A two-element bar as shown in Figure PA-12 with element lengths L, cross-sectional area A, and Young?s modulus E can be shown to have a stiffness matrix of

?

Show that the det (|k|) = 0 and hence that ?k is positive semi definite and the matrix is also singular. Now fix the left end (set u₁ = 0) and show that the reduced [k] is

and that the det ([k]) is no longer 0.

Transcribed Image Text:

1 -1 - 1 AE [k] = -1 2 -1 (k] = 2 -1 AE -1