Paper format. National Examinations (Professional Engineers Ontario),
December 2019 — 16-Civ-B9 The Finite Element Method. Three hours; four
pages; three problems worth 25, 25 and 50 marks, and the front page instructs candidates
to answer all proposed problems. Closed book with one aid sheet written on both
sides; approved Casio or Sharp calculator. Candidates are urged to submit a clear
statement of any interpretive assumption with the answer paper, which matters here
because Problem 1 leaves the applied load $P$ as a symbol and Problem 3 carries a sign
misprint in one of the coefficients it asks you to derive.
Reference texts for this subject.
- Logan, D. L., A First Course in the Finite Element Method, 6th ed., Cengage
— the plane truss element and its direction-cosine transformation (Ch. 3), thermal
(initial-strain) equivalent nodal loads (§5.6), Hermite beam elements (Ch. 4), and
the bilinear rectangle in plane stress (Ch. 6 and Ch. 10).
- Cook, R. D., Malkus, D. S., Plesha, M. E. and Witt, R. J., Concepts and
Applications of Finite Element Analysis, 4th ed., Wiley — isoparametric and
bilinear elements and the strain-displacement matrix (Ch. 6), completeness and rigid-body
modes (Ch. 3), and the exploitation of structural symmetry (§8.2).
- Bathe, K.-J., Finite Element Procedures, 2nd ed. — the principle of
virtual work as the origin of the finite element equations (Ch. 4) and the general
treatment of initial strains in three dimensions.
- Hibbeler, R. C., Structural Analysis, 10th ed., Pearson — matrix
stiffness analysis of trusses and beams, member end forces, and the sign conventions used
below for shears and bending moments.
