Plane Finite Elements for Two-Dimensional Problems: Application of the Computer Algebra System Maxima

✍ Scribed by Andreas Öchsner, Resam Makvandi

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 257
• Category: Library

✦ Synopsis

This book is intended as a study aid for the finite element method. Based on the free computer algebra system Maxima, we offer routines to symbolically or numerically solve problems from the context of two-dimensional problems. For this rather advanced topic, classical ‘hand calculations’ are difficult to perform and the incorporation of a computer algebra system is a convenient approach to handle, for example, larger matrix operations. The mechanical theories focus on the classical two-dimensional structural elements, i.e., plane elements, thin or classical plates, and thick or shear deformable plate elements. The use of a computer algebra system and the incorporated functions, e.g., for matrix operations, allows to focus more on the methodology of the finite element method and not on standard procedures. Furthermore, we offer a graphical user interface (GUI) to facilitate the model definition. Thus, the user may enter the required definitions in a source code manner directly in wxMaxima or use the GUI which is able to execute wxMaxime to perform the calculations.

✦ Table of Contents

Preface
Contents
Symbols and Abbreviations
Latin Symbols (Capital Letters)
Latin Symbols (Small Letters)
Greek Symbols (Small Letters)
Mathematical Symbols
Indices, Superscripted
Indices, Subscripted
Abbreviations
1 Introduction
References
2 Maxima—A Computer Algebra System
References
3 Plane Elements
3.1 Calculation of the Elemental Stiffness Matrix
3.1.1 Elements with Four Nodes
3.1.2 Elements with Three Nodes
3.1.3 Maxima Modules for Stiffness Matrices
3.1.4 Maxima Examples to Calculate the Stiffness Matrix
3.2 Elemental and Global Principal Finite Element Equation
3.2.1 Elements with Four Nodes
3.2.2 Elements with Three Nodes
3.2.3 Maxima Modules for the Finite Element Equation
3.2.4 Maxima Examples for the Principal Finite Element Equation
References
4 Classical Plate Elements
4.1 Calculation of the Elemental Stiffness Matrix
4.1.1 Elements with Four Nodes
4.1.2 Maxima Modules for Stiffness Matrices
4.1.3 Maxima Examples to Calculate the Stiffness Matrix
4.2 Elemental and Global Principal Finite Element Equation
4.2.1 Elements with Four Nodes
4.2.2 Maxima Modules for the Finite Element Equation
4.2.3 Maxima Examples for the Principal Finite Element Equation
References
5 Shear Deformable Plate Elements
5.1 Calculation of the Elemental Stiffness Matrix
5.1.1 Elements with Four Nodes
5.1.2 Maxima Modules for Stiffness Matrices
5.1.3 Maxima Examples to Calculate the Stiffness Matrix
5.2 Elemental and Global Principal Finite Element Equation
5.2.1 Elements with Four Nodes
5.2.2 Maxima Modules for the Finite Element Equation
5.2.3 Maxima Examples for the Principal Finite Element Equation
References
6 Graphical User Interface
Reference
7 Source Codes
7.1 Maxima Library
7.2 Graphical User Interface
Reference
Appendix Index
Index