Consider the fourth order differential equation describing the transverse displacement of a beam under bending with effective stiffness EI=1, where E the Young's Modulus and I the secondmoment of area:-u""(x) = f(x), 0 < x < 1.With this problem we need four boundary conditions, such as:u(0) = 1, u' (0) = 0, 6
u"(1) = 0, u"'(1) = -1.
a) Determine a symmetric weak form for this problem, and state appropriate spaces for u and test function v. b) Can we use continuous piecewise linear approximations for u for this problem? Do a wide literature review and propose a solution for the choice of the basis functions for the symmetric weak formulation that you proposed above. What basic physical parameters (displacement, curvature) this basis satisfy