Problem 3: FEA - BEAM (20 Points)

Consider the beam fixed at both ends as shown in the diagram below. It is modeled using three

elements with lengths L₁, L2, L3 and moment of inertia I1, I2, I3 respectively. The elastic modulus is

same for all the beams. There is a distributed load Q on element 1 and a point load P acting at the

center of element 2.

Element 1

Element 2

Element 3

a) Draw a schematic diagram of the 3 elements with the loads and moments distributed along the

nodes. Indicate the degree of freedom at each node.

b) What is the total degree of freedom of the system? What is the size of the global stiffness matrix

and force vector?

c) Write down the elemental stiffness matrix for element 3.

d) Assemble the stiffness matrix of elements 3 into the global stiffness matrix (i.e., which rows and

columns do these components go?)

e) What are the known values of the global displacement vector d and force vector f?

f) Explain the procedure to obtain reduced stiffness matrix from global stiffness matrix for the

given structure. What is the size of the reduced stiffness matrix?

g) Write down the steps to perform a finite element structural analysis in Solidworks. Assume that

you are given the CAD model.