Gina Cavallo
MANE-6940 Studies in Mechanics of Solids
June 2014
3.- Consider a cantilever beam with the following characteristics: L=1 m; b=1 m; h = 0.1 m; E =
2e11 Pa; ν = 0.3; P = 104 N.
a) Use the solution above to explore the displacement field ux, uy and explain your findings.
See Maple Attachment
b) Use the small strain-displacement relationships to obtain expressions for the strain tensor
components exx, eyy, exy . Explore the strain field and explain your findings.
When we plot exy, we see that for 0<y<-h/2 (the bottom half of the beam), exy is greatest at the
free end of the beam and is 0 at the fixed end. The same can be observed for the top half of the
beam.
c) Use Hooke’s law to obtain expressions for the stress tensor components σxx, σyy, σxy. Explore
the stress field and explain your findings.
d) Obtain an expression for the stress function, explore it and explain your findings.
See Maple Attachment