Programming the Finite Element Method
Home > Science, Technology & Agriculture > Mechanical engineering and materials > Programming the Finite Element Method
Programming the Finite Element Method

Programming the Finite Element Method

|
     0     
5
4
3
2
1




Out of Stock


Notify me when this book is in stock
About the Book

This title demonstrates how to develop computer programmes which solve specific engineering problems using the finite element method. It enables students, scientists and engineers to assemble their own computer programmes to produce numerical results to solve these problems. The first three editions of Programming the Finite Element Method established themselves as an authority in this area. This fully revised 4th edition includes completely rewritten programmes with a unique description and list of parallel versions of programmes in Fortran 90. The Fortran programmes and subroutines described in the text will be made available on the Internet via anonymous ftp, further adding to the value of this title.

Table of Contents:
Preface. Acknowledgement. 1. Preliminaries: Computer Strategies. 1.1 Introduction. 1.2 Hardware. 1.3 Memory management. 1.4 Vector processors. 1.5 Parallel processors. 1.6 BLAS libraries. 1.7 MPI libraries. 1.8 Applications software. 1.8.1 Arithmetic. 1.8.2 Conditions. 1.8.3 Loops. 1.9 Array features. 1.9.1 Dynamic arrays. 1.9.2 Broadcasting. 1.9.3 Constructors. 1.9.4 Vector subscripts. 1.9.5 Array sections. 1.9.6 Whole--array manipulations. 1.9.7 Intrinsic procedures for arrays. 1.9.8 Additional Fortran 95 features. 1.9.9 Subprogram libraries. 1.9.10 Structured programming. 1.10 Conclusions. References. 2. Spatial Discretisation by Finite Elements. 2.1 Introduction. 2.2 Rod element. 2.2.1 Rod stiffness matrix. 2.2.2 Rod mass element. 2.3 The eigenvalue equation. 2.4 Beam element. 2.4.1 Beam element stiffness matrix. 2.4.2 Beam element mass matrix. 2.5 Beam with an axial force. 2.6 Beam on an elastic foundation. 2.7 General remarks on the discretisation process. 2.8 Alternative derivation of element stiffness. 2.9 Two--dimensional elements: plane strain and plane stress. 2.10 Energy approach. 2.11 Plane element mass matrix. 2.12 Axisymmetric stress and strain. 2.13 Three--dimensional stress and strain. 2.14 Plate--bending element. 2.15 Summary of element equations for solids. 2.16 Flow of fluids: Navier--Stokes equations. 2.17 Simplified flow equations. 2.17.1 Steady state. 2.17.2 Transient state. 2.17.3 Advection. 2.18 Further coupled equations: Biot consolidation. 2.19 Conclusions. References. 3. Programming Finite Element Computations. 3.1 Introduction. 3.2 Local coordinates for quadrilateral elements. 3.2.1 Numerical integration for quadrilaterals. 3.2.2 Analytical integration for quadrilaterals . 3.3 Local coordinates for triangular elements. 3.3.1 Numerical integration for triangles. 3.4 Multi--element assemblies. 3.5 "Element--by--element" or "Mesh--free" techniques. 3.5.1 Conjugate gradient method. 3.5.2 Preconditioning. 3.5.3 Unsymmetric systems. 3.5.4 Symmetric non--positive definite equations. 3.5.5 Symmetric eigenvalue systems. 3.6 Incorporation of boundary conditions. 3.7 Programming using building blocks. 3.7.1 Black box routines. 3.7.2 Special purpose routines. 3.7.3 Plane elastic analysis using quadrilateral elements. 3.7.4 Plane elastic analysis using triangular elements. 3.7.5 Axisymmetric strain of elastic solids. 3.7.6 Plane steady laminar fluid flow. 3.7.7 Mass matrix formation. 3.7.8 Higher--order 2D elements. 3.7.9 Three--dimensional elements. 3.7.10 Assembly of elements. 3.8 Solution of equilibrium equations. 3.9 Evaluation of eigenvalues and eigenvectors. 3.9.1 Jacobi algorithm. 3.9.2 Lanczos algorithm. 3.10 Solution of first order time dependent problems. 3.11 Solution of coupled Navier--Stokes problems. 3.12 Solution of coupled transient problems. 3.12.1 Absolute load version. 3.12.2 Incremental load version. 3.13 Solution of second order time dependent problems. 3.13.1 Modal superposition. 3.13.2 Newmark or Crank--Nicolson method. 3.13.3 Wilson's method. 3.13.4 Explicit methods and other storage--saving strategies. References. 4. Static Equilibrium of Structures. 4.1 Introduction. Program 4.1 One--dimensional analysis of axially loaded elastic rods using 2--node rod elements. Program 4.2 Analysis of elastic pin--jointed frames using 2--node rod elements in two or three dimensions. Program 4.3 Analysis of elastic beams using 2--node beam elements (elastic foundation optional). Program 4.4 Analysis of elastic rigid--jointed frames using 2--node beam/rod elements in two or three dimensions. Program 4.5 Analysis of elastic--plastic beams or rigid--jointed frames using 2--node beam or beam/rod elements in one, two or three dimensions. Program 4.6 Stability (buckling) analysis of elastic beams using 2--node beam elements (elastic foundation optional). Program 4.7 Analysis of plates using 4--node rectangular plate elements. Homogeneous material with identical elements. Mesh numbered in x-- or y--direction. 4.2 Concluding remarks. 4.3 Exercises. References. 5. Static Equilibrium of Linear Elastic Solids. 5.1 Introduction. Program 5.1 Plane or axisymmetric strain analysis of an elastic solid using 3--, 6--, 10--, or 15--node right--angled triangles or 4--, 8--, or 9--node rectangular quadrilaterals. Mesh numbered in x(r)-- or y(z)--direction. Program 5.2 Non--axisymmetric analysis of an axisymmetric elastic solid using 8--node rectangular quadrilaterals. Mesh numbered in r-- or z--direction. Program 5.3 Three--dimensional analysis of an elastic solid using 8--, 14--, or 20--node brick hexahedra. Mesh numbered in x--z planes then in the y--direction. Program 5.4 General two-- (plane strain) or three--dimensional analysis of elastic solids. Program 5.5 Three--dimensional strain of an elastic solid using 8--, 14--, or 20--node brick hexahedra. Mesh numbered in x--z planes then in the y--direction. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. Program 5.6 Three--dimensional strain of an elastic solid using 8--, 14--, or 20--node brick hexahedra. Mesh numbered in x--z planes then in the y--direction. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. Vectorised version. 5.2 Exercises. References. 6. Material Non--linearity. 6.1 Introduction. 6.2 Stress--strain behaviour. 6.3 Stress invariants. 6.4 Failure criteria. 6.4.1 Von Mises. 6.4.2 Mohr--Coulomb and Tresca. 6.5 Generation of body loads. 6.6 Viscoplasticity. 6.7 Initial stress. 6.8 Corners on the failure and potential surfaces. Program 6.1 Plane strain bearing capacity analysis of an elastic--plastic (von Mises) material using 8--node rectangular quadrilaterals. Viscoplastic strain method. Program 6.2 Plane strain bearing capacity analysis of an elastic--plastic (von Mises) material using 8--node rectangular quadrilaterals. Viscoplastic strain method. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. Program 6.3 Plane strain slope stability analysis of an elastic--plastic (Mohr--Coulomb) material using 8--node rectangular quadrilaterals. Viscoplastic strain method. Program 6.4 Plane strain earth pressure analysis of an elastic--plastic (Mohr--Coulomb) material using 8--node rectangular quadrilaterals. Initial stress method. 6.9 Elasto--plastic rate integration. 6.9.1 Forward Euler method. 6.9.2 Backward Euler method. 6.10 Tangent stiffness approaches. 6.10.1 Inconsistent tangent matrix. 6.10.2 Consistent tangent matrix. 6.10.3 Convergence criterion. Program 6.5 Plane strain bearing capacity analysis of an elastic--plastic (von Mises) material using 8--node rectangular quadrilaterals. Initial stress method. Tangent stiffness. Consistent return algorithm. Program 6.6 Plane strain bearing capacity analysis of an elastic--plastic (von Mises) material using 8--node rectangular quadrilaterals. Initial stress method. Tangent stiffness. Consistent return algorithm. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. 6.11 The geotechnical processes of embanking and excavation. 6.11.1 Embanking. Program 6.7 Plane strain construction of an elastic--plastic (Mohr--Coulomb) embankment in layers on a foundation using 8--node quadrilaterals. Viscoplastic strain method. 6.11.2 Excavation. Program 6.8 Plane strain construction of an elastic--plastic (Mohr--Coulomb) excavation in layers using 8--node quadrilaterals. Viscoplastic strain method. 6.12 Undrained analysis. Program 6.9 Axisymmetric "undrained" strain of an elastic--plastic (Mohr--Coulomb) solid using 8--node rectangular quadrilaterals. Viscoplastic strain method. Program 6.10 Three--dimensional strain analysis of an elastic--plastic (Mohr--Coulomb) slope using 20--node hexahedra. Viscoplastic strain method. Program 6.11 Three--dimensional strain analysis of an elastic--plastic (Mohr--Coulomb) slope using 20--node hexahedra. Viscoplastic strain method. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. 6.13 Exercises. References. 7. Steady State Flow. 7.1 Introduction. Program 7.1 One--dimensional analysis of steady seepage using 2--node line elements. Program 7.2 Plane or axisymmetric analysis of steady seepage using 4--node rectangular quadrilaterals. Mesh numbered in x(r)-- or y(z)-- direction. Program 7.3 Analysis of plane free--surface flow using 4--node quadrilaterals. "Analytical" form of element conductivity matrix. Program 7.4 General two-- (plane) or three--dimensional analysis of steady seepage. Program 7.5 General two-- (plane) or three--dimensional analysis of steady seepage. No global conductivity matrix assembly. Diagonally preconditioned conjugate gradient solver. 7.2 Exercises. References. 8. Transient Problems: First Order (Uncoupled). 8.1 Introduction. Program 8.1 One--dimensional consolidation analysis using 2--node line elements. Implicit time integration using the "theta" method. Program 8.2 Plane or axisymmetric consolidation analysis using 4--node rectangular quadrilaterals. Mesh numbered in x(r)-- or y(z)--direction. Implicit time integration using the "theta" method. 8.2 Mesh--free Strategies in Transient Analysis. Program 8.3 Plane or axisymmetric consolidation analysis using 4--node rectangular quadrilaterals. Mesh numbered in x(r)-- or y(z)--direction. Implicit time integration using the "theta" method. No global stiffness matrix assembly. Diagonal preconditioner conjugate gradient solver. Program 8.4 Plane or axisymmetric analysis of the consolidation equation using 4--node rectangular quadrilaterals. Mesh numbered in x(r)-- or y(z)--direction. Explicit time integration using the "theta = 0" method. Program 8.5 Plane or axisymmetric analysis of the consolidation equation using 4--node rectangular quadrilaterals. Mesh numbered in x(r)-- or y(z)--direction. "theta" method using an element--by--element product algorithm. 8.3 Comparison of Programs 8.2, 8.3, 8.4, and 8.5. Program 8.6 General two-- (plane) or three--dimensional analysis of the consolidation equation. Implicit time integration using the "theta" method. Program 8.7 Plane analysis of the diffusion--convection equation using 4--node rectangular quadrilaterals. Implicit time integration using the "theta" method. Self--adjoint transformation. Program 8.8 Plane analysis of the diffusion--convection equation using 4--node rectangular quadrilaterals. Implicit time integration using the "theta" method. Untransformed solution. 8.4 Exercises. References. 9. Coupled Problems. 9.1 Introduction. Program 9.1 Analysis of the plane steady state Navier--Stokes equation using 8--node rectangular quadrilaterals for velocities coupled to 4--node rectangular quadrilaterals for pressures. Mesh numbered in x-- or y--direction. Freedoms numbered in the order u--p--v. Program 9.2 Analysis of the plane steady state Navier--Stokes equation using 8--node rectangular quadrilaterals for velocities coupled to 4--node rectangular quadrilaterals for pressures. Mesh numbered in x-- or y--direction. Freedoms numbered in the order u--p--v. Element--by--element solution using BiCGStab(l) with no preconditioning. No global matrix assembly. Program 9.3 Plane strain consolidation analysis of a Biot poro--elastic solid using 8--node rectangular quadrilaterals for displacements coupled to 4--node rectangular quadrilaterals for pressures. Freedoms numbered in the order u--v--uw. Incremental version. Program 9.4 Plane strain consolidation analysis of a Biot poro--elastic--plastic (Mohr--Coulomb) material using 8--node rectangular quadrilaterals for displacements coupled to 4--node rectangular quadrilaterals for pressures. Freedoms numbered in the order u--v--uw. Incremental version. Viscoplastic strain method. Program 9.5 Plane strain consolidation analysis of a Biot poro--elastic solid using 8--node rectangular quadrilaterals for displacements coupled to 4--node rectangular quadrilaterals for pressures. Freedoms numbered in the order u--v--uw. Absolute load version. No global stiffness matrix assembly. Diagonally preconditioned conjugate gradient solver. 9.2 Exercises. References. 10. Eigenvalue Problems. 10.1 Introduction. Program 10.1 Eigenvalue analysis of elastic beams using 2--node beam elements. Lumped mass. Program 10.2 Eigenvalue analysis of an elastic solid in plane strain using 4-- or 8--node rectangular quadrilaterals. Lumped mass. Mesh numbered in x-- or y--direction. Program 10.3 Eigenvalue analysis of an elastic solid in plane strain using 4--node rectangular quadrilaterals. Lanczos Method. Consistent mass. Mesh numbered in x-- or y--direction. Program 10.4 Eigenvalue analysis of an elastic solid in plane strain using 4--node rectangular quadrilaterals. Lanczos Method. Lumped mass. Element--byelement formulation. Mesh numbered in x-- or y--direction. 10.2 Exercises. References. 11. Forced Vibrations. 11.1 Introduction. Program 11.1 Forced vibration analysis of elastic beams using 2--node beam elements. Consistent mass. Newmark time stepping. Program 11.2 Forced vibration analysis of an elastic solid in plane strain using 4-- or 8--node rectangular quadrilaterals. Lumped mass. Mesh numbered in x-- or y--direction. Modal superposition. Program 11.3 Forced vibration analysis of an elastic solid in plane strain using rectangular 8--node quadrilaterals. Lumped or consistent mass. Mesh numbered in x-- or y--direction. Implicit time integration using the "theta" method. Program 11.4 Forced vibration analysis of an elastic solid in plane strain using rectangular 8--node quadrilaterals. Lumped or consistent mass. Mesh numbered in x-- or y--direction. Implicit time integration using Wilson's method. Program 11.5 Forced vibration analysis of an elastic solid in plane strain using rectangular uniform size 4--node quadrilaterals. Mesh numbered in the xor y--direction. Lumped or consistent mass. Mixed explicit/implicit time integration. Program 11.6 Forced vibration analysis of an elastic solid in plane strain using rectangular 8--node quadrilaterals. Lumped or consistent mass. Mesh numbered in x-- or y--direction. Implicit time integration using the "theta" method. No global matrix assembly. Diagonally preconditioned conjugate gradient solver. Program 11.7 Forced vibration analysis of an elastic--plastic (von Mises) solid in plane strain using rectangular 8--node quadrilateral elements. Lumped mass. Mesh numbered in x-- or y--direction. Explicit time integration. 11.2 Exercises. References. 12. Parallel Processing of Finite Element Analyses. 12.1 Introduction. 12.2 Differences between parallel and serial programs. 12.2.1 Parallel libraries. 12.2.2 Global variables. 12.2.3 MPI library routines. 12.2.4 The pp appendage. 12.2.5 Reading and writing. 12.2.6 Problem--specific boundary condition routines. 12.2.7 rest instead of nf. 12.2.8 Gathering and scattering. 12.2.9 Reindexing. 12.2.10 Domain composition. 12.2.11Load balancing. Program 12.1 Three dimensional analysis of an elastic solid. Compare Program 5.5. Program 12.2 Three dimensional analysis of an elasto--plastic (Mohr--Coulomb) solid. Compare Program 6.11. Program 12.3 Three dimensional Laplacian flow. Compare Program 7.5. Program 12.4 Three dimensional transient flow-- implicit analysis in time. Compare Program 8.3. Program 12.5 Three dimensional transient flow--explicit analysis in time. Compare Program 8.4. Program 12.6 Three dimensional steady state Navier--Stokes analysis. Compare Program 9.2. Program 12.7 Three--dimensional analysis of Biot poro--elastic solid. Compare Program 9.2. Program 12.8 Eigenvalue analysis of three--dimensional elastic solid. Compare Program 10.4. Program 12.9 Forced vibration analysis of a three--dimensional elastic solid. Implicit integration in time. Compare Program 11.4. Program 12.10 Forced vibration analysis of three--dimensional elasto--plastic solid. Explicit integration in time. Compare Program 11.5. 12.3 Performance data for a "Beowulf" PC cluster. 12.4 Conclusions. References. A. Equivalent Nodal Loads. B. Shape Functions and Element Node Numbering. C. Plastic Stress--strain Matrices and Plastic Potential Derivatives. D. main Library Subroutines. E. geom Library Subroutines. F. Parallel Library Subroutines. Author Index. Subject Index.


Best Sellers


Product Details
  • ISBN-13: 9780470849705
  • Publisher: John Wiley and Sons Ltd
  • Publisher Imprint: John Wiley & Sons Ltd
  • Edition: Revised edition
  • Language: English
  • Spine Width: 34 mm
  • Width: 171 mm
  • ISBN-10: 0470849703
  • Publisher Date: 13 Aug 2004
  • Binding: Paperback
  • Height: 244 mm
  • Returnable: N
  • Weight: 1030 gr


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Programming the Finite Element Method
John Wiley and Sons Ltd -
Programming the Finite Element Method
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Programming the Finite Element Method

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals

    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!