ABSTRACT
So far we have followed the classical approach in modeling, i.e. we have approximated the unknown, using basis functions. We have seen that by using B-splines or NURBS we get an increase in accuracy with fewer parameters as compared with Lagrange polynomials. This is because these functions have properties that make them more suitable for approximation. Let us now look at an alternative to this approach. In choosing the functions for the approximation of the unknown we go one step further: We choose functions that exactly satisfy the differential equations. In elasticity this means that compatibility and equilibrium conditions are exactly satisfied, surely a big improvement. Therefore, we change the paradigm: We use functions that satisfy the DE exactly and approximate only the boundary conditions.
