This is a repository of some useful files from the Advanced Mechanics of Solids course running in the Spring semester of 2023. It is a Depth course for the 4th year Dual Degree students in the Mechanical Systems Design specialization as well as for the 1st year Master of Technology students in the same specialization.
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Simply-Supported Beam under Uniformly-Distributed Loading This file demonstrates the use of SymPy to easily a problem involving the use of the Airy stress function and the biharmonic equation of 2D elasticity.
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Polar Utilities This file contains a compilation of various useful function definitions to work with Airy stress functions in the polar coordinate system. It can be invoked using
from polarUtilities import *from another Jupyter Notebook file. -
Polar Strain-Displacment This file contains the derivation of the strain-displacement relations in polar coordinates.
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Stress Equilibrium Equations in Cylindrical Coordinates This file contains the derivation of the stress equilibrium equations in cylindrical coordinates.
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Rotating Disk Problem This file contains the solution of the rotating disk problem. It contains explanatory notes and comments. There are a few minor changes from the way it was implemented in class. This problem is an example of a plane stress case and the solution method is based on obtaining a governing differential equation in the radial displacement variable starting from the stress equilibrium equation in the radial direction.
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Flamant Problem This file contains the solution of the Flamant problem, where a vertical point load acts on an elastic half space.
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Curved Bar under Pure Bending This file contains the solution to the problem where a curved bar is subjected to pure bending. This is again a problem where the Airy stress function is a pure function of the radial coordinate variable.
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Curved Bar under Horizontal Load This file contains the solution to the problem where a curved bar is subjected to a horizontal load at one of its ends and is clamped at the other end.