The Finite Element Method: Its Basis and Fundamentals, Eighth Edition offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in a kind of detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition includes a significant addition of content addressing coupling problems, including: Finite element analysis formulations for coupled problems; Details of algorithms for solving coupled problems; Examples showing how algorithms can be used to solve for piezoelectricity and poroelasticity problems. Focusing on the core knowledge, mathematical and analytical tools needed for successful application, this book is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. List of figures - p. xxi 8. List of tables - p. xxxi 9. Biography - p. xxxiii 10. Preface - p. xxxv 11. 1: The standard discrete system and origins of the finite element method - p. 1 12. 2: Problems in linear fields - p. 21 13. 3: Weak forms and approximate solutions: 1-D field problems - p. 29 14. 4: Finite element approximate solutions: 1-D field problems - p. 41 15. 5: Finite element forms exact at nodes - p. 63 16. 6: Variational forms and finite element approximation: 1-D problems - p. 73 17. 7: Field problems: a multi-dimensional finite element method - p. 95 18. 8: Shape functions, derivatives and integration - p. 127 19. 9: Problems in linear elasticity - p. 179 20. 10: Elasticity: two and three dimensional finite elements - p. 201 21. 11: The patch test, reduced integration, and non-conforming elements - p. 243 22. 12: Mixed formulation and constraints – complete field methods - p. 269 23. 13: Incompressible problems, mixed methods and other procedures of solution - p. 299 24. 14: Transient analysis of solids - p. 337 25. 15: Finite element solutions: multi-physics problems - p. 351 26. 16: Multi-physics battery simulation - p. 379 27. 17: Multidomain mixed approximations - p. 385 28. 18: The time dimension – semi-discretization of field and dynamic problems - p. 403 29. 19: Plate bending approximation: thin and thick plates - p. 429 30. 20: Shells as a special case of three-dimensional analysis - p. 489 31. 21: Computer procedures for finite element analysis - p. 513 32. A: Matrix algebra - p. 519 33. B: Some vector algebra - p. 527 34. C: Mathematical properties, error estimates and convergence - p. 533 35. D: Tensor-indicial notation in elasticity problems - p. 543 36. E: Solution of simultaneous linear algebraic equations - p. 553 37. F: Integration by parts – Green's theorem - p. 563 38. G: Triangle and tetrahedron integrals - p. 565 39. H: Matrix diagonalization or lumping - p. 567 40. I: Recovery process - p. 575 41. Author index - p. 589 42. Subject index - p. 599
The Finite Element Method: Its Basis and Fundamentals, Eighth Edition offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in a kind of detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition includes a significant addition of content addressing coupling problems, including: Finite element analysis formulations for coupled problems; Details of algorithms for solving coupled problems; Examples showing how algorithms can be used to solve for piezoelectricity and poroelasticity problems. Focusing on the core knowledge, mathematical and analytical tools needed for successful application, this book is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. List of figures - p. xxi 8. List of tables - p. xxxi 9. Biography - p. xxxiii 10. Preface - p. xxxv 11. 1: The standard discrete system and origins of the finite element method - p. 1 12. 2: Problems in linear fields - p. 21 13. 3: Weak forms and approximate solutions: 1-D field problems - p. 29 14. 4: Finite element approximate solutions: 1-D field problems - p. 41 15. 5: Finite element forms exact at nodes - p. 63 16. 6: Variational forms and finite element approximation: 1-D problems - p. 73 17. 7: Field problems: a multi-dimensional finite element method - p. 95 18. 8: Shape functions, derivatives and integration - p. 127 19. 9: Problems in linear elasticity - p. 179 20. 10: Elasticity: two and three dimensional finite elements - p. 201 21. 11: The patch test, reduced integration, and non-conforming elements - p. 243 22. 12: Mixed formulation and constraints – complete field methods - p. 269 23. 13: Incompressible problems, mixed methods and other procedures of solution - p. 299 24. 14: Transient analysis of solids - p. 337 25. 15: Finite element solutions: multi-physics problems - p. 351 26. 16: Multi-physics battery simulation - p. 379 27. 17: Multidomain mixed approximations - p. 385 28. 18: The time dimension – semi-discretization of field and dynamic problems - p. 403 29. 19: Plate bending approximation: thin and thick plates - p. 429 30. 20: Shells as a special case of three-dimensional analysis - p. 489 31. 21: Computer procedures for finite element analysis - p. 513 32. A: Matrix algebra - p. 519 33. B: Some vector algebra - p. 527 34. C: Mathematical properties, error estimates and convergence - p. 533 35. D: Tensor-indicial notation in elasticity problems - p. 543 36. E: Solution of simultaneous linear algebraic equations - p. 553 37. F: Integration by parts – Green's theorem - p. 563 38. G: Triangle and tetrahedron integrals - p. 565 39. H: Matrix diagonalization or lumping - p. 567 40. I: Recovery process - p. 575 41. Author index - p. 589 42. Subject index - p. 599
