22-Mec-B10 Finite Element Analysis
Worked solutions to 7 past sittings (2013–2017), 49 questions. Pick a sitting, or start from a topic below.
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Eight-node hexahedron (5 sittings): May 2017 Q7 · December 2016 Q7 · May 2016 Q7 · December 2014 Q6 · December 2013 Q6
- Jacobian (5 sittings): May 2017 Q7 · December 2016 Q7 · May 2016 Q7 · December 2014 Q6 · December 2013 Q6
- Shape functions (5 sittings): May 2017 Q5 · December 2016 Q2 · May 2016 Q7 · December 2014 Q4 · December 2013 Q1
- Isoparametric quadrilateral (4 sittings): December 2017 Q6 · December 2016 Q6 · December 2014 Q7 · December 2013 Q7
- Strains (4 sittings): May 2017 Q7 · December 2016 Q7 · May 2016 Q7 · December 2014 Q6
- Jacobian matrix (3 sittings): December 2017 Q6 · December 2016 Q6 · December 2013 Q7
- Basis (2 sittings): December 2016 Q4 · December 2013 Q1
- Composite wall (2 sittings): May 2017 Q1 · December 2016 Q3
- Galerkin–Ritz equivalence (2 sittings): December 2016 Q4 · December 2013 Q1
- Six-node transition element (2 sittings): May 2017 Q5 · December 2016 Q2
- Stresses (2 sittings): May 2017 Q6 · December 2013 Q5
Questions by sitting
December 2017
- Question 1: Geometric isotropy of polynomial interpolations
- Question 2: Seven-node transition element and mesh compatibility
- Question 3: Gauss quadrature over a mapped rectangular domain
- Question 4: Collocation solution for an axially loaded cantilevered bar
- Question 5: One-dimensional finite element model of a composite wall
- Question 6: Isoparametric quadrilateral — Jacobian matrix and mapping validity
- Question 7: The 20-node quadratic Serendipity prism
May 2017
- Question 1: Composite wall — three conduction elements with a convective face
- Question 2: Least-squares cubic solution of a loaded bar
- Question 3: Gauss quadrature over a bilinearly mapped rectangle
- Question 4: Geometric isotropy of a bilinear element
- Question 5: Six-node transition element — shape functions and field recovery
- Question 6: Constant-strain triangle in plane strain — stresses and principal values
- Question 7: Eight-node hexahedron — shape functions, Jacobian and strains
December 2016
- Question 1: Gauss quadrature over a bilinearly mapped rectangle
- Question 2: Six-node transition element — shape functions and field interpolation
- Question 3: Composite wall — three-element one-dimensional conduction with convection
- Question 4: Basis and shape functions, mesh convergence, Galerkin–Ritz equivalence, and Timoshenko beam locking
- Question 5: Least-squares cubic solution for a bar under a linearly varying axial load
- Question 6: Isoparametric quadrilateral — Jacobian matrix and element validity
- Question 7: Eight-node hexahedron — shape functions, Jacobian and strains
May 2016
- Question 1: Collocation solution of a bar under a linearly varying axial load
- Question 2: Gauss quadrature over a rectangular domain
- Question 3: Rigid plane frame — nodal displacements, member forces and reactions
- Question 4: Shape functions of a seven-node transition element
- Question 5: Geometric isotropy of polynomial field representations
- Question 6: Thermal stresses in a three-bar assemblage
- Question 7: Eight-node hexahedron — shape functions, Jacobian and strains
December 2014
- Question 1: Spring assemblage by the principle of minimum potential energy
- Question 2: One-dimensional heat conduction in a rod with an internal source
- Question 3: Shape functions of a seven-node transition element
- Question 4: Basis functions, shape functions and geometric isotropy
- Question 5: Plane-strain constant-strain triangle — element and principal stresses
- Question 6: Eight-node hexahedron — shape functions, Jacobian and strains
- Question 7: Isoparametric quadrilateral — Jacobian and the validity of a mapping
December 2013
- Question 1: Basis vs. shape functions, Galerkin–Ritz equivalence, adaptivity, and Timoshenko beam convergence [20 marks]
- Question 2: Gauss quadrature of a field variable over a rectangular domain [20 marks]
- Question 3: Geometric isotropy of a bilinear square element [20 marks]
- Question 4: Collocation solution for a cantilevered bar under a linearly varying axial load [20 marks]
- Question 5: Stresses and principal stresses in a plane-strain triangular element [20 marks]
- Question 6: Eight-node hexahedron — shape functions, field variables, Jacobian and strains [20 marks]
- Question 7: Isoparametric quadrilateral — Jacobian matrix and the effect of node numbering [20 marks]
Undated paper
- Question 1: Gauss quadrature of a field variable over a rectangular domain
- Question 2: Bubnov–Galerkin cubic solution for an axially loaded cantilevered bar
- Question 3: One-dimensional finite element heat conduction in a rod
- Question 4: Shape functions of a seven-node transition element, and a Serendipity mesh interface
- Question 5: Stresses in a constant-strain triangular plane-strain element
- Question 6: Isoparametric mapping and the Jacobian of four-node quadrilaterals
- Question 7: Shape functions of the 20-noded quadratic Serendipity prism