Problems of Elasticity involving polar coordinates seems to be long and messy at times. So I thought of building this repository 'Elasticity_TermProject' to solve the Notch and Crack Problem. This repository was used as a part of term-project in the course Applied Elasticity. The problems have been solved in MATLAB Live Script to exploit the full use of symbolic toolbox. The main idea to use symbolic toolbox to solve problems of elasticity has been taken from the repository Elasticity developed by Dr. Jeevanjyoti Chakraborty who happens to be my professor on the same course.
I have written down the list of functions used in the package and short description of them.
- The function del_delx() and del_dely() contains code to convert simple derivatives in cartesian coordinates to polar coordinates using transformation laws.
- The function polarLaplacian() uses del_delx() and del_dely() to compute the laplacian of an input function in polar coordinates.
- The function polarBiharmonic() computes the biharmonic of an input function in polar coordinates.
- The functions cartesianStressMatrix() and polarStressMatrix() can be used to determine the Stress Matrix in cartesian and polar coordinate system respectively.
- Similarly the functions cartesianStrainMatrix() and polarStrainMatrix() can be used to determine the Strain Matrix in cartesian and polar coordinate system respectively.
- The function polarStrainMatrix_Stress() is used to obtain the Strain matrix when the stress matrix is given as input.
This is the list of basic functions that I have developed. Obviously the list is not exhaustive and functions are being continuously built on and modified accordingly.
For more suggestions or information, you can drop me a mail at [email protected]