Geometric non-linearity:fundmantal question-shallow truss problem

Hi,

I've been looking at he chapter 2 of Crisfield's book on "Non-linear Finite Element Analysis".

Basically, my aim is to write a finite element program to carry out non-linear`analysis (geometric non-linearity) of structure comprised

of shallow truss elements.

The chapter 2 of Crisfield's book gives a set of sub-routines in Fortran as well as- to start with it derives the finite element equations

for a shallow truss element using the principle of virtual work.

I haave got some fundmantal doubts in the derivation of finite element equations which I state below.

I shall be grateful if someone good kindly help me regarding the same:

To start with-in deriving the finiteb element equations using the principle of virtual work we proceed as follows:

1) First and foremost, the shallow truss element is a 2 noded element with 2 degrees of freedom at each node.

2) We write the shape functions- which express the displacements inside the nodes to nodal displacements

3) The shallow truss element is an isoparametric element and the same shape functions which are used to express the displacements are also

used to express the geometry.

4) We get the strain epsolon

5) We get the increase in strain del_epsilon due to increase in displacements del_w and del_u (where 'w' and 'u' are verical and

horizontal displacements respectively)

6)We get the virtuial strain

7) We write the virtual work equation

8)We express the tangent stiffness matrix which is the ratio of small change in internal force to small change in  virtual dislacement

My questions are:

A)Please correct me if any of my steps are incorrect above

B)We get the tangent stiffness matrix as above- but what are we finding when we solve F = k u ('k' being tangent stiffness matrix) in each incremental step (say we are using incremental procedure) ---? Are we solving for the virtual displacements- we are actually solving for the real displacements- right? But the above steps pertain to a virtual displacement?

C)Though I underatsnd the above steps, I do not follow how the above steps (hence principle of virtual work) leads us to solving the displacements for each incremental step using incremental procedure for solving the geometric non-lienar problem.

Please help-i shall be obliged.