Paper format. National Examinations, December 2013 — 07-Mec-B10 Finite Element Analysis, 3 hours, open book (any textbooks, references or notes; any non-communicating calculator). Seven questions of equal value [20 marks each]; candidates attempt any five, and all questions are to be solved within the context of the finite element method. Every one of the seven questions is worked below, because the full set is more useful as a study resource than a five-question subset.
Reference texts. The worked answers below are keyed to the standard finite-element texts used for this subject:
- Logan, A First Course in the Finite Element Method, 6th ed. — Ch. 6 (constant-strain triangle), Ch. 10 (isoparametric formulation, Gauss quadrature).
- Reddy, An Introduction to the Finite Element Method, 4th ed. — Ch. 2–3 (weighted-residual methods, collocation, Galerkin vs. Ritz), Ch. 5 (Timoshenko beam elements and shear locking).
- Cook, Malkus, Plesha & Witt, Concepts and Applications of Finite Element Analysis, 4th ed. — Ch. 6 (isoparametric elements, the Jacobian and element distortion).
- Bathe, Finite Element Procedures, 2nd ed. — Ch. 4–5 (interpolation, numerical integration, locking phenomena).
- Zienkiewicz, Taylor & Zhu, The Finite Element Method: Its Basis and Fundamentals, 7th ed. — Ch. 6 (shape functions, completeness and geometric invariance), Ch. 15 (adaptivity, h- and p-refinement).
- Hutton, Fundamentals of Finite Element Analysis — Ch. 6 (interpolation functions, geometric isotropy).
