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A Finite Element Primer for Beginners : The Basics / / by Tarek I. Zohdi
| A Finite Element Primer for Beginners : The Basics / / by Tarek I. Zohdi |
| Autore | Zohdi Tarek I |
| Edizione | [2nd ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XIII, 135 p. 41 illus.) |
| Disciplina | 620.00151535 |
| Soggetto topico |
Mechanics
Mechanics, Applied Computer mathematics Computational complexity Physics Fluid mechanics Mathematical models Solid Mechanics Computational Science and Engineering Complexity Numerical and Computational Physics, Simulation Engineering Fluid Dynamics Mathematical Modeling and Industrial Mathematics |
| ISBN | 3-319-70428-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Figures -- 1 Weighted Residuals and Galerkin's Method for a Generic 1D Problem -- 1.1 Introduction: Weighted Residual Methods -- 1.2 Galerkin's Method -- 1.3 An Overall Framework -- 2 A Model Problem: 1D Elastostatics -- 2.1 Introduction: A Model Problem -- 2.2 Weak Formulations in One Dimension -- 2.3 An Example -- 2.4 Some Restrictions -- 2.5 Remarks on Nonlinear Problems -- 3 A Finite Element Implementation in One Dimension -- 3.1 Introduction -- 3.2 Weak Formulation -- 3.3 FEM Approximation -- 3.4 Construction of FEM Basis Functions -- 3.5 Integration and Gaussian Quadrature -- 3.5.1 An Example -- 3.6 Global/Local Transformations -- 3.7 Differential Properties of Shape Functions -- 3.8 Post-Processing -- 3.9 A Detailed Example -- 3.9.1 Weak Form -- 3.9.2 Formation of the Discrete System -- 3.9.3 Applying Boundary Conditions -- 3.9.4 Massive Data Storage Reduction -- 3.10 Quadratic Elements -- 4 Accuracy of the Finite Element Method in One Dimension -- 4.1 Introduction -- 4.2 The ``Best Approximation'' Theorem -- 4.3 The Principle of Minimum Potential Energy -- 4.4 Simple Estimates for Adequate FEM Meshes -- 4.5 Local Mesh Refinement -- 5 Iterative Solutions Schemes -- 5.1 Introduction: Minimum Principles and Krylov Methods -- 5.1.1 Numerical Linear Algebra -- 5.1.2 Krylov Searches and Minimum Principles -- 6 Weak Formulations in Three Dimensions -- 6.1 Introduction -- 6.2 Hilbertian Sobolev Spaces -- 6.3 The Principle of Minimum Potential Energy -- 6.4 Complementary Principles -- 7 A Finite Element Implementation in Three Dimensions -- 7.1 Introduction -- 7.2 FEM Approximation -- 7.3 Global/Local Transformations -- 7.4 Mesh Generation and Connectivity Functions -- 7.5 Warning: Restrictions on Elements -- 7.5.1 Good and Bad Elements: Examples -- 7.6 Three-Dimensional Shape Functions.
7.7 Differential Properties of Shape Functions -- 7.8 Differentiation in the Referential Coordinates -- 7.8.1 Implementation Issues -- 7.8.2 An Example of the Storage Scaling -- 7.9 Surface Jacobians and Nanson's Formula -- 7.10 Post-Processing -- 8 Accuracy of the Finite Element Method in Three Dimensions -- 8.1 Introduction -- 8.2 The ``Best Approximation'' Theorem -- 8.3 Simple Estimates for Adequate FEM Meshes Revisited for Three Dimensions -- 8.4 Local Error Estimation and Adaptive Mesh Refinement -- 8.4.1 A Posteriori Recovery Methods -- 8.4.2 A Posteriori Residual Methods -- 9 Time-Dependent Problems -- 9.1 Introduction -- 9.2 Generic Time Stepping -- 9.3 Application to the Continuum Formulation -- 10 Summary and Advanced Topics -- Appendix A Elementary Mathematical Concepts -- A.1 Vector Products -- A.2 Vector Calculus -- A.3 Interpretation of the Gradient of Functionals -- A.4 Matrix Manipulations -- A.4.1 Determinant -- A.4.2 Eigenvalues -- A.4.3 Coordinate Transformations -- Appendix B Basic Continuum Mechanics -- B.1 Deformations -- B.2 Equilibrium/Kinetics of Solid Continua -- B.2.1 Postulates on Volume and Surface Quantities -- B.2.2 Balance Law Formulations -- B.3 Referential Descriptions of Balance Laws and Nanson's Formula -- B.4 The First Law of Thermodynamics/An Energy Balance -- B.5 Linearly Elastic Constitutive Equations -- B.5.1 The Infinitesimal Strain Case -- B.5.2 Linear Elastic Constitutive Laws -- B.5.3 Material Component Interpretation -- B.6 Related Physical Concepts -- B.6.1 Heat Conduction -- B.6.2 Solid-State Diffusion-Reaction -- B.6.3 Conservation Law Families -- Appendix C Convergence of Recursive Iterative Schemes -- Appendix D Selected in-Class Exam Problems -- D.1 Sample Problem 1 -- D.2 Sample Problem 2 -- D.3 Sample Problem 3 -- D.4 Sample Problem 4 -- D.5 Sample Problem 5 -- D.6 Sample Problem 6. D.7 Sample Problem 7 -- D.8 Sample Problem 8 -- D.9 Sample Problem 9 -- D.10 Sample Problem 10 -- D.11 Sample Problem 11 -- D.12 Sample Problem 12 -- D.13 Sample Problem 13 -- D.14 Sample Problem 14 -- D.15 Sample Problem 15 -- D.16 Sample Problem 16 -- D.17 Sample Problem 17 -- Appendix E Selected Computer Projects -- E.1 Assignment Format -- E.2 Sample Project 1: The Basics of FEM -- E.3 Sample Project 2: Higher-Order Elements -- E.4 Sample Project 3: Potential and Efficient Solution Techniques -- E.5 Sample Project 4: Error Estimation and Adaptive Meshing Using the Exact Solution as a Test -- E.6 Sample Project 5: 3D Formulations for Elasticity -- E.7 Sample Project 6: Implementation of the Finite Element Method in 2D -- E.8 Sample Project 7: Time-Dependent Problems. |
| Record Nr. | UNINA-9910299585903321 |
Zohdi Tarek I
|
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A Finite Element Primer for Beginners : The Basics / / by Tarek I. Zohdi
| A Finite Element Primer for Beginners : The Basics / / by Tarek I. Zohdi |
| Autore | Zohdi Tarek I |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (113 p.) |
| Disciplina | 620.00151535 |
| Collana | SpringerBriefs in Applied Sciences and Technology |
| Soggetto topico |
Mechanics
Mechanics, Applied Fluid mechanics Computational complexity Computer mathematics Mathematical models Physics Solid Mechanics Engineering Fluid Dynamics Complexity Computational Science and Engineering Mathematical Modeling and Industrial Mathematics Numerical and Computational Physics, Simulation |
| ISBN | 3-319-09036-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Weighted residuals and Galerkin’s method for a generic 1-D problem -- A model problem: 1-D elastostatics -- A finite element implementation in one dimension -- Accuracy of the finite element method -- Element by element iterative solutions schemes -- Weak formulations in three dimensions -- A finite element implementation in three dimensions -- Accuracy of the finite element method -- Time-dependent problems -- Summary and advanced topics. |
| Record Nr. | UNINA-9910299858203321 |
|
Zohdi Tarek I
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Modeling and Simulation of Functionalized Materials for Additive Manufacturing and 3D Printing: Continuous and Discrete Media : Continuum and Discrete Element Methods / / by Tarek I. Zohdi
| Modeling and Simulation of Functionalized Materials for Additive Manufacturing and 3D Printing: Continuous and Discrete Media : Continuum and Discrete Element Methods / / by Tarek I. Zohdi |
| Autore | Zohdi Tarek I |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XIX, 298 p. 83 illus., 34 illus. in color.) |
| Disciplina | 670.113 |
| Collana | Lecture Notes in Applied and Computational Mechanics |
| Soggetto topico |
Manufactures
Manufacturing, Machines, Tools, Processes |
| ISBN | 3-319-70079-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | From the Content: Introduction: Additive/3D Printing Materials-filaments, Functionalized-inks and Powders.- PART I-Continuum Methods (CM) : Basic Continuum Mechanics -- CM Approaches: Characterization of Particle-functionalized Materials -- CM Approaches: Estimation and Optimization of the Effective Properties of Mixtures.- CM Approaches: Numerical thermo-mechanical Formulations. |
| Record Nr. | UNINA-9910299892203321 |
|
Zohdi Tarek I
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||