Academic literature on the topic 'Lagrange FE'
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Journal articles on the topic "Lagrange FE"
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Arcuş, Constantin M. "Mechanical systems in the generalized Lie algebroids framework." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450023. http://dx.doi.org/10.1142/s0219887814500236.
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Mechanical systems, called by use, mechanical (ρ, η)-systems, Lagrange mechanical (ρ, η)-systems or Finsler mechanical (ρ, η)-systems, are presented. The canonical (ρ, η)-semi(spray) associated to a mechanical (ρ, η)-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical (ρ, η)-systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the (ρ, η)-semispray associated to a regular Lagrangian L and external force Fe and we derive the equations of Euler–Lagrange type. So, a new solution for the Weinstein's problem in the general framework of generalized Lie algebroids is presented.
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Jia, Cheng, and Hui Hui Chen. "Study of Performance of US-FE-LSPIM QUAD4 Element on Mesh Distortion." Advanced Materials Research 490-495 (March 2012): 3008–12. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.3008.
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This US-FE-LSPIM QUAD4 element is formed by using two different sets of shape functions for the trial and test functions, viz. sets of FE-LSPIM QUAD4 element shape functions and sets of classical isoparametric shape functions. For some test problems, the US-FE-LSPIM QUAD4 element has good accuracy. And by compared with FE-LSPIM QUAD4 element, the proposed element does not need to use Penalty method or Lagrange multiplier method to ensure fulfilment of exact essential boundary condition along the entire length of the edge. This paper further studies the performance of US-FE-LSPIM QUAD4 element on mesh distortion. Numerical test examples show that the element exhibits high precisions even under the mesh distortions. The US-FE-LSPIM QUAD4 element displays good tolerance to the mesh distortions
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Ivančo, Vladimír, and Martin Orečný. "Modelling a Liquid Material in Drop Test Simulations of a Cask for Liquid Radioactive Waste." Applied Mechanics and Materials 611 (August 2014): 145–55. http://dx.doi.org/10.4028/www.scientific.net/amm.611.145.
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The aim of this paper is the comparison of different material models for the simulation of fluid impact on a cask for transport of radioactive liquid material. Simulated is a 9 m drop test performed according to International Atomic Energy Agency regulations. In order to reduce computational time, proposed is to model the transported fluid as a hypothetic linearly elastic material. This enables us to use less time demanding FE explicit dynamic analysis based on Lagrange formulation only instead of combination of Lagrange and Euler formulations. Compared are the results obtained for three elastic material and three fluid models based on different equations of state.
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Tirvaudey, Marie, Robin Bouclier, Jean-Charles Passieux, and Ludovic Chamoin. "Non-invasive implementation of nonlinear isogeometric analysis in an industrial FE software." Engineering Computations 37, no. 1 (July 25, 2019): 237–61. http://dx.doi.org/10.1108/ec-03-2019-0108.
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Purpose The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over the past decade, its massive deployment in industrial analysis still appears quite marginal. This is partly due to its implementation, which is not straightforward with respect to the elementary structure of finite element (FE) codes. This often discourages industrial engineers from adopting isogeometric capabilities in their well-established simulation environment. Design/methodology/approach Based on the concept of Bézier and Lagrange extractions, a novel method is proposed to implement IGA from an existing industrial FE code with the aim of bringing human implementation effort to the minimal possible level (only using standard input-output of finite element analysis (FEA) codes, avoid code-dependent subroutines implementation). An approximate global link to go from Lagrange polynomials to non-uniform-rational-B-splines functions is formulated, which enables the whole FE routines to be untouched during the implementation. Findings As a result, only the linear system resolution step is bypassed: the resolution is performed in an external script after projecting the FE system onto the reduced, more regular and isogeometric basis. The novel procedure is successfully validated through different numerical experiments involving linear and nonlinear isogeometric analyses using the standard input/output of the industrial FE software Code_Aster. Originality/value A non-invasive implementation of IGA into FEA software is proposed. The whole FE routines are untouched during the novel implementation procedure; a focus is made on the IGA solution of nonlinear problems from existing FEA software; technical details on the approach are provided by means of illustrative examples and step-by-step implementation; the methodology is evaluated on a range of two- and three-dimensional elasticity and elastoplasticity benchmarks solved using the commercial software Code_Aster.
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Petrolo, M., MH Nagaraj, E. Daneshkhah, R. Augello, and E. Carrera. "Static analysis of thin-walled beams accounting for nonlinearities." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 6 (October 14, 2021): 2967–80. http://dx.doi.org/10.1177/09544062211032997.
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This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom.
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Gruttmann, Friedrich, and Werner Wagner. "Ein neues FE-Modell zur Berechnung von geschichteten Platten mit kontinuierlichen interlaminaren Schubspannungen/A new FE–model for the computation of layered plates with continuous interlaminar transverse shear stresses." Bauingenieur 91, no. 05 (2016): 179–87. http://dx.doi.org/10.37544/0005-6650-2016-05-39.
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In dieser Arbeit werden geschichtete Platten unter statischer Belastung betrachtet. Es wird ein Mehrfeldfunktional vorgeschlagen, dessen zugehörige Euler–Lagrange–Gleichungen neben dem Kräfte– und Momentengleichgewicht der Schnittgrößen lokale Gleichgewichtsbeziehungen in Spannungen liefert. Innerhalb eines finiten Plattenelements mit vier Knoten werden die Verwölbungen mit schichtweisen kubischen Ansatzfunktionen interpoliert. Dies hat zur Folge, dass die interlaminaren Schubspannungen automatisch kontinuierlich und die Spannungsrandbedingungen exakt erfüllt sind. Elimination der Wölb– und Lagrangeparameter auf Elementebene führt zu einem gemischt–hybriden Plattenelement mit fünf Freiheitsgraden an den Knoten. Damit können übliche Verschiebungsrandbedingungen angesetzt werden.
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Su, Wen Zheng. "Finite Element Formulation for the Vibration Analysis of Couple-Stress Continuum." Applied Mechanics and Materials 367 (August 2013): 156–60. http://dx.doi.org/10.4028/www.scientific.net/amm.367.156.
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This paper proposed a finite element formulation to analysis the vibration of couple-stress continuum. A four-node discrete couple-stress element relaxed the requirement of C1 continuity is developed. This element is modified by a bubble function, based on the classical four-ode Lagrange element. The element includes the internal bending constants and the internal initial moment of rotation. Numerical examples show that the present FE scheme is accurate for the eigenvalue analysis of couple-stress continuum structures, especially for the low order frequency analysis.
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González, Jose A., K. C. Park, and Ramon Abascal. "A Partitioned Formulation for FEM/BEM Coupling in Contact Problems Using Localized Lagrange Multipliers." Key Engineering Materials 618 (July 2014): 23–48. http://dx.doi.org/10.4028/www.scientific.net/kem.618.23.
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This paper presents a state-of-the-art in the use of localized Lagrange multipliers (LLMs)for 3D frictional contact problems coupling the Finite Element Method (FEM) and the BoundaryElement Method (BEM). Resolution methods for the contact problem between non-matching mesheshave traditionally been based on a direct coupling of the contacting solids using classical Lagrangemultipliers. These methods tend to generate strongly coupled systems that require a deep knowledgeof the discretization characteristics on each side of the contact zone complicating the process ofmixing different numerical techniques. In this work a displacement contact frame is inserted betweenthe FE and BE interface meshes, discretized and finally connected to the contacting substructuresusing LLMs collocated at the mesh-interface nodes. This methodology will provide a partitionedformulation which preserves software modularity and facilitates the connection of non-matching FEand BE meshes.
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Adhikari, Balakrishna, and B. N. Singh. "Buckling Characteristics of Laminated Functionally-Graded CNT-Reinforced Composite Plate under Nonuniform Uniaxial and Biaxial In-Plane Edge Loads." International Journal of Structural Stability and Dynamics 20, no. 02 (December 23, 2019): 2050022. http://dx.doi.org/10.1142/s0219455420500224.
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In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.
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Feng, Yong, Mu Lan Wang, Bao Sheng Wang, and Jun Ming Hou. "Influence of the Process Variables on the Temperature Distribution in AISI 1045 Turning." Advanced Materials Research 557-559 (July 2012): 1364–68. http://dx.doi.org/10.4028/www.scientific.net/amr.557-559.1364.
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High-speed metal cutting processes can cause extremely rapid heating of the work material. Temperature on the machined surface is critical for surface integrity and the performance of a precision component. However, the temperature of a machined surface is challenging for in-situ measurement.So, the finite element(FE) method used to analyze the unique nonlinear problems during cutting process. In terms of heat-force coupled problem, the thermo-plastic FE model was proposed to predict the cutting temperature distribution using separated iterative method. Several key techniques such as material constitutive relations, tool-chip interface friction and separation and damage fracture criterion were modeled. Based on the updated Lagrange and arbitrary Lagrangian-Eulerian (ALE) method, the temperature field in high speed orthogonal cutting of carbon steel AISI-1045 were simulated. The simulated results showed good agreement with the experimental results, which validated the precision of the process simulation method. Meanwhile, the influence of the process variables such as cutting speed, cutting depth, etc. on the temperature distribution was investigated.
Dissertations / Theses on the topic "Lagrange FE"
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Mouhcine, Houda. "Formal Proofs in Applied Mathematics : A Coq Formalization of Simplicial Lagrange Finite Elements." Electronic Thesis or Diss., université Paris-Saclay, 2024. https://theses.hal.science/tel-04884651.
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Cette thèse est dédiée au développement de preuves formelles de théorèmes et propositions mathématiques dans le domaine de l'analyse réelle, en utilisant l'assistant de preuve Coq pour garantir leur exactitude. Le cœur de ce travail est divisé en deux parties principales.La première partie se concentre sur l'utilisation de Coq pour formaliser des principes mathématiques clés tels que le principe d'induction de Lebesgue et le théorème de Tonelli, permettant le calcul d'intégrales doubles sur des espaces produits en intégrant de manière itérative par rapport à chaque variable. Ce travail s'appuie sur des recherches antérieures en théorie de la mesure et sur l'intégrale de Lebesgue.La deuxième partie de cette thèse fonctionne dans le cadre de la méthode des éléments finis (MEF), une technique numérique largement utilisée pour résoudre des équations aux dérivées partielles (EDP). La MEF joue un rôle important dans de nombreux programmes de simulation industrielle, notamment dans l'approximation des solutions à des problèmes complexes tels que le transfert de chaleur, la dynamique des fluides et les simulations de champs électromagnétiques. Plus spécifiquement, nous visons à construire des éléments finis, en nous concentrant sur les éléments finis de Lagrange simpliciaux avec des degrés de liberté répartis uniformément. Ce travail mobilise un large éventail de concepts algébriques, y compris les familles finies, les monoïdes, les espaces vectoriels, les espaces affines, les sous-structures et les espaces de dimensions finies.Pour mener à bien cette étude, nous formalisons dans Coq en logique classique plusieurs composants fondamentaux. Nous commençons par construire un élément fini général, puis nous procédons à la définition de plusieurs composants fondamentaux, y compris la construction de l'espace d'approximation de Lagrange, l'expression de sa base de polynômes de Lagrange et la formalisation des transformations géométriques affines et de la propriété d'unisolvance des éléments finis de LagrangeThis thesis is dedicated to developing formal proofs of mathematical theorems and propositions within the field of real analysis using the Coq proof assistant to ensure their correctness. The core of this work is divided into two main parts.The first part focuses on using Coq to formalize key mathematical principles such as the Lebesgue induction principle and the Tonelli theorem, allowing the computation of double integrals on product spaces by iteratively integrating with respect to each variable. This work builds upon previous research in measure theory and the Lebesgue integral.The second part of this thesis operates within the framework of the Finite Element Method (FEM), a widely used numerical technique for solving partial differential equations (PDEs). FEM plays an important role in numerous industrial simulation programs, particularly in approximating solutions to complex problems such as heat transfer, fluid dynamics, and electromagnetic field simulations. Specifically, we aim to construct finite elements, focusing on simplicial Lagrange finite elements with evenly distributed degrees of freedom. This work engages a broad range of algebraic concepts, including finite families, monoids, vector spaces, affine spaces, substructures, and finite-dimensional spaces.To conduct this study, we formalize in Coq in classical logic several foundational components. We begin by constructing a general finite element, then proceed to define several foundational components, including the construction of the Lagrange approximation space, expressing its Lagrange polynomial basis, and formalizing affine geometric transformations and the unisolvence property of Lagrange finite elements
Conference papers on the topic "Lagrange FE"
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Wang, Xiaoyun, and James K. Mills. "Substructuring Dynamic Modeling and Active Vibration Control of a Smart Parallel Platform." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60411.
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A substructuring approach to derive dynamic models for closed-loop mechanisms is applied to model a flexible-link planar parallel platform with Lead Zirconate Titanate (PZT) transducers. The Lagrangian Finite Element (FE) formulation is used to model flexible linkages, in which translational and rotary degrees of freedom exist. Craig-Bampton mode sets are extracted from these FE models and then used to assemble the dynamic model of the planar parallel platform through the application of Lagrange’s equation and the Lagrange multiplier method. Electromechanical coupling models of surface-bonded PZT transducers with the host flexible linkages are introduced to the reduced order dynamic models of flexible linkages. The assembled system dynamic model with moderate model order can represent essential system dynamic behavior and maintain kinematic relationships of the planar parallel platform. A Proportional, Integral, and Derivative (PID) control law is used as the motion control law. Strain rate feedback (SRF) active vibration control is selected as the vibration control law. Motion control simulation results with active vibration control and simulation results without active vibration control are compared. The comparison shows the effectiveness of active vibration control.
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Hiermaier, Stefan, and Martin Sauer. "Adaptive FE-Meshfree-Modelling for Impacts of Liquid Filled Vessels on Thin Walled Structures." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55189.
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A principal approach to simulate the airplane impact and the collapse of World Trade Center North Tower has been shown by Quan and Birnbaum [4]. Using the general purpose hydrocode AUTODYN the impact damage, fire induced strength reduction and progressive collapse were investigated. Both for the fuel propagation after tank break up and the thermodynamic burn processes assumptions have been taken. It is the aim of this paper to focus on the numerical aspects of simulating the fluid propagation after vessel break up. The release of a fluid out of a broken vessel after impact is not easily represented in a numerical simulation as the fluid flow and its interaction with structures can not be modelled using Lagrangian type element formulations. These elements, typically applied for structural analyses, fail under massive deformation and usually need then to be taken out of the simulation. Typical fluid dynamic discretization methods, so called Eulerian grids, would have to cover the whole space potentially being reached by the fluid flow and are therefore inefficient in a large three dimensional simulation. As an alternative method a coupled discretization using Lagrange elements and Lagrange type meshfree methods is proposed here. Meshfree methods have been introduced to structural dynamics more then ten years ago specifically to simulate processes including large deformation [1]. Originally developed as pure meshfree code, the EMI SOPHIA [3] provides now a new form of adaptivity that allows for more efficiency and accuracy. This is achieved by the use of finite elements as long as deformation is capable for the elements. At definable strain or failure thresholds any element can be transformed into one or more meshfree particles. This way, mass and volume of the original elements are conserved. As the particles interact with each other as well as with the remaining elements, all physical processes can be modelled continuously. The purpose of this study was to contribute to numerical simulation of the airplane impacts into the World Trade Center. It includes impact simulations of cylindrical vessels filled with water against thin walled rectangular shaped bars. It shows that coupled discretizations and specifically an adaptive FE-meshfree discretization offer the flexibility needed to gain both accuracy and efficiency in the simulation.
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Saghafi, Mehdi, and Harry Dankowicz. "Nondegenerate Continuation Problems for the Excitation Response of Nonlinear Beam Structures." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13115.
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This paper investigates the dynamics of a slender beam subjected to transverse periodic excitation. Of particular interest is the formulation of nondegenerate continuation problems that may be analyzed numerically, in order to explore the parameter-dependence of the steady-state excitation response, while accounting for geometric nonlinearities. Several candidate formulations are presented, including finite-difference (FD) and finite-element (FE) discretizations of the governing scalar, integro-partial differential boundary-value problem (BVP), as well as of a corresponding first-order-in-space, mixed formulation. As an example, a periodic BVP — obtained from a Galerkin-type, FE discretization with continuously differentiable, piecewise-polynomial trial and test functions, and an elimination of Lagrange multipliers associated with spatial boundary conditions — is analyzed to determine the beam response via numerical continuation using a MATLAB-based software suite. In the case of an FE discretization of the mixed formulation with continuous, piecewise-polynomial trial and test functions, it is shown that the choice of spatial boundary conditions may render the resultant index-1, differential-algebraic BVP equivariant under a symmetry group of state-space translations. The paper demonstrates several methods for breaking the equivariance in order to obtain a nondegenerate continuation problem, including a projection onto a symmetry-reduced state space or the introduction of an artificial continuation parameter. As is further demonstrated, an orthogonal collocation discretization in time of the BVP gives rise to ghost solutions, corresponding to arbitrary drift in the algebraic variables. This singularity is resolved by using an asymmetric discretization in time.
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Carrera, E., A. Pagani, and M. Petrolo. "Static and Dynamic Analysis of Aircraft Structures by Component-Wise Approach." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63600.
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This paper proposes an advanced approach to the analysis of reinforced-shell aircraft structures. This approach, denoted as Component-Wise (CW), is developed by using the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation allowing for the straightforward implementation of any-order one-dimensional (1D) beam theories. Lagrange-like polynomials are used to discretize the displacement field on the cross-section of each component of the structure. Depending on the geometrical and material characteristics of the component, the capabilities of the model can be enhanced and the computational costs can be kept low through smart discretization strategies. The global mathematical model of complex structures (e.g. wings or fuselages) is obtained by assembling each component model at the cross-section level. Next, a classical 1D finite element (FE) formulation is used to develop numerical applications. It is shown that MSC/PATRAN can be used as pre- and post-processor for the CW models, whereas MSC/NASTRAN DMAP alters can be used to solve both static and dynamic problems. A number of typical aeronautical structures are analyzed and CW results are compared to classical beam theories (Euler-Bernoulli and Timoshenko), refined models and classical solid/shell FE solutions from the commercial code MSC/NASTRAN. The results highlight the enhanced capabilities of the proposed formulation. In fact, the CW approach is clearly the natural tool to analyze wing structures, since it leads to results that can be only obtained through three-dimensional elasticity (solid) elements whose computational costs are at least one-order of magnitude higher than CW models.
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Aguirre-Rivas, Donovan A., and Karim H. Muci-Küchler. "Higher Order Finite Elements for the Accurate Prediction of Temperature Gradients in Heat Conduction Problems." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-39948.
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When the Finite Element Method (FEM) is used to solve heat conduction problems in solids, the domain is typically discretized using elements that only include the nodal values of the temperature as Degrees of Freedom (DOFs). If the values of the spatial temperature gradients are needed, they are typically computed by differentiating the functional representation for the temperature inside the elements. Unfortunately, this differentiation process usually leads to less accurate results for the temperature gradients as compared to the temperature values. For elliptic problems, like steady state heat conduction, with Neumann Boundary Conditions (BCs), recent research related to Adini’s element suggests that higher order elements that include spatial derivatives of the primary field variable as nodal DOFs are promising for obtaining accurate values for those quantities as well as providing a higher order of convergence than conventional elements. In this paper, steady state and transient heat conduction problems which involve Dirichlet BCs or both Dirichlet and Neumann BCs are studied and a new auxiliary BC is proposed to increase the accuracy of the FE solution when Dirichlet BCs are present. Examples are used to illustrate that Adini’s elements converge faster and are more computationally economical than the conventional Lagrange linear elements and Serendipity quadratic elements when auxiliary BCs are used.
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Masi, Enrica, Benoiˆt Be´dat, Mathieu Moreau, and Olivier Simonin. "Euler-Euler Large-Eddy Simulation Approach for Non Isothermal Particle-Laden Turbulent Jet." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55143.
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This paper presents an Euler-Euler Large-Eddy Simulation (LES) approach for the numerical modeling of non isothermal dispersed turbulent two-phase flows. The proposed approach is presented and validated by a priori tests from an Euler-Lagrange database, provided using discrete particle simulation (DPS) of the particle phase coupled with direct numerical simulation (DNS) of the turbulent carrier flow, in a non isothermal particle-laden temporal jet configuration. A statistical approach, the Mesoscopic Eulerian Formalism (MEF) [Fe´vrier et al., J. Fluid Mech., 2005, vol. 533, pp. 1–46], is used to write local and instantaneous Eulerian equations for the dispersed phase and then, by spatial averaging, to derive the LES equations governing the filtered variables. In this work, the MEF approach is extended to scalar variables transported by the particles in order to develop LES for reactive turbulent dispersed two-phase flows with mass and heat turbulent transport. This approach leads to separate the instantaneous particle temperature distribution in a Mesoscopic Eulerian field, shared by all the particles, and a Random Uncorrelated distribution which may be characterized in terms of Eulerian fields of particle moments such as the uncorrelated temperature variance. In this paper, the DPS-DNS numerical database is presented, LES Eulerian equations for the dispersed phase are derived in the frame of the Mesoscopic approach and models for the unresolved subgrid and random uncorrelated terms are proposed and a priori tested using the DPS-DNS database.
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Guarnera, Daniele, Enrico Zappino, Alfonso Pagani, and Erasmo Carrera. "Finite Element Models of One Dimensional Flows With Node-Dependent Accuracy." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86852.
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The formulation of simplified models in the description of flow fields can be highly interesting in many complex network such as the circulatory system. This work presents a refined one-dimensional finite element model with node-dependent kinematics applied to incompressible and laminar flows. In the framework of 1D-FE modelling, this methodology is a new development of the Carrera Unified Formulation (CUF), which is largely employed in structural mechanics. According to the CUF, the weak formulation of the Stokes problem is expressed in terms of fundamental nuclei and, in this novel implementation, the kinematics can be defined node by node, realizing different levels of refinements within the main direction of the pipe. Such feature allows to increase the accuracy of the model only in the areas of the domain where it is required, i.e. particular boundary condition, barriers or sudden expansion. Some typical CFD examples are proposed to validate this novel technique, including Stokes flows in uniform and non-uniform domains. For each numerical example, different combinations of 1D models have been considered to account for different kinematic approximations of flows, and in particular, models based on Taylor and Lagrange expansion have been used. The results, compared with ones obtained from uniform kinematics 1D models and with those come from available tools, highlight the capability of the proposed model in handling non-conventional boundary conditions with ease and in preserving the computational cost without any accuracy loss.
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Almeida, P., C. Gibert, F. Thouverez, and J. P. Ousty. "Numerical Analysis of Bladed Disk-Casing Contact With Friction and Wear." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-43435.
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In order to increase the aerodynamic performances of their engines, aircraft engine manufacturers try to minimize the clearance between rotating and stationary parts in axial and centrifugal compressors. Consequently, the probability of contact increases, leading to undesirable phenomena caused by forced excitation of the natural modes, or by modal interaction. Due to the complexity of these phenomena, many numerical studies have been conducted to gain a better understanding of the physics associated with them, looking primarily at their respective influence on potential unstable behaviors. However, the influence of other physical phenomena, such as friction and wear, remains poorly understood. The aim of this work is to show some effects associated with friction and wear on the dynamic behavior resulting from blade-to-casing interaction. The numerical study reported here is based on a simplified finite element model of a rotating bladed disk and a flexible casing. The contact algorithm uses an explicit time marching scheme with the Lagrange multipliers method. Friction and wear are formulated using respectively Coulomb’s and Archard’s Laws. The rotational speed is set to critical speed giving rise to modal interaction between a backward mode of the casing and a counter-rotating mode of the bladed disk with one nodal diameter. Contact is initiated by a dynamic excitation of the stator. In the presence of friction, the system becomes unstable when a sideband of the excitation frequency coincides with a one nodal diameter mode of the bladed disk. The introduction of wear leads to a vibration reduction, while the abradable material is removed by the wear process. The number of wear lobes produced on the casing is related to the ratio between the vibration frequency of the blades and the rotating speed. The ratio obtained by means of the FE model corroborates experimental observations.
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Azzara, Rodolfo, Erasmo Carrera, and Alfonso Pagani. "Nonlinear Vibration Correlation and Buckling Analysis of Flat Plates and Shells." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-69580.
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Abstract The employment of nondestructive techniques in aerospace industries is rising thanks to advances in technologies and analysis. This part of the aerospace testing industry is essential to design and validate the new structures’ methodology and safety. Therefore, robust and reliable nondestructive methods have been extensively studied for decades in order to reduce safety problems and maintenance cost. One of the most important and employed nondestructive methods to compute large-scale aerospace structures’ critical buckling load is the Vibration Correlation Technique (VCT). This methodology allows to obtain the buckling load and equivalent boundary conditions by interpolating the natural frequencies of the structures for progressively increasing loadings without considering instabilities. VCT has been successfully investigated and employed for many structures, but it is still under development for composite shell structures. The present work provides a numerical model for carrying out virtual VCT to predict the buckling load, to characterize the natural frequencies variation with progressive higher loadings, and to provide an efficient means for verifying the experimental VCT results. The proposed nonlinear methodology is based on the well-established Carrera Unified Formulation (CUF). CUF represents a hierarchical formulation in which the structural model’s order is considered the analysis’s input. According to CUF, any theory is degenerated into generalized kinematics and is compactly handled. By adopting this formulation, the nonlinear governing equations and the relative FE arrays of the two-dimensional (2D) theories are written in terms of Fundamental Nuclei (FNs). FNs represent the basic building blocks of the proposed formulation. In order to investigate far nonlinear regimes, the full Green-Lagrange strain tensor is considered. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method. For an assessment of the robustness of the virtual VCT, several flat plate and shell structures are studied and compared with the solutions found in the available VCT literature. The results prove that the proposed approach provides results with an excellent correlation with the experimental ones, allowing to investigate the buckling load and the natural frequencies variation in the nonlinear regime with high reliability.
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Zappino, Enrico, Navid Zobeiry, Rebecca Masia, and Marco Petrolo. "Rapid Numerical Assessment of Process-Induced Dimensional Changes and Residual Stresses in Large Aerospace Composite Parts." In ASME 2024 Aerospace Structures, Structural Dynamics, and Materials Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/ssdm2024-121518.
Full textAbstract:
Abstract Process-induced deformations (PIDs) are a major issue in fabricating composite aerostructures, hindering the assembly process. For example, geometrical mismatches between spars and wing skins can lead to considerable assembly delays during the assembly of a composite wing box. In these cases, shims with specific geometries, based on the mismatch of the original parts, are fabricated and used to meet the current tight tolerances in aerospace. Given such parts ‘complex and large geometry, process simulations to assess PIDs are often quite slow. This paper aims to evaluate the effect of geometry and design details on PIDs and residual stresses of composite spars efficiently and robustly. Typical cross-sectional geometries such as the Omega shape are considered. Furthermore, the impact of design details, including ply drop-off, on PIDs such as spring-in angles, warpage, and 3D stress distributions are evaluated along long spars. The structural modeling is handled using 1D higher-order layer-wise theories based on the Carrera Unified Formulation (CUF) to speed up the process simulation of large parts. Such theories are necessary to detect relevant mechanical behaviors: transverse stretching, shear deformation, anisotropy, and layer-wise changes of the physical properties. On the other hand, using 1D theories significantly impacts the computational overhead as there are no aspect ratio constraints on the finite elements (FE), thus leading to much fewer degrees of freedom than 2D or 3D models. Although 1D, the model provides the complete 3D strain and stress fields as the primary unknowns — in this paper, pure displacements — are expanded using higher-order Lagrange polynomials to remove the typical assumptions of 1D modes, e.g., rigid cross-sections, null or constant shear distributions. The evolution of material properties, such as the evolution of the degree of cure, viscoelastic moduli, and free strains, are characterized using established DSC and DMA tests. Accordingly, a cure-hardening instantaneously linear elastic (CHILE) constitutive model is adopted for numerical simulations. The results are verified through analytical formulations and published data in the literature. The proposed simulation approach allows for rapid evaluation of residual stresses and PIDs. Due to its numerical efficiency, the effect of various design parameters can be quickly evaluated. Therefore, this tool can explore the design space for large and complex composite parts and potentially develop mitigation strategies.