Structural Idealisation Questions and Answers

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 give the two correspondences on which airframe finite element modelling is built. Statement 3 confuses two element types: a rod carries axial load only, while a beam carries bending and often torsion as well. Using a rod where a beam is needed removes a load path entirely, which is one of the commonest modelling errors.

Answer: B

The first two are the classical idealisation and the second two its finite element counterparts. Combining rods with shear panels reproduces the hand method inside a solver, which is why the combination remains common in airframe stress offices.

Answer: C

Correct answer: A-2, B-1, C-4, D-3

The bracket in the boom area formula is \( 2 + \sigma_2/\sigma_1 \), so it takes the value of the ratio plus two. A ratio of one, uniform stress, gives three; a ratio of zero, the far end unstressed, gives two; a ratio of minus one, equal and opposite, gives one; and a half gives two and a half. The panel therefore contributes most where the stress does not vary along it, which is the physical sense of the expression.

Answer: D

Each has a recognisable signature, and learning to read them is most of what makes a modeller reliable. Only the third is a genuine feature of the mathematics rather than a mistake, and it calls for a different method rather than a finer mesh.

Answer: A

Correct answer: A-2, B-1, C-4, D-3

Each technique answers a different need. Submodelling gives detailed stress in a critical region without meshing the whole structure finely. Symmetry conditions reduce the model when structure and load are both symmetric. Spring elements represent joint flexibility at a fraction of the cost of modelling the fasteners. And summing the reactions against the applied load is the simplest check that the model is in equilibrium and the loads went where intended.

Answer: B

Correct answer: A-2, B-4, C-1, D-3

Each quantity has its own arguments. The boom area contributed by a panel depends on its thickness, its length and the ratio of the stresses at its two ends. The effective width depends on the skin thickness and on the square root of the stiffener stress. The idealised second moment of area is built from the boom areas and their distances from the neutral axis. The refinement ratio is simply the global element size over the submodel element size.

Answer: C

Correct answer: To beat the real structure for accuracy

An idealisation is a deliberate simplification and can never be more accurate than the structure it represents - that is not what it is for. The three legitimate purposes are all present in the other options: making the load path explicit so that the analyst must decide what carries what, reducing an intractable geometry to something that can be analysed, and allowing options to be compared quickly while the design is still moving.

Answer: D

Correct answer: It grows as the stiffener stress increases

This is the false statement, and it reverses the relation. Since \( 2w \propto 1/\sqrt{\sigma} \), the effective width narrows as the stiffener stress rises - which is the mechanism behind the loss of efficiency near ultimate load. The other three are all correct: it is proportional to thickness, it represents skin still carrying direct stress, and it narrows towards ultimate.

Answer: A

Correct answer: Constraining everything is the safe choice

This is incorrect and it is the more insidious of the two boundary condition errors. Over-constraint removes the rigid body modes but prevents the structure deforming as it would in reality, so load is drawn into the artificial supports and the stresses near them are wrong - and unlike under-constraint, which stops the solution outright, it produces a plausible answer. The other three statements are all correct.

Answer: B

Correct answer: Reactions summing to within a fraction of a per cent of the applied load

That is the equilibrium check passing, which is reassurance rather than a symptom. The other three all indicate trouble: reactions exceeding the applied load mean the loads or constraints are wrong, a singular stiffness matrix means the structure is insufficiently restrained, and a peak stress rising without limit at a sharp corner means a modelling singularity that no amount of refinement will resolve.