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Mixed Finite Element Method

In this book, based on 16 years of work on the finite element method, the author presents the essence of a new, direct approach to the FEM. The work is focused on the mixed method and shows how reliable results may be obtained with fewer equations than usual. The basic principles, the fundamentals a...

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Bibliographic Details
Main Author: Poceski, Apostol
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1992, 1992
Edition:1st ed. 1992
Series:Lecture Notes in Engineering
Subjects:
Engineering Mathematics
Numerical Analysis
Engineering / Data Processing
Mathematical And Computational Engineering Applications
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 6.2. Mixed rectangular element
  • 6.3. Analysis of dome shell
  • 6.4. Analysis of cylindrical roof shell
  • 6.5. Analysis of cylindrical pipe
  • 6.6. Analysis of hyperbolic paraboloid shell
  • 6.7. Comments and tasks for further research
  • 7. Three-Dimensional Elements
  • 7.1. Introduction
  • 7.2. Three-dimensional elements
  • 7.3. Mixed element of 36 d.o.f.
  • 7.4. Prismatic element of 36 d.o.f.
  • 7.5. Reduced three-dimensional element for plate bending analysis
  • 7.6. Analysis of thick plates
  • 7.7. Further development of three-dimensional elements
  • 8. Further Development of the Finite Element Method
  • 8.1. From one-dimensional to two-dimensional elements; accuracy
  • 8.2. Displacement interpolation function
  • 8.3. On the degrees of freedom
  • 8.4. Some remarks on the application of the energy variational principles
  • 8.5. The mathematical (direct) approach of development of finite elements
  • 8.6. Application of the FEM for solution of different problems
  • 1. Basic Principles
  • 1.1. Introduction
  • 1.2. The principle of virtual displacements
  • 1.3. The unit force theorem
  • 1.4. The unit displacement theorem
  • 1.5. Energy variational principles
  • 2. Fundamentals of the Finite Element Method
  • 2.1. Historical development of the method
  • 2.2. The concept of analysis by the finite element method
  • 2.3. Energetic approaches of development of finite elements
  • 2.4. Application of the unit displacement and unit force theorems
  • 2.5. Energetic approach by boundary integration
  • 2.6. The essence of the method
  • 2.7. Isoparametric formulation
  • 2.8. The direct method of development of finite elements
  • 2.9. The progress of the mixed method
  • 3. The Mixed Method in Analysis of Beam Systems
  • 3.1. Introduction
  • 3.2. Mixed beam element
  • 3.3. Analysis of beam systems
  • 3.4. Beam on elastic supports
  • 3.5. Dynamics of beams
  • 3.6. Stability of the beam systems
  • 3.7. Coupled action of axial and transverse forces
  • 4. Plate Bending Analysis
  • 4.1. Rectangular element with independently assumed displacements and moments
  • 4.2. Compatible element derived by boundary integration
  • 4.3. Rectangular element derived by the direct method
  • 4.4. Accuracy of the rectangular elements
  • 4.5. Element for analysis of moderately thick plates
  • 4.6. Isoparametric formulation
  • 4.7. Quadrilateral element
  • 4.8. Quadratic isoparametric element
  • 4.9. Curved boundary element of complex displacement function
  • 4.10. Accuracy of isoparametric elements
  • 4.11. Practical application
  • 4.12. Dynamics of plates
  • 4.13. Stability of plates
  • 5. Two-Dimensional Problems
  • 5.1. Differential equations of the problems
  • 5.2. Shortcomings of the previously developed elements
  • 5.3. Rectangular mixed plane stress element
  • 5.4. Quadrilateral element
  • 5.5. Element ofcurved contours
  • 5.6. Convergency and accuracy of the presented elements
  • 6. Shells
  • 6.1. Differential equations of shells
  • 8.7. Further development of the mixed method
  • References

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