FEM_PlateBending is a Python implementation of the Finite Element Method applied to a Kirchoff plate subjected to forces acting normal to its mid-surface plane. The theoretical background is based on the book "The Implementation of the Finite Element Method" by Viktor Hristovski. FEM_PlateBending consists on the following:

The Jupyter Notebook "FEM_PlateBending.ipynb" is a step-by-step guide explaining the theoretical background and its Python implementation. Each of the steps are followed by a code section in which the reader can directly relate the theoretical background with the code section using it. The reader can try different examples by modifying the desired geometrical and mechanical properties as well as the structural problem's boundary conditions.

The main script main.py allows a flexible use of this program. Here, the user can controll the geometric and mechanical properties of the plaate and define load vectors and boundary conditions using the utility functions given in "Utilities.py". I will keep adding utility functions to include new load and boundary condition scenarios.

The LocalStiffness.py script calculates the local stifness matrices for each rectangular mesh element considering each plate element being either from a solid or a voided material. These matrices are stored in an array $K_{ij}$ which is then given to the global matrix assembler class FEM_Assemble in the GlobalStiffness.py script. This class constructs the global stiffness matrix $K$ by allocating the nodal stiffness provided by each adjacent plate element having either solid or voided material properties.

Installation

1. Download this repository to your local drive.
2. Create a new virtual environment and activate it.
3. Install the requirements specified in rquirements.txt by typing "pip install -r requirements.txt".
4. Youre ready to define the plate geometry, load vector "F", and boundary conditions in the main script "main.py".