User:Eml4500.f08.ateam.nobrega/week 2

Lecture 3

Continuation from Lecture 2: Global Force Displacement relationship



In compact notation the above listed FD relationship equation simplifies to:

$$[ Kij ]$$*$${ dj }$$ = $${ Fi }$$

The K-spring factor is a 6x6 matrix, where as the d and F matrix are composed of a 6x1 matrix.



The capital letter K represents the global stiffness matrix. d is the global displacement matrix. The capital letter F represents the global force matrix.

The letter k represents the elemental stiffness matrix. The letter f represents the elemental force matrix.

How to go from an elemental matrix to a global matrix? The matrix has to go through an assembly process to go form an elemental matrix to a global matrix.

Identify the correspondence between elemental displacement dof's and global displacement dof's.

Global level:

{d1, d2, ............, d6}

Elemental level:

* Element 1:{d(1)1, d(1)2, d(1)3, d(1)4} * Element 2:{d(2)1, d(2)2, d(2)3, d(2)4}

Identification global-local dof:



Node 2 d2 = d2(1) d3 = d3(1) = d1(2) d4 = d4(1) = d2(3) Node 3 d5 = d3(2) d6 = d4(2)

Conceptual step of assembly: (topology of K)



The colored portion in the figure above represents the overlap between the two elemental matrices of K.