchical meshes demonstrates that also in this case our
adaptive scheme returns the desired accuracy while strongly improving the
computational efficiency.Comment: 20 pages, 12 figure
Patch-wise Quadrature of Trimmed Surfaces in Isogeometric Analysis
This work presents an efficient quadrature rule for shell analysis fully
integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models
may consist of trimmed parts such as holes, intersections, cut-offs etc.
Therefore, IGA should be able to deal with these models in order to fulfil its
promise of closing the gap between design and analysis. Trimming operations
violate the tensor-product structure of the used Non-Uniform Rational B-spline
(NURBS) basis functions and of typical quadrature rules. Existing efficient
patch-wise quadrature rules consider actual knot vectors and are determined in
1D. They are extended to further dimensions by means of a tensor-product.
Therefore, they are not directly applicable to trimmed structures. The herein
proposed method extends patch-wise quadrature rules to trimmed surfaces.
Thereby, the number of quadrature points can be signifficantly reduced.
Geometrically linear and non-linear benchmarks of plane, plate and shell
structures are investigated. The results are compared to a standard trimming
procedure and a good performance is observed
Non-prismatic Timoshenko-like beam model
The present paper combines an effective beam theory with a simple and accurate numerical technique opening the door to the prediction of the structural behavior of planar beams characterized by a continuous variation of the cross-section geometry, that in general deeply influences the stress distribution and, therefore, leads to non-trivial constitutive relations. Accounting for these peculiar aspects, the beam theory is described by a mixed formulation of the problem represented by six linear Ordinary Differential Equations (ODEs) with non-constant coefficients depending on both the cross-section displacements and the internal forces. Due to the ODEs complexity, the solution can be typically computed only numerically also for relatively simple geometries, loads, and boundary conditions; however, the use of classical numerical tools for this problem, like a (six-field) mixed finite element approach, might entail several issues (e.g., shear locking, ill-conditioned matrices, etc.). Conversely, the recently proposed isogeometric collocation method, consisting of the direct discretization of the ODEs in strong form and using the higher-continuity properties typical of spline shape functions, allows an equal order approximation of all unknown fields, without affecting the stability of the solution. This makes such an approach simple, robust, efficient, and particularly suitable for solving the system of ODEs governing the non-prismatic beam problem. Several numerical experiments confirm that the proposed mixed isogeometric collocation method is actually cost-effective and able to attain high accuracy
Computational methods in cardiovascular mechanics
The introduction of computational models in cardiovascular sciences has been
progressively bringing new and unique tools for the investigation of the
physiopathology. Together with the dramatic improvement of imaging and
measuring devices on one side, and of computational architectures on the other
one, mathematical and numerical models have provided a new, clearly
noninvasive, approach for understanding not only basic mechanisms but also
patient-specific conditions, and for supporting the design and the development
of new therapeutic options. The terminology in silico is, nowadays, commonly
accepted for indicating this new source of knowledge added to traditional in
vitro and in vivo investigations. The advantages of in silico methodologies are
basically the low cost in terms of infrastructures and facilities, the reduced
invasiveness and, in general, the intrinsic predictive capabilities based on
the use of mathematical models. The disadvantages are generally identified in
the distance between the real cases and their virtual counterpart required by
the conceptual modeling that can be detrimental for the reliability of
numerical simulations.Comment: 54 pages, Book Chapte
Combining the Morris Method and Multiple Error Metrics to Assess Aquifer Characteristics and Recharge in the Lower Ticino Basin, in Italy
Groundwater flow model accuracy is often limited by the uncertainty in model
parameters that characterize aquifer properties and aquifer recharge. Aquifer
properties such as hydraulic conductivity can have an uncertainty spanning
orders of magnitude. Meanwhile, parameters used to configure model boundary
conditions can introduce additional uncertainty. In this study, the Morris
Method sensitivity analysis is performed on multiple quantities of interest to
assess the sensitivity of a steady-state groundwater flow model to uncertain
input parameters. The Morris Method determines which of these parameters are
less influential on model outputs. Uninfluential parameters can be set constant
during subsequent parameter optimization to reduce computational expense.
Combining multiple quantities of interest (e.g., RMSE, groundwater fluxes) when
performing both the Morris Method and parameter optimization offers a more
complete assessment of groundwater models, providing a more reliable and
physically consistent estimate of uncertain parameters. The parameter
optimization procedure also provides us an estimate of the residual uncertainty
in the parameter values, resulting in a more complete estimate of the remaining
uncertainty. By employing such techniques, the current study was able to
estimate the aquifer hydraulic conductivity and recharge rate due to rice field
irrigation in a groundwater basin in Northern Italy, revealing that a
significant proportion of surficial aquifer recharge (approximately 81-94%)
during the later summer is due to the flood irrigation practices applied to
these fields.Comment: second submission after minor revision
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