Geometric non linearity question from Crisfield's book

Hi,

I am reading the book on-Non linear finite element analysis by M.A.Crisfield-as some of you know(as I've posted questions earlier too),it's more of a self study that I am doing-I have got some fundamental questions in chapter 3-the topic on:

Section 3.3 A Truss element based on Green's strain.

Basically the author has divided into 3 sections wherein we have:

Section 3.3.1 Geometry and stress strain relationships
Section 3.3.2 Equilibrium and internal force vector
Section 3.3.3 The tangent stiffness matrix

Now-to summarize the tasks carried out in these sections-we have:

Section 3.3.1:Geometry and strain displacement relationships-

A)We have the initial position of the truss element
B)We express the final position of the truss element
C)We express for Green's strain
D)We express Green's strain expression in form of strain displacement matrix
E)We write an expression for incremental Green's strain

Question I: Are my above interpretations of the steps correct?

Section
3.3.2:Equilibrium and internal force vector

A)Here the author first writes the virtual work expression (equation 3.62 of the text)

Question:

II)In equation 3.63, I do not understand that how-internal force qi is given by:

Integration over volume of (Green's stress x strain displacement matrix)-
Should not the integration carried over the area?

regards,

kajal