## Python Lab Tutorials: Lab 1

1. Write a function in Python whose inputs are another function and two values and . If , the output of the function should be the vector , otherwise, the function should return the message: “Please ensure that is less than “. Show that this function works properly for different cases.
2. Use a “for” loop to create a function whose input is a vector of numbers. The function should check for the first occurrence of a number whose absolute value is less than 0.0005. The function should output the index number and that particular value. For example, if the input is the vector , then the output should be . If none of the absolute values of the components of the vector is less than 0.0005, the function should output: “N/A”. Repeat the problem using a “while” loop.
3. The von Mises stress (or sometimes called equivalent stress) gives a positive measure of the state of stress given by the symmetric stress matrix:

is defined as:

Create a function in Python whose argument is a matrix and whose output is the von Mises stress. Use this function to show that the equivalent stress is the same for the following stress matrices (units of MPa):