Relevant bibliographies by topics / Fully nonlinear operators

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fully nonlinear operators'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Fully nonlinear operators"

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Esteban, Maria J., Patricio Felmer, and Alexander Quaas. "Eigenvalues for Radially Symmetric Fully Nonlinear Operators." Communications in Partial Differential Equations 35, no. 9 (August 10, 2010): 1716–37. http://dx.doi.org/10.1080/03605301003674848.

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Väth, Martin. "Degeneracy results for fully nonlinear integral operators." Indagationes Mathematicae 31, no. 5 (September 2020): 893–916. http://dx.doi.org/10.1016/j.indag.2020.06.009.

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Niu, Pengcheng, Leyun Wu, and Xiaoxue Ji. "Positive solutions to nonlinear systems involving fully nonlinear fractional operators." Fractional Calculus and Applied Analysis 21, no. 2 (April 25, 2018): 552–74. http://dx.doi.org/10.1515/fca-2018-0030.

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Abstract In this paper we consider the following fractional system $$\begin{array}{} \displaystyle \left\{ \begin{gathered} F(x,u(x),v(x),{\mathcal{F}_\alpha }(u(x))) = 0,\\ G(x,v(x),u(x),{\mathcal{G}_\beta }(v(x))) = 0, \\ \end{gathered} \right. \end{array}$$ where 0 < α, β < 2, 𝓕α and 𝓖β are the fully nonlinear fractional operators: $$\begin{array}{} \displaystyle {\mathcal{F}_\alpha }(u(x)) = {C_{n,\alpha }}PV\int_{{\mathbb{R}^n}} {\frac{{f(u(x) - u(y))}} {{{{\left| {x - y} \right|}^{n + \alpha }}}}dy} ,\\ \displaystyle{\mathcal{G}_\beta }(v(x)) = {C_{n,\beta }}PV\int_{{\mathbb{R}^n}} {\frac{{g(v(x) - v(y))}} {{{{\left| {x - y} \right|}^{n + \beta }}}}dy} . \end{array}$$ A decay at infinity principle and a narrow region principle for solutions to the system are established. Based on these principles, we prove the radial symmetry and monotonicity of positive solutions to the system in the whole space and a unit ball respectively, and the nonexistence in a half space by generalizing the direct method of moving planes to the nonlinear system.
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Kuo, Hung-Ju, and Neil S. Trudinger. "Schauder estimates for fully nonlinear elliptic difference operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 6 (December 2002): 1395–406. http://dx.doi.org/10.1017/s030821050000216x.

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In this paper, we are concerned with discrete Schauder estimates for solutions of fully nonlinear elliptic difference equations. Our estimates are discrete versions of second derivative Hölder estimates of Evans, Krylov and Safonov for fully nonlinear elliptic partial differential equations. They extend previous results of Holtby for the special case of functions of pure second-order differences on cubic meshes. As with Holtby's work, the fundamental ingredients are the pointwise estimates of Kuo-Trudinger for linear difference schemes on general meshes.
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Birindelli, Isabeau, and Stefania Patrizi. "A Neumann eigenvalue problem for fully nonlinear operators." Discrete & Continuous Dynamical Systems - A 28, no. 2 (2010): 845–63. http://dx.doi.org/10.3934/dcds.2010.28.845.

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Caffarelli, Luis, Luis Duque, and Hernán Vivas. "The two membranes problem for fully nonlinear operators." Discrete & Continuous Dynamical Systems - A 38, no. 12 (2018): 6015–27. http://dx.doi.org/10.3934/dcds.2018152.

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Patrizi, Stefania. "The Neumann problem for singular fully nonlinear operators." Journal de Mathématiques Pures et Appliquées 90, no. 3 (September 2008): 286–311. http://dx.doi.org/10.1016/j.matpur.2008.04.007.

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Tarsia, Antonio. "Near operators theory and fully nonlinear elliptic equations." Journal of Global Optimization 40, no. 1-3 (January 22, 2008): 443–53. http://dx.doi.org/10.1007/s10898-007-9227-0.

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Birindelli, Isabeau, Françoise Demengel, and Fabiana Leoni. "Ergodic pairs for singular or degenerate fully nonlinear operators." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 75. http://dx.doi.org/10.1051/cocv/2018070.

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We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations. We further characterize the ergodic constant as the infimum of constants for which there exist bounded sub-solutions. As intermediate results of independent interest, we prove a priori Lipschitz estimates depending only on the norm of the zeroth order term, and a comparison principle for equations having no zero order terms.
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Montanari, Annamaria, and Ermanno Lanconelli. "Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems." Journal of Differential Equations 202, no. 2 (August 2004): 306–31. http://dx.doi.org/10.1016/j.jde.2004.03.017.

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Dissertations / Theses on the topic "Fully nonlinear operators"

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Neji, Ali. "Existence unicité et régularité de solutions de problèmes non linéaires et complètement non linéaires elliptiques singuliers." Thesis, Cergy-Pontoise, 2019. http://www.theses.fr/2019CERG1017.

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Dans cette thèse on s'intéresse à l'existence, et la régularité pour des équations aux dérivées partielles non linéaires relatives au p-Laplacien , avec des termes d'ordre critiques ou sous critique, utilisant dans un cas le lemme du col d'Ambrozetti Rabinowitz, dans l'autre la concentration compacité de P L Lions. On considère ensuite un problème qui présente un terme d'ordre zéro qui "explose " près du bord, sur le modèle d'un article de Lazer mackenna, la différence essentielle étant ici que l'on a aussi un terme d'ordre 0 linéaire, qui demande donc l'utilisation de certaines fonctions propres. Une généralisation de ce problème à des cas complètement non linéaires et donc à des solutions de viscosité est étudiée dans la dernière partie de la thèse
We studied in this thesis the properties of existence and regularity for various nonlinear partial differential equations of elliptic type. We proved the existence of weak solutions to certain problems involving the p-Laplacian operator using critical point theory and the mountain pass theorem . We have also showed the existence of viscosity solutions for singular equations involving fully nonlinear operators
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Dehghani, Ahad. "Solving unconstrained nonlinear programs using ACCPM." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=96820.

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In this thesis, we address three main subjects. Wefirst introducethe relation between linear inequality systems and linear programmingproblems, and continue by introducing the analyticcenter of a polyhedron and its calculation. Secondly, we study themultiple analytic center cutting plane method ACCPM and its proximalvariant. Finally, since ACCPM and proximal ACCPM are well knowntechniques for convexprogramming problems, we propose a sequential convex programming methodbased on ACCPM and convexification techniques to tackle unconstrainedproblems with a non-convex objective function in the last chapter. Wealso report a comparison of ourmethod with some existing algorithms: the steepest descent method andnonlinear conjugate gradient algorithms
Dans cette thèse, nous abordons trois thèmes principaux. Nous commençons par présenter la relation entre les systèmes d'inégalités linéaires et les problèmes de programmation linéaire. Nous poursuivons avec l'introduction de la notion de centre analytique d'un polyèdre et son calcul. Deuxièmement, nous étudions la méthode des coupes analytiques multiples ACCPM et sa variante proximale. En-fin, puisque ACCPM et sa variante proximale sont des techniques bien connues pour les problèmes de programmation convexe, nous proposons une méthode de programmation séquentielle convexe fondée sur ACCPM ainsi que des techniques de convexification destinées à traiter les problèmes dont la fonction objectif est non convexe dans le dernier chapitre. Nous présentons aussi une comparaison de nos méthode avec certains algorithmes existants tels que la méthode la plus forte pente et la méthode du gradient conjugué non linéaire.
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To, Lap C. "Nonlinear control techniques in alumina refineries." Curtin University of Technology, School of Chemical Engineering, 1996. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=12276.

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Nonlinearities exist in all process control systems. The use of linear control techniques is valid only in a narrow range of operation. Therefore, in this thesis, multivariable nonlinear control techniques are considered. The target process is the single effect evaporative process of the liquor burning unit in Alcoa's alumina refinery in Kwinana and the proposed triple effects unit in the Wagerup refinery. Two types of nonlinear control strategies using differential geometry were studied, namely, the input output linearization (Kravaris and Soroush, 1990) and the input state linearization (Hunt et al, 1983a). The research has successfully demonstrated the superiority and simplicity of the nonlinear controller through simulations and plant implementations. An integrated software package using MAPLE V.3 as the computing environment was developed to automate the solution algorithms and to graphically simulate the closed loop dynamics of different processes using the two nonlinear control strategies.The issue of robustness of the nonlinear controller was addressed by developing a procedure called uncertainty vector adjustment. The effectiveness of the new strategy was successfully demonstrated on the simulated liquor burning process. Furthermore, the stability of the adjustment technique was proved and its theoretical bounds were established using Lyapunov function analysis.A comparative study of geometric nonlinear filter and extended Kalman filter was conducted to reduce the requirement of full state feedback necessary for nonlinear control using either input output linearization or input state linearization. The simulation of the single effect evaporation unit of the liquor burning process showed that the geometric nonlinear filter is superior to the extended Kalman filter in terms of nonlinear tracking performances.The plant trials of the input output linearization ++
in Alcoa's Kwinana alumina refinery demonstrated the practicability and feasibility of implementing nonlinear control in an industrial setting and also fostered a closer gap between academia and industry. The trials established guidelines for implementing a global linearizing controller on site, including conversion of the relevant constraints and the output of an industrial proportional and integral controller to the equivalent proportional and integral action required by the nonlinear controller. The results showed that the performance of the nonlinear controller was better than the current linear controller on site in terms of responsiveness and resistance to disturbances. Hence, the nonlinear control strategy enables the process to settle faster.All in all, efforts have been made in this thesis to minimise the use of abstract mathematical language and, in some cases, simplify the language so that nonlinear control theory can be understood by a wider range of audience, especially industrial practitioners. It is hoped that the insights provided in the dissertation will encourage more industrial implementations of nonlinear controllers and forge more interaction to close the widening gap between academic and industrial practice in process control.Keywords: nonlinear control, differential geometry, symbolic algebra, evaporator process, uncertainty vector adjustment, geometric nonlinear filter.
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Soares, Quitalo Veronica Rita Antunes de. "Regularity of a segregation problem with an optimal control operator." 2013. http://hdl.handle.net/2152/21210.

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It is the main goal of this thesis to study the regularity of solutions for a nonlinear elliptic system coming from population segregation, and the free boundary problem that is obtained in the limit as the competition parameter goes to infinity [mathematical symbol]. The main results are existence and Hölder regularity of solutions of the elliptic system, characterization of the limit as a free boundary problem, and Lipschitz regularity at the boundary for the limiting problem.
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Books on the topic "Fully nonlinear operators"

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Fitzpatrick, Patrick. Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems. Providence, R.I: American Mathematical Society, 1993.

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Book chapters on the topic "Fully nonlinear operators"

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Sirakov, Boyan. "Nonuniqueness for the Dirichlet Problem for Fully Nonlinear Elliptic Operators and the Ambrosetti–Prodi Phenomenon." In Analysis and Topology in Nonlinear Differential Equations, 405–21. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04214-5_24.

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Lunardi, Alessandra. "Stability and local invariant manifolds in fully nonlinear parabolic equations." In Semigroups of Linear and Nonlinear Operations and Applications, 185–203. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1888-0_10.

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Aizicovici, Sergiu, D. Motreanu, and Nicolae Pavel. "Fully Nonlinear Programming Problems with Closed Range Operators." In Differential Equations And Control Theory. CRC Press, 2001. http://dx.doi.org/10.1201/9780203902189.ch2.

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Conference papers on the topic "Fully nonlinear operators"

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Gao*, Zhaoqi, Ru-shan Wu, Zhibin Pan, and Jinghuai Gao. "Full Waveform Inversion Algorithm Based on a Time-shift Nonlinear Operator." In SEG Technical Program Expanded Abstracts 2015. Society of Exploration Geophysicists, 2015. http://dx.doi.org/10.1190/segam2015-5838205.1.

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Christiansen, Torben B., Harry B. Bingham, Allan P. Engsig-Karup, Guillaume Ducrozet, and Pierre Ferrant. "Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10861.

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A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichlet-to-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes.
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Rampazzo, Fabiano P., Joa˜o Luis B. Silva, Daniel P. Vieira, Antonio L. Pacifico, Lazaro Moratelli Junior, and Eduardo A. Tannuri. "Numerical and Experimental Tools for Offshore DP Operations." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50010.

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DP crane vessel operation can be analyzed based on the uncoupled system or considering the fully coupled system. Parameters such as top-crane acceleration, thruster capability and vessel motions are evaluated for several environmental conditions. Numerical and experimental tools are used and the important result of this analysis is the maximum condition in such that the operation can be safely executed. Those operations are critical, since the vessel is kept in close proximity with other unit and large loads are transported in a pendulum configuration. A precise positioning of the crane-vessel is required, in order to avoid unsafe relative motions, as well as keep the load being transported on a stable position. The uncoupled analysis approach does not consider the influence of the other unit in the crane vessel. This paper presents a methodology for evaluating a DP crane vessel in the offshore operations (DP crane vessel, load being transported, mooring and assistance lines, platform) considering the fully coupled method based on integration of the in house codes with the commercial code WAMIT® system. The methodology is based on the integration of numerical and experimental tools. The dimensions of the transported modules and the proximity of the vessels change the behavior of the vessel motions and line tensions. So, a full nonlinear time domain simulator (TPN – Numerical Offshore Tank) is used to perform the coupled analysis of the system subjected to several environmental conditions, considering also the dynamics of the suspended load and the hydrodynamic interference between the bodies. In order to calibrate the numerical model, several experimental tests are performed such as wind tests with some positions of the crane, tests in towing tanks to evaluated the current effects, thrusters tests to calibrate DP algorithm and wave test with the two bodies. In some cases a complementary CFD analysis is requested in order to evaluate the current and wind shadow effect. Several alternative relative positions between the vessels can be evaluated. This methodology results a more accurate estimative of the system performance.
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Nayfeh, Ali H., and Ziyad N. Masoud. "Delayed Position-Feedback Controller for the Reduction of Payload Pendulations of Rotary Cranes." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21601.

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Abstract In this work, we show that in rotary cranes, it is possible to reduce payload pendulations significantly by controlling the translational and rotational degrees of freedom of the crane. Such a control can be achieved with the heavy equipment that is already part of the crane so that retrofitting existing cranes with such a controller would require a small effort. Moreover, the control is superimposed on the commands of the operator transparently. The successful control strategy is based on delayed-position feedback of the payload motion in-plane and out-of-plane of the crane. Its effectiveness is demonstrated with a fully nonlinear three-dimensional computer simulation and with an experiment on a scaled model of a rotary crane. The results demonstrate that the pendulations can be significantly reduced, and therefore the operations rate can be greatly increased. The effectiveness of the controller is demonstrated for both rotary and gantry modes of operation of the crane.
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Cugnon, Frédéric, Luke Berglind, Denys Plakhotnik, and Mikel Armendia. "Simulation of Machining Operations Using the Virtual Machine Tool Concept." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85217.

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This paper focusses on the dynamic modeling of the machine tool including its Computer Numeric Control (CNC), and its interaction with the machining process. To properly simulate modern machine tools in machining condition, which show close interaction between the dynamic behavior of the mechanical structure, drives, and the CNC, we use an integrated methodology that combines control and MBS capabilities in a nonlinear FEA solver called SAMCEF Mecano. To fully capture the dynamic behavior of the machine, force interactions between the cutting tool and the workpiece are also considered. A strong coupling between the mechatronic model of the machine tool and a machining simulation tool is implemented. A specialized cutting force element has been developed. It considers the dynamics of the tool tip combined with the tool workpiece engagement to generate cutting forces. The use of such digital twin model is demonstrated considering some industrial machining operations.
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Surana, K. S., and H. Vijayendra Nayak. "Solutions of Higher Class and Their Computations for Polymer Flows: Oldroyd-B Constitutive Model." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17145.

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Abstract This paper presents formulations, computations and investigations of the solutions of class C00 and C11 for two dimensional viscoelastic fluid flows in u, v, p, τijp, τijs with Oldroyd-B constitutive model using p-version Least Squares Finite Element Formulation (LSFEF). The main thrust of the research work presented in the paper is to employ ‘right class of interpolations’ and the best computational strategy to establish: i) when does Oldroyd-B model begins to fail in simulating the correct physics of flow ii) when and why does the proposed computational process fail iii) is there a correlation between i) and ii). Fully developed flow between parallel plates and the stick-slip problems are used as model problems. The investigations presented in this paper reveal the following. a) The manner in which the stresses are non-dimensionalized significantly influences the performance of the iterative procedure of solving nonlinear algebraic equations. b) Solutions of the class C00 are always the wrong class of solutions of GDEs in variables u, v, p, τijp and τijs and thus spurious. c) C11 class of solutions are the right class of solutions of the GDEs in variables u, v, p, τijp and τijs. d) In the flow domains, containing sharp gradients of the dependent variables, conservation of mass is difficult to achieve at lower p-levels (worse for coarse meshes). e) An augmented form of GDEs are proposed that always ensure conservation of mass at all p-levels regardless of the mesh and the nature of the solution gradients. f) We demonstrate that Oldroyd-B model describes correct physics of dilute polymer solutions of constant viscosity only for a limited range of Deborah numbers. Beyond this range, the computed solutions are not in agreement with the flow physics (thus spurious) even though the proposed computational process works exceptionally well. g) Numerical studies with graded meshes and high p-levels presented in this paper are aimed towards establishing and demonstrating detail behavior of local as well as global nature of the computed 10 solutions, h) Various norms are proposed and tested to judge local and global dominance of elasticity or viscous behavior 1) New definitions are proposed for elongational (extensional) viscosity. The proposed definitions are more in conformity and agreement with the flow physics compared to currently used definitions j) A significant aspect and strength of our work is that we utilize straightforward p-version LSFEF with C00 and C11 type interpolations without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used.
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Wang, Fengxia. "Modal Based Geometric Stiffening Formulation for Dynamics Simulation of Multibody Systems." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64773.

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This work concerns the implementation of nonlinear modal reduction to flexible multi-body dynamics. Linear elastic theory will lead to instability issues with rotating beamlike structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In this work, in order to improve the convergence characteristic and also to reduce the computation time in flexible multi-body dynamics, which is extremely important for complicated large systems, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. The example used in this work is a rotating Euler-Bernoulli beam, two nonlinear reduced models were established based on modal coordinates, the first reduced model created from theoretical bending and axial mode shapes by Galerkin method; the second reduced model is derived by the standard matrix operator from a full finite element model. Transient simulation results of lower degrees of freedom from above two reduced models are compared with those obtained from full nonlinear finite element model.
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Kurup, Nishu V., Shan Shi, Zhongmin Shi, Wenju Miao, and Lei Jiang. "Study of Nonlinear Internal Waves and Impact on Offshore Drilling Units." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50304.

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Internal waves near the ocean surface have been observed in many parts of the world including the Andaman Sea, Sulu Sea and South China Sea among others. The factors that cause and propagate these large amplitude waves include bathymetry, density stratification and ocean currents. Although their effects on floating drilling platforms and its riser systems have not been extensively studied, these waves have in the past seriously disrupted offshore exploration and drilling operations. In particular a drill pipe was ripped from the BOP and lost during drilling operations in the Andaman sea. Drilling riser damages were also reported from the south China Sea among other places. The purpose of this paper is to present a valid numerical model conforming to the physics of weakly nonlinear internal waves and to study the effects on offshore drilling semisubmersibles and riser systems. The pertinent differential equation that captures the physics is the Korteweg-de Vries (KdV) equation which has a general solution involving Jacobian elliptical functions. The solution of the Taylor Goldstein equation captures the effects of the pycnocline. Internal wave packets with decayed oscillations as observed from satellite pictures are specifically modeled. The nonlinear internal waves are characterized by wave amplitudes that can exceed 50 ms and the present of shearing currents near the layer of pycnocline. The offshore drilling system is exposed to these current shears and the associated movements of large volumes of water. The effect of internal waves on drilling systems is studied through nonlinear fully coupled time domain analysis. The numerical model is implemented in a coupled analysis program where the hull, moorings and riser are considered as an integrated system. The program is then utilized to study the effects of the internal wave on the platform global motions and drilling system integrity. The study could be useful for future guidance on offshore exploration and drilling operations in areas where the internal wave phenomenon is prominent.
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Palme´, Thomas, Peter Breuhaus, Mohsen Assadi, Albert Klein, and Minkyo Kim. "Early Warning of Gas Turbine Failure by Nonlinear Feature Extraction Using an Auto-Associative Neural Network Approach." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-45991.

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This study investigates the application of nonlinear Principal Component Analysis (PCA), implemented through the use of Auto-Associative Neural Network (AANN), for early warning of impending gas turbine failure. The study is based on a real operational data set that includes a compressor failure. The analyzed data set consists of measured operational parameters whose identity are unknown, hence this study presents a purely data driven approach to the problem of early warning. In this case study, the use of AANNs for early detection of abnormal engine behavior could have provided the operator with a warning a few days prior to the fully developed failure, which resulted in a forced shut-down and extensive maintenance. Furthermore, a comparison is made between the nonlinear PCA by AANNs and the standard PCA model, which is an inherently linear method. The result shows that the AANN provides a more reliable detection of the failure by a higher residual generation during failure mode as well as fewer false indications prior to the failure. Consequently, this study shows that nonlinear PCA as performed with AANNs can be a valuable data driven tool for early warning of gas turbine failure.
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Surana, K. S., and H. Vijayendra Nayak. "Computations of Numerical Solutions of Higher Class in 2D Polymer Flows: Upper Convected Maxwell Model." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17144.

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Abstract This paper presents formulations, computations and investigations of the solutions of classes C00 and C11 for two-dimensional viscoelastic fluid flows in primitive variables u, v, p, τxx, τxy, τyy with Upper Convected Maxwell (UCM) constitutive model using p-version least squares finite element formulation (LSFEF). The main emphasis of the investigations, undertaken in this research work, is to employ the right classes of interpolations and the best computational strategy to address, to illuminate on and perhaps, to answer and resolve whether the “continued obsession of developing newer and newer computational strategies to obtain solutions of Maxwell constitutive equations for ever increasing Deborah number (De) is as meritorious as currently believed. The stick-slip problem is used as a model problem in all investigations. Our investigations reveal the following: a) The manner in which the governing differential equations (GDEs) are non-dimensionalized influences the performance of the iteration procedure for solving nonlinear algebraic equations and thus, computational efficiency achieved. b) C00 class of solutions are always the wrong class of solutions and are spurious. c) In the flow domains, containing sharp gradients of dependant variables, conservation of mass is difficult to achieve specially at lower p-levels. d) C11 solutions are in conformity with the continuity considerations in GDEs. e) An augmented form of the GDEs and associated C00 and C11 formulations are proposed that always ensure conservation of mass regardless of mesh, p-levels and the nature of solution gradients. This approach yields the most desired classes of C11 solutions. f) We demonstrate that UCM constitutive model cannot describe the flow physics at any Deborah number for dilute polymer solutions of constant viscosity due to the fact that I) in UCM model, solvent stresses are a function of Deborah number. Thus, solvent stresses are wrong at any non-zero Deborah number. II) and solvent shear stresses produce elastic normal stresses. Numerical studies presented in the paper support theses findings. UCM model only generates correct flow physics for De = 0 (Newtonian flow). g) Numerical studies, with graded meshes and high p-levels presented in the paper, are aimed towards establishing and demonstrating detailed behavior of local as well as global nature of the computed solutions. Numerical studies are carefully designed and conducted to establish failure of UCM model in describing flow physics as well as failure of computational process. h) various norms are proposed and tested to judge local and global dominance of elasticity or viscous behavior. i) New definitions are proposed for elongational (extensional) viscosity. The proposed definitions are more in conformity and agreement with the flow physics compared to currently used definition. j) A very significant feature of our research work is that we utilize straight forward p-version LSFEF with C00 and C11 type interpolations without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used. Fully developed flow between parallel plates and stick-slip problems are used as model problems. It is concluded that UCM constitutive model always simulates incorrect behavior for dilute polymer solutions of constant viscosity regardless of Deborah number (except De = 0) and thus, development of newer computational schemes to achieve success at higher Deborah number is of no consequence.
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Reports on the topic "Fully nonlinear operators"

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Pocher, Liam, Nathaniel Morgan, Travis Peery, and Jonathan Mace. Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems. Office of Scientific and Technical Information (OSTI), August 2020. http://dx.doi.org/10.2172/1648057.

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