Search Results - "Galerkin method"

Error Estimates for Advanced Galerkin Methods by Rüter, Marcus Olavi

Table of Contents: “…Introduction -- Newtonian and Eshelbian Mechanics -- Boundary Value Problems -- Galerkin Methods -- Numerical Integration -- Energy Norm A Posteriori Error Estimates -- Goal-oriented A Posteriori Error Estimates in Linearized Elasticity -- Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity -- Numerical Examples -- The Nonstandard Dyadic Product Operators -- Push-forward and Pull-back Operations -- Tensor derivatives -- A Generalized Nitsche Method -- The J-integral in Elastic FractureMechanics -- Linearizations -- Materials investigated in this monograph -- Functional Analysis-A Synopsis.…”
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Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations by Cohen, Gary, Pernet, Sébastien

Table of Contents: “…Classical Continuous Models and their Analysis -- The Basic Equations -- Functional Issues -- Plane Wave Solutions -- Definition of Different Types of Finite Elements -- 1D Mass-Lumping and Spectral Elements -- Quadrilaterals and Hexahedra -- Triangles and Tetrahedra -- Purely 3D Elements -- Tetrahedral and Triangular Edge Elements -- Hexahedral and Quadrilateral Edge Elements -- H(div) Finite Elements -- Other Mixed Elements -- Hexahedral and Quadrilateral Spectral Elements for Acoustic Waves -- Second Order Formulation of the Acoustics Equation -- First Order Formulation of the Acoustics Equation -- Comparison of the Methods -- Dispersion Relation -- Reflection-Transmission by a Discontinuous Interface -- hp-a priori Error Estimates -- The Linear Elastodynamics System -- Discontinuous Galerkin Methods -- General Formulation for Linear Hyperbolic Problems -- Approximation by Triangles and Tetrahedra -- Approximation by Quadrilaterals and Hexahedra -- Comparison of the DG Methods for Maxwell's Equations -- Plane Wave Analysis -- Interior Penalty Discontinuous Galerkin Methods -- The Maxwell's System and Spurious Modes.…”
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Advanced Finite Element Technologies

Table of Contents: “…Least-squares mixed finite elements for hyperelasticity -- Discretization methods for solids undergoing finite deformations -- On the use of anisotropic triangles with mixed finite elements: application to an "immersed" boundary with the incompressible Stokes problem -- Stress-based finite element methods in linear and nonlinear solid mechanics -- Topics of mathematical fundamentals, mixed methods in elasticity, and plasticity -- Discontinuous Galerkin methods ND reduced order models.…”
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Direct and Large-Eddy Simulation XI

Table of Contents: “…Assessment of High-Order Discontinuous Galerkin Methods for LES of Transonic Flows -- Chapter 13. …”
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Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

Table of Contents: “…Okulov -- Global Galerkin method for stability studies in incompressible CFD and other possible applications, by A. …”
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Simulation Based Engineering in Solid Mechanics by Rao, J.S

Table of Contents: “…Stress -- Strain Relations -- 2.6 Strain Energy and Work -- 2.7 Von Mises Stress -- 3 Euler-Lagrange Equations -- 3.1 General Approach for solving Structural Problems -- 3.2 Other Applications of Euler-Lagrange Equation leading to Optimization -- 3.3 Derivation of Euler-Lagrange Equation through Delta Operator -- 4 Axially Loaded 1-D Structures -- 4.1 Simply Supported Bar -- 4.2 Simply Supported - Free Bar -- 4.3 Finite Element Method -- 4.4 Thermal Stresses -- 4.5 Principle of Virtual Work4.6 Minimization of Total Potential Energy -- 5 Twisting of a Rod -- 5.1 Finite Element Method for Torsion -- 5.2 Two Elements and Stiffness Matrix Assembly -- 5.3 Ritz Method for Torsion -- 6 Bending of a Beam -- 6.1 Bending by Energy Method -- 6.2 Beam with Axial Load (Beam-Column) -- 6.3 Strength ofMaterials Approach -- 6.4 Beam Solution by Energy Method -- 6.5 Beam Finite Element -- 6.6 Buckling revisited -- 6.7 Galerkin Method for Tapered Beams -- 6.8 General Structures by Commercial Solvers -- 7. …”
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Advances in Simulation of Wing and Nacelle Stall Results of the Closing Symposium of the DFG Research Unit FOR 1066, December 1-2, 2014, Braunschweig, Germany /

Table of Contents: “…The Delay of RANS-to-LES Transition in Hybrid RANS-LES Approaches and Some Recently Proposed Remedies -- Computations of Separated Flows with a Hybrid RANS/LES Approach -- Hybrid RANS/LES Study of the Development of an Airfoil-Generated Vortex -- Interaction of Three-Dimensional Disturbances with the Flow around a Two-Element High-Lift Airfoil -- The Discontinuous Galerkin Method as an Enabling Technology for DNS and LES of Industrial Aeronautical Applications -- Body Force Modelling of Internal Geometry for Jet Noise Prediction -- Numerical Studies of Turbulent Flow Influence on a Two-Element Airfoil -- CFD for Prediction of Flow Separation from Aircraft Tail Surfaces -- Zonal RANS-LES Computation for Near-Stall-Airfoil Flow -- Criteria for Crosswind Variations during Approach and Touchdown at Airports -- Development and Improvement of Two Methods of Different Complexity to Simulate Atmospheric Boundary Layer Turbulence for Aircraft Design Studies -- Simulation of Interaction of Aircraft with Gust and Resolved LES-Simulated Atmospheric Turbulence -- A New Method to Generate Anisotropic Synthetic Turbulence for LES -- Numerical Simulation of the Turbulent Flow Around a Wing -- Integration- and Intake-Induced Flow Distortions and their Impact on Aerodynamic Fan Performance -- Flow Investigations in a Stalling Nacelle Inlet Under Disturbed Inflow -- Realistic Inlet Distortion Patterns Interacting with a Transonic Compressor Stage -- Unsteady CFD Simulation of Transonic Axial Compressor Stages with Distorted Inflow -- Transitional Shock-Wave/Boundary-Layer Interactions in Intakes at Incidence.…”
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Dynamic Stability of Columns under Nonconservative Forces Theory and Experiment / by Sugiyama, Yoshihiko, Langthjem, Mikael A., Katayama, Kazuo

Table of Contents: “…Preface -- 1 Fundamentals -- 1.1 Beam and Column -- 1.2 Stability and Stability Criteria -- 1.3 Experiments with Columns -- 1.4 Preliminary Tests -- 1.5 Influence of Support Conditions -- 1.6 Nonconservative Forces -- 1.7 Discussion -- References -- 2 Columns under Conservative Forces -- 2.1 Cantilevered Columns -- 2.2 Pinned-pinned Columns -- 2.3 Standing Cantilevered Columns -- 2.4 Discussion -- References -- 3 Columns under a Follower Force -- 3.1 Beck's Column -- 3.2 Vibrations of Beck's Column -- 3.3 Stability in a Finite Time Interval -- 3.4 Character of Beck's Column -- 3.5 Nonconservative Nature of a Follower Force -- 3.6 Discussion -- References -- 4 Columns with Damping -- 4.1 Cantilevered Columns with Damping -- 4.2 Stability Analysis -- 4.3 Beck's Column with Damping Introduced -- 4.4 Pflüger's Column with Internal Damping -- 4.5 Dynamic Responses -- 4.6 Discussion -- References -- 5 Energy Consideration on the Role of Damping -- 5.1 Energy Considerations -- 5.2 Equation of Motion and Stability Analysis -- 5.3 Energy Expressions -- 5.4 Flutter Configurations and Phase Angles Functions -- 5.5 Energy Balance with Small Internal Damping -- 5.6 Energy Balance with Both Internal and External Damping -- 5.7 Energy Growth Rate -- 5.8 Introduction of Small Internal Damping at the Undamped Flutter Bound -- 5.9 Discussion -- References -- 6 Cantilevered Pipes Conveying Fluid -- 6.1 Basic Equations of Motion -- 6.2 Finite Element Formulation -- 6.3 Eigenvalue Branches Related to Flutter -- 6.4 Flutter Configurations -- 6.5 Effect of Internal Damping -- 6.6 Discussion -- References -- 7 Cantilevered Pipes with a Mechanical Element -- 7.1 Pipes with an Elastic Spring -- 7.2 Pipes with a Lumped Mass -- 7.3 Pipes with a Damper -- 7.4 Coefficient of Damping of a Dashpot Damper -- 7.5 Discussion -- References -- 8 Columns under a Follower Force with a Constant Line of Action -- 8.1 Reut's Column -- 8.2 Stability Analysis of a Generalized Reut's Column -- 8.3 Approximate Solution by the Galerkin Method -- 8.4 Non-self-adjointness of Boundary Value Problems -- 8.5 Discussion -- References -- 9 Generalized Reut's Column -- 9.1 Stability Analysis -- 9.2 Realization of Reut Force -- 9.3 Experimental Setup -- 9.4 Experimental Results -- 9.5 Reut's Column with a Damper -- 9.6 Discussion -- References -- 10 Columns under a Rocket-based Follower Force -- 10.1 Equation of Motion and Stability Analysis -- 10.2 Rocket Motors -- 10.3 Test Columns -- 10.4 Preliminary Tests -- 10.5 Flutter Test -- 10.6 Discussion -- References -- 11 Columns under a Rocket-based Follower Force and with a Lumped Mass -- 11.1 Finite Element Formulation and Stability Analysis -- 11.2 Rocket Motors -- 11.3 Estimate of the Effect of a Lumped Mass on the Flutter Limit -- 11.4 Flutter Test -- 11.5 Discussion -- References -- 12 Columns under a Rocket-based Subtangential Follower Force -- 12.1 Mathematical Model and Finite Element Formulation -- 12.2 Rocket Motors -- 12.3 Test Columns -- 12.4 Stability Estimates -- 12.5 Experiment with Columns under a Rocket-based Subtangential Follower Force -- 12.6 Discussion -- References -- 13 Pinned-pinned Columns under a Pulsating Axial Force -- 13.1 The Mathieu Equation -- 13.2 Stability of the Solution to the Mathieu Equation -- 13.3 Pinned-pinned Columns -- 13.4 Vibrations in the Vicinity of Upper and Lower Boundaries I -- 13.5 Vibrations in the Vicinity of Upper and Lower Boundaries II -- 13.6 Effect of a Phase Angle in Excitation -- 13.7 Discussions -- References -- 14 Parametric Resonances of Columns -- 14.1 Mathieu-Hill Equations -- 14.2 Hsu's Approach -- 14.3 Coupled Mathieu Equation of Columns -- 14.4 Hsu's Resonance Conditions -- 14.5 Estimate of the Principal Regions of Resonances -- 14.6 Experiment with Columns Having Clamped-clamped and Clamped-pinned Ends -- 14.7 Columns under a Pulsating Follower Force -- 14.8 Discussion -- References -- 15 Parametric Resonances of Columns with Damping -- 15.1 Approaches to Mathieu-Hill Equations -- 15.2 Hsu'sApproach to Coupled Hill Equations -- 15.3 Effect of Damping -- 15.4 Second-order Approximation -- 15.5 Discussion -- References -- 16 Columns under a Pulsating Reut Force -- 16.1 Columns under a Pulsating Generalized Reut Force -- 16.2 Finite Difference Formulation and Stability Analysis -- 16.3 Experiment with Columns under a Pulsating Reut Force -- 16.4 Discussion -- References -- 17 Remarks about Approaches to the Dynamic Stability of Structures -- References -- Appendix: Suggested Exercises. .…”
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