1,720,990 research outputs found
Cellular Automata and Artificial Neural Networks to Model Processes Governed by Differential Equations
No full textA thermo-mechanical model for Nb3Sn filaments and wires: strain field for different strand layouts
No full textIn Nb3Sn CIC conductors, the superconducting compound is distributed into fine filaments and embedded in a resistive matrix for electrical and thermal stability. Nb3Sn formation requires a solid state diffusion reaction at high temperature, which causes an Sn gradient inside the filaments. It is well known that the critical parameters vary with composition (Sn content) and strain state. In this work the complete 3D strain field is computed for different wire layouts. First, the relation between the grade of filament reaction and strain is investigated: superconducting wires are studied, taking into consideration non-homogeneous Nb3Sn filaments, i.e. considering an unreacted core of pure Nb. Furthermore, the case when the filaments agglomerate together to give a ‘macrofilament’ is also taken into consideration (internal tin wires). A finite element discretization fine enough to take into consideration non-homogeneous filaments would result in a very high number of unknowns, which could be beyond the capacity of today’s computers. Therefore a thermo-mechanical model is formulated, based on the generalized self-consistent method, suitably developed to deal with the material nonlinearity and the coupling between the thermal and mechanical fields. In this way, equivalent homogeneous properties are obtained and the analysis of the wires becomes feasible. An appropriate unsmearing technique finally gives the strain state in the real, not homogenized, materials
Modelling of nonstationary heat conduction problems in micro-periodic composites using homogenisation theory with corrective terms
No full textHOMOGENISATION BASED on the asymptotic series expansion is used to model a nonstationary behaviour of a rigid heat conductor with micro-periodic structure. A usual first-order approximation (which cannot be assumed as a satisfactory solution for time-dependent problems) is treated as a suitable starting point for further corrections that make it admissible. An initial correction takes into account some fast processes acting on the level of the microstructure and guarantees that the initial condition is satisfied. Some higher-order correctors arc intended to improve the first-order approximation far from the onset of the process, for composites with strongly different properties of components or for the case of a rough microstructure. A numerical example shows that the role of the initial corrector is prevailing in the model
Application of the Homogenization method to the analysis of superconducting coils
No full textAn application of the homogenisation method to the analysis of superconductingcoils for nuclear fusion devices is presented. The proposed procedure is composed of three parts. First effective coefficients and second order correctors are calculated. Only one cell of periodicity made up of the cross-section of a single conductor together with its bonded epoxy layer is taken into account for this purpose. In the next step the finite element method is applied to solve the problem of the global mechanical behaviour of the whole homogenised structure. Finally, given the global behaviour, the code for homogenisation is used again to obtain the local stress image. Numerical results dealing with the validation of the procedure and a realistic example complete this paper
A Thermo-mechanical Model for Nb3Sn Filaments and Wires
No full textFor electrical and thermal stability the Nb3Sn compound is distributed into fine filaments (up to about 50 micrometers diameter) and embedded in a resistive matrix. Nb3Sn formation requires a solid state diffusion reaction at high temperature, which causes Sn gradient inside the filaments. It is well known that the critical parameters vary with composition (Sn content) and strain state. In this work the relation between compositional variations and strain is investigated: Nb3Sn wires are studied taking into consideration non-homogeneous filaments. A finite element discretization fine enough to take into consideration Sn gradient would result in a number of unknowns which is far beyond the capacity of nowadays computers. Therefore a thermo-mechanical model is developed, based on a self consistent homogenisation, suitably developed to deal with the material non-linearity and the coupling between the thermal and mechanical field. In this way the equivalent homogeneous properties are obtained and the analysis of the wires becomes possible. An appropriate unsmearing technique gives finally the strain state in the real, not homogenized materials
Thermo-Mechanics of Superconducting Coils for Fusion Reactors
No full textAn analysis of a superconducting coil used in fusion devices reveals that a wide spectrum of coupled physical problems should be taken into account during its design. This is also a good example of a general analysis of a hierarchical structure. Due to the large number of repetitive superconducting strands, the single cable can be considered as a homogeneous body in meso-scale, each strand being at the same time a micro composite of several components. A bundle of cables makes in turn a substantial part of a larger, D shaped superconducting coil.
The above problems are numerically analysed using various, specialised algorithms of FE method.
The single strand has its internal structure. It is made of filaments of superconducting alloy embedded in a matrix of bronze. The detailed geometry of the microstructure depends on the strand type. At this stage the classical model of Kirchhoff-Bernoulli beam is applicable, for which the beam type stiffness is computed by means of homogenisation theory and beam-type kinematical hypothesis.
A triplet of strands can be seen as a single beam, but in this case the Kirrchhoff-Bernoulli hypothesis is not sufficient to define the mechanics of the structure. The common mechanical work of the triplet is influenced by friction between strands, their pointwise contacts and the helicoidal geometry. We propose a mixed Kirchhoff-Timoshenko approach with a torsion-tension coupling to model the beam-like behaviour at this stage and at the higher order cabling stages. Thus we are performing a successive substitution of discrete models involving many beams (three at the level of the triplet, four at the level of quadruplet) with a single, continuous beam model, that can be qualitatively different and the parameters of which can be deduced from the preceding cabling stages. This recursive substitution allows to maintain the number of beam elements in the model around a reasonable optimum. Since the thermo-mechanical loading is applied at the macro level, the analysis of the macro structure is indispensable. On the other hand, the most important engineering phenomena are related to the micro components of the composite. In our approach we can recover the micro-structural effects from the results at the macro level via suitable unsmearing procedures.
All along the hierarchically organised FE analysis of the structure we deal with coupled thermo-mechanical phenomena and local material yielding occurring at the level of the micro structure.
The lecture is illustrated with some examples revealing the specific properties of the different beam models at several cabling stages and with an overview of the model of the bundle of strands
ANN-FE modelling of coupled hygro-thermo-mechanical phenomena in deformable porous media with sorption hysteresis
No full textNon-linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN-FE code has been developed and tested for 1-D and 2-D problems concerning cyclic wetting-drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary-porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN-FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro-thermal behaviour of capillary-porous materials. © 2001 John Wiley & Sons, Ltd.
Non-linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN-FE code has been developed and tested for 1-D and 2-D problems concerning cyclic wetting-drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary-porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN-FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro-thermal behaviour of capillary-porous materials
Multiscale analysis of the influence of the triplet helicoidal geometry on the strain state of a Nb3Sn based strand for ITER coils
No full textA theoretical model of a beam of unidirectional composites - based on the homogenisation theory and a refined kinematical hypothesis - is used for the analysis of the influence of the helicoidal geometry of a superconducting strand triplet on its strain state. The triplet is the first cabling stage of the superconducting cables used to wind the coils of ITER fusion reactor. The multiscale modelling strategy is presented, for which a finite element code has been developed. A triplet of Nb3Sn based strands subjected to an axial stretch is analysed, and the resulting complete 3D strain state in the Nb3Sn filament is recovered. An “extra” strain is found due to the helicoidal geometry of the triplet. Discussion of the results concludes the paper
A multilevel homogenised model for superconducting strand thermomechanics
No full textIn the present concept of ITER fusion reactor the Toroidal Field and the Central Solenoid coils are made of Nb3Sn based strands with the Cable-In-Conduit-Conductor (CICC) technology. It is well known that the critical parameters of the Nb3Sn strand material are strain sensitive; experimental investigations on short samples of basic strands and subsize CICC cables already demonstrated significant effects of residual strain on the critical parameters. In this paper a method is proposed to analyse in detail the thermal strain induced by the cool down from the strand reaction temperature to the coil working conditions. The superconducting strand can be regarded as a very good example of a hierarchical structure, since there is a clear distinction between the micro scale of the Nb3Sn filaments, the meso scale of the SC filament groups and the macro scale of the strand, where it can be regarded as homogeneous. A constitutive relation for the homogenised micro and meso-components is deduced from the knowledge of the respective internal structures, starting from an accurate description of the single representative cells. This two-scales homogenisation technique is associated with an efficient Finite Element procedure for computing effective material coefficients to be used with standard orthotropic 3-D elements in structural codes. Finally the finite elements routines developed for the unsmearing process provide the real stress and strain values over each single material, which are essential to catch the local features needed for engineering design
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