Problem #1: Finite element beam problem

L=1m

Radius of the beam r=2 cm, and elastic modulus E = 200 GPa. Assume the beam is undergoing

a small linearly elastic deformation.

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a) Using MATLAB, analytically compute the deflection at the free end of the beam using the

following equation:

P = 100 N

Px²

6EI

(3L - x)

b) Using the finite element method (FEM) with five beam elements of equal length:

Generate the individual stiffness matrices K₂ for each element of the beam and assemble

them into the global stiffness matrix Kg. Print each of the individual matrices and the

global stiffness matrix.

Calculate and print the displacements and rotations (in degree) for each node of the beam.

Calculate and print the reaction forces and moments at each node of the beam.

c) On the same figure, plot the vertical deflection throughout the beam for both analytical and

FEM solution. Include title, axis labels, legends, and grid. Compare and discuss the two

solutions.

d) Discuss how you would increase the bending stiffness of the beam when the cross-sectional

area and material must be kept the same.

e) Perform Model (Frequency) Analysis of the beam in Solidworks. Take screen shot of the

first three modal shapes along with their frequencies (make sure the values are readable).

f) Validate the 1st natural frequency from part (e) using analytical modal analysis for

cantilever beam