Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 215

Fig. P.6.6

(a) Formthe[B]matrix.
(b) Obtainthestiffnessmatrix[Ke].
Why,ingeneral,isafiniteelementsolutionnotanexactsolution?

P.6.9 Itisrequiredtoformthestiffnessmatrixofatriangularelement123foruseinstressanalysisproblems.
Thecoordinatesoftheelementare(1,1),(2,1),and(2,2),respectively.
(a) Assumeasuitabledisplacementfieldexplainingthereasonsforyourchoice.
(b) Formthe[B]matrix.
(c) Form the matrix which gives, when multiplied by the element nodal displacements, the stresses in the
element.Assumeageneral[D]matrix.