Plane Finite Elements for Two-Dimensional Problems

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Andreas Öchsner, Resam Makvandi

   Pages 1-2

3. Maxima—A Computer Algebra System

   • Andreas Öchsner, Resam Makvandi

   Pages 3-7

4. Plane Elements

   • Andreas Öchsner, Resam Makvandi

   Pages 9-100

5. Classical Plate Elements

   • Andreas Öchsner, Resam Makvandi

   Pages 101-136

6. Shear Deformable Plate Elements

   • Andreas Öchsner, Resam Makvandi

   Pages 137-166

7. Graphical User Interface

   • Andreas Öchsner, Resam Makvandi

   Pages 167-171

8. Source Codes

   • Andreas Öchsner, Resam Makvandi

   Pages 173-246

9. Back Matter

   Pages 247-248

   PDF

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.

• Plate Elements
• Plane Elements
• Shear Deformable Plate Elements
• Maxima Computer Algebra
• Two-Dimensional Elements
• Finite Element Method
• FEM
• Numerical Methods
• Computational Mechanics

• Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen am Neckar, Germany

  Andreas Öchsner

• Institute of Mechanics, Otto von Guericke University Magdeburg, Magdeburg, Germany

  Resam Makvandi

Andreas Öchsner is Full Professor for lightweight design and structural simulation at the Esslingen University of Applied Sciences, Germany. Having obtained a Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), Germany;, he served as Research and Teaching Assistant at the University of Erlangen–Nuremberg from 1997 to 2003 while working to complete his Doctor of Engineering Sciences (Dr.-Ing.) degree. From 2003 to 2006, he was Assistant Professor at the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007–2013) as Full Professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also Head of the Advanced Materials and Structure Lab. From 2014–2017, he was Full Professor at the School of Engineering, Griffith University, Australia, and Leader of the Mechanical Engineering Program (Head of Discipline and Program Director).

Resam Makvandi is a Ph.D. candidate and research fellow at the Institute of Mechanics, Otto von Guericke University of Magdeburg, Germany. He completed his B.Sc. degree at the Islamic Azad University, Ahvaz Branch, Iran (2010) and his M.Eng. degree at the University of Technology, Malaysia (2013), both in Mechanical Engineering.

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