Introduction

In the last lecture, two examples were solved using the Ritz method. The basis functions chosen were a set of polynomials (equation 3.21), for which all the derivatives are continuous over the whole domain. But, as the second example shows, such functions are neither able to provide a good approximation to the first derivative nor able to capture a jump in the derivative unless a very large number of terms is chosen. Since, the stresses are the first derivatives of the displacement, these basis functions are not adequate for providing a good approximation to the point wise stresses. In this lecture, a new set of basis functions is proposed which can do this job in a better way.