Finite Element Method

John Burkardt, at Florida State, has posted an excellent suite of Matlab routines for various partial differential equations.  They can be found here. 

In developing weak forms for beams, the second derivation of weight function appears. So it is concluded that we need a C1 continuity element for beams. In order to use the C1 continuity between elements, the displacements and the derivatives of the displacement at the nodes must be degrees of freedom. So we should use slope (instead of curvature, which is second derivation of displacement). Also the loads imposed to the structure are considered force (that products displacement) and moment (that products rotation-slop) but we don't have such physical vision about what products curvature. So if we use curvature instead of rotation, we will face the problem of choosing load for that degree of freedom:d=[u1 θ1 u2 θ1]T : f=[V1 m1 V2 m2]Td=[u1 κ1 u2 κ1]T : f=[V1 ?1 V2 ?2]