The purpose of this assignment is to familiarize yourself with the basics of finite element programming. Part of that is shape functions and gaussian quadrature. Both of these will be useful for the final project as well. Specifically the following tasks are to be performed: 1. Write a Matlab script (m-file) that uses Gaussian quadrature to evaluate integrals of first order (linear) and second order (quadratic) polynomials in 1D. Create a function that determines the Gauss point locations and weights based on an input number of points. Create a function that has the polynomial transformed from x to ? coordinates. And finally create a function that uses the other two to compute the value of the integral. 3 2. Write a Matlab script (m-file) that computes the 1D linear shape functions given nodal coordinates at a location x inside that element. Create a function that takes nodal coordinates x1 and x2 and a location x1 = x = x2, that computes the values of the shape function matrix [N], the derivatives in [B], and the mapping jacobian J.
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