Intro
Clearing the mist behind basic program structures of the FEA (finite element analysis) is an important part for better understanding of the finite element method. MATLAB is convenient for this role since it manipulates matrices and vectors unparalleled in the engineering industry. These algebraic operations constitute a major part in the FEA program. As an extra, MATLAB has built-in graphics features to help the user visualize numerical results in two- and three-dimensional plots. Graphical representation being of extreme importance when interpreting the finite element results.
To fully utilize the curriculum the objective of the thesis was set on preparing a standalone nonlinear shell finite element code in MATLAB environment. The final program is equipped with a graphical user interface (GUI) for visualizing there results and gathering the initial input data.
Tasks of the thesis are covered in the literature overview focusing on various shell finite elements (Kirchhoff-Love, Reissner-Mindlin) with special attention to their material and geometric nonlinearities and also on the FEM method,and program buildup. Developing the GUI with the help of built-in functions of MATLAB, such as APP DESIGNER and GUIDE.
A large chapter will be dedicated to the framework for the linear analysis of a general shell element problem, considering the possibility of adaptation for specific cases/problems. The main aim of the thesis will be the adaptation of geometric nonlinearities, extending the code to handle them, but excluding all kinds of material models.
With these tasks successfully completed, all that remains is to compare the results given by the code to reference results obtained from commercial software and analytical solutions. Nonlinear effects should be investigated as a final step, via specific problems.
Chapters follow the main idea of the tasks set up earlier in a logical matter. The thesis starts with the presentation of the general finite element programming overview, followed by the idea of isoparametric elements, a concept which revolutionized the solution of partial differential equations for solid continua, chapter III sums up the most general types of plates and shells. The next part is based around the linear solver for shells, presented through a fixed shell loaded by a point load. Nonlinear analysis, GUI and results follow.
Detailed structure of the website can be found in the “Table of contents”, on the left side menu. Hopefully, the Reader finds that we managed to cover the topic of finite element , and I managed to give a satisfying overview of a possible program structure that can be a basis of a user-friendly software as well.