98-Civ-B9 — Applications of the Finite Element Method, National
Examinations, December 2016. Three hours, open book, any non-communicating
calculator permitted. Five printed pages: a front page of instructions, three
equal-value problems, and Appendix A carrying the strain-displacement matrix and the
stiffness matrix of the constant-strain triangle. The front page instructs the candidate
to attempt only two of the three; because this set is a study resource, all three
are solved in full below.
Reference texts for this subject.
- Logan, D. L., A First Course in the Finite Element Method, 6th ed., Cengage
— bar and beam elements (Ch. 3–4), the constant-strain triangle and thermal
loading (Ch. 6 and §6.5), isoparametric quadrilaterals (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 — continuity requirements,
the Jacobian, integration order, spurious zero-energy modes and element quality.
- Bathe, K.-J., Finite Element Procedures, 2nd ed. — the variational basis,
convergence, and the meaning of the weak form.
- Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd ed., McGraw-Hill
— the compatibility equation and the Airy stress function used in Problem 1.
- Hibbeler, R. C., Structural Analysis, 10th ed., Pearson — shear and moment
diagram conventions and fixed-end actions used to check Problem 2.
- CSA A23.3, Design of Concrete Structures, and the ISIS Canada design manuals
— the Canadian code framework behind the reinforcement-modelling question.
