The Finite Element Method for the Analysis of Non-Linear and ...

The first two analysis types, although significantly simplified, can lead to valuable conclusions
concerning the behavior of the structure and the possible collapse mechanism. The applied procedure
can be described in brief as follows. In the case of 2-D analysis the structure is assumed to consist of a
finite number of nodes interconnected by a finite number of elements. The types of elements have
been It may described expensive in section 3. toIn calculate the case of the 3-D tangent analysis the stiffness structure matrix. is assumed Into the consist of the
aforementioned Modified Newton-Raphson 2-D frames, assuming a rigid iteration diaphragm scheme assemblage it is of only their calculated horizontal dof’s in the per floor
slab. Loads may be applied at the nodes or along the elements. In both cases though, they are
transformed beginning to nodal of each loads. new load step
Modified Newton (Raphson)Method
Figure 5. Modified Newton Raphson Method
In the quasi-Newton iteration schemes the secant stiffness matrix is used
instead of the tangent matrix
After the formation of the stiffness matrix the equilibrium equations are solved by an efficient
algorithm based on the Gaussian elimination method. The structure stiffness is stored in a banded form
Institute of Structural Engineering Method of Finite Elements II 28