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The aim of this article is to analyze free vibrations of the tower shaft that drives the accessory gearbox used in a turbofan aircraft engine. The engine is used to power a midsize business jet. The problem was solved in two ways:...
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The aim of this article is to analyze free vibrations of the tower shaft that drives the accessory gearbox used in a turbofan aircraft engine. The engine is used to power a midsize business jet. The problem was solved in two ways: by a frequency response measurement test and by employing the dynamic FEA (Finite Element Analysis) that can predict the modal shapes quite accurately (Ramil et al., 2004 and Li et al., 2004). The analysis conducted on an accurate model shows that results were very close to those achieved during the frequency response measurement test. However, working with such a complex model is time-consuming, impossible for preliminary analysis and, as demonstrated in this article, unnecessary. The purpose of this study was to work out a method that would minimize the total time necessary to conduct the analysis while maintaining the good level of accuracy.
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Abstract Edge‐based and face‐based smoothed finite element methods (ES‐FEM and FS‐FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mes...
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Abstract Edge‐based and face‐based smoothed finite element methods (ES‐FEM and FS‐FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element‐based formulation of ES‐FEM and FS‐FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element‐based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS‐FEM applications found in the literature. Shape functions for non‐simplex 3D elements are proposed in order to apply FS‐FEM to any standard finite element.
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In this paper, single action die and double action die hot forging problems are analyzed by a combined FEM, which consists of the volumetrically elastic and deviatorically rigid-plastic FEM and the heat transfer FEM. The volumetri...
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In this paper, single action die and double action die hot forging problems are analyzed by a combined FEM, which consists of the volumetrically elastic and deviatorically rigid-plastic FEM and the heat transfer FEM. The volumetrically elastic and deviatorically rigid-plastic FEM has some merits in comparison with the conventional rigid-plastic FEMs. Differences of calculated results for the two forging processes can be clearly seen in this paper. It is also verified that these calculated results are similar to those of the conventional rigid-plastic FEM in comparison with analyses of the same numerical examples by the penalty rigid-plastic FEM.
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Deformation and temperature of hot backward extrusion are complex owing to interaction between deformation and temperature. In this paper, two- and one-way axisymmetric hot backward extrusion problems are analyzed by a combined fi...
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Deformation and temperature of hot backward extrusion are complex owing to interaction between deformation and temperature. In this paper, two- and one-way axisymmetric hot backward extrusion problems are analyzed by a combined finite element method, which consists of the volumetrically elastic and deviatorically rigid-plastic finite element method and the heat transfer finite element method. The volumetrically elastic and deviatorically rigid-plastic finite element method is different from the conventional rigid-plastic finite element methods, and has some merits in comparison with the conventional methods. Because contact surfaces between workpiece and tools of the one-way extrusion are different from those of the two-way one, the deformation and temperature of the one-way extrusion are different from those of the two-way one. Contours of effective strain rate, effective strain, temperature, effective stress and hydrostatic stress, as well as plots at different reductions for the two extrusions are obtained successfully. Differences of calculated results for the two extrusions can be clearly seen through comparative analyses. Because the bulk modulus is introduced into the volumetrically elastic and deviatorically rigid-plastic finite element method, influence of temperature on hydrostatic stress can be considered in this paper.
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Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation....
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Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points on the accuracy of the computation is also studied. Two-dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS-enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element method (FEM). Moreover, NEFEM outperforms Cartesian FEM and p-FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations.
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In this work we review a unified formulation for spectral fuzzy, spectral stochastic, and spectral fuzzy-stochastic FEM. We propose some modifications for the fuzzy and fuzzy-stochastic FEM involving local bases in the non-determi...
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In this work we review a unified formulation for spectral fuzzy, spectral stochastic, and spectral fuzzy-stochastic FEM. We propose some modifications for the fuzzy and fuzzy-stochastic FEM involving local bases in the non-deterministic dimensions and the incorporation of extended FEM into the non-deterministic FEM. These modifications were previously used for stochastic FEM only. We discuss advantages of the proposed techniques for problems with uncertainties in the geometry and demonstrate their application to computational homogenization of heterogeneous materials with geometrical uncertainties in the microstructure. We address also some theoretical aspects of fuzzy FEM, that have not been tackled in the literature, namely the inner product of fuzzy variables. We address also another important problem, which becomes often the target of criticism of fuzzy approach. The membership function of the fuzzy input has often some degree of arbitrariness: it is known only approximately or it is constructed based on some assumptions. Here we propose a fuzzy FEM representation, which requires only the modal value and support of the fuzzy input parameters and is completely independent of the membership function's shape. We also discuss the case of imprecise probabilities which allows for severe dimension reduction of the non-deterministic problem if the accurate spectral simulation technique is used. Application of dimension reduction is also demonstrated on the example of computational homogenization. (C) 2019 Elsevier B.V. All rights reserved.
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This paper presents a novel methodology for the solution of nonlinear problems using the Stable Generalized/eXtended Finite Element Method (SGFEM) in two-scale approach. The nonlinear analysis is performed in a coarse mesh and the...
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This paper presents a novel methodology for the solution of nonlinear problems using the Stable Generalized/eXtended Finite Element Method (SGFEM) in two-scale approach. The nonlinear analysis is performed in a coarse mesh and the solution of a local problem, represented by a fine mesh, is used to enrich the partition of unity of the coarse mesh in the so-called global-local strategy. The SGFEM is adopted to deal with the problem of ill-conditioning of the stiffness matrix triggered by the enrichment strategy. Here, this problem is investigated for the first time for global-local analysis of physically nonlinear problem. In addition to the use of SGFEM, it is noteworthy that the relationship between the incremental-iterative process and changes in the constitutive variables are simultaneously updated on both scales. Differently from original GFEM global-local strategies, the evolution of the state variables is conduced only in the global scale. The local problem heritages the material degradation of the global scale, by using a mapping technique, and provides the numerically obtained functions that enriches the global approximation. Different constitutive models and material laws are adopted to incorporate the material degradation. Numerical examples are presented for validating this approach and to show its generality and efficiency. (C) 2020 Elsevier B.V. All rights reserved.
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The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution schem...
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The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation NVIDIA's parallel computing solution, the Compute Unified Device Architecture (CUDA) is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets.
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Der Einsatz von Simulationswerkzeugen hat bei der Entwicklung der Fendt Traktoren eine lange Tradition. Ein Vorgehen nach dem Motto "Probieren geht uber Studieren" ist bei den heutigen kurzen Entwicklungszyklen nicht mehr moglich,...
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Der Einsatz von Simulationswerkzeugen hat bei der Entwicklung der Fendt Traktoren eine lange Tradition. Ein Vorgehen nach dem Motto "Probieren geht uber Studieren" ist bei den heutigen kurzen Entwicklungszyklen nicht mehr moglich, Wiederholungsschleifen fur fehlgeschlagene Versuche sind in den Verfahrens ablaufen kaum mehr eingeplant. Welche Vielfalt an Problemstellungen sich inzwischen mit Simulationen bearbeiten lassen, zeigt die Pkw-Branche. Fur die Entwicklung von landtechnischen Fahrzeugen stellt sich jedoch die Frage, welche Simulationswerkzeuge bei den deutlich kleineren Stuckzahlen und Personalressourcen sinnvoll einsetzbar sind.
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An adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations. The analy...
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An adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations. The analysis is carried out for the lowest order Crouzeix-Raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels. Important tools in the convergence proof are a discrete local efficiency and a quasi-orthogonality property. The proof does neither require regularity of the solution nor uses duality arguments. As a consequence on the data control, no particular mesh design has to be monitored.
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