Structural Idealisation Questions and Answers

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the value. Building an idealisation forces a decision about what carries what - which member takes the bending, which the shear, where the load enters and how it reaches the supports. A finite element model can be built and run without ever making that decision explicitly, which is why it can produce a plausible answer to a badly posed problem. The hand model is the check on the thinking, not on the arithmetic.

Answer: D

The reason is true, but the assertion overstates it. Once convergence has been reached, further refinement changes the answer negligibly while costing more work. Demonstrating that the change has become small is the point at which refinement should stop.

Answer: A

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason explains the cure. A rigid body mode is a direction in which the structure can move with no strain and therefore no restoring force, which makes the stiffness matrix singular. The remedy is to supply the restraint that is genuinely missing, not to add an arbitrary constraint or a soft spring, since an artificial restraint attracts load into itself and corrupts the answer.

Answer: B

The first two describe the method. The third contradicts the second: the skin's contribution is not thrown away but lumped into the booms, which is what makes the idealised section carry the same direct load as the real one.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: effective width is the strip still working after buckling, and it varies as the inverse square root of the stiffener stress. Statement 3 reverses that relation - as the stress rises towards ultimate, the effective width narrows, which is precisely why the structure grows less efficient the harder it is worked.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct. Statement 3 is the classic trap: at a re-entrant corner or a point load the elasticity solution is genuinely infinite, so the computed stress rises without limit as the mesh is refined and never converges at all. A rising peak stress there is the model working correctly, and the remedy is to model the real fillet radius or to use a different criterion, not to refine further.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 describe the two errors that lie either side of correct restraint. Statement 3 is the dangerous one: fixing everything removes the rigid body modes but also prevents the structure deforming as it really would, so load is attracted into the artificial supports and the stresses near them are wrong. The correct number of constraints is the number the real support arrangement provides, and no more.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are the two standard checks and both are worth doing. Statement 3 claims far too much: agreement with a hand calculation shows only that the model is not grossly wrong in the respect the hand calculation covers. Both may share the same misunderstanding of the load path or the same error in the input, and neither addresses whether the idealisation itself was appropriate.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 describe the method and its purpose. Statement 3 inverts the arrangement - the submodel must be very much finer than the global model, typically by a factor of ten or twenty, since detail in the critical region is the whole object. The coarse model supplies the displacements on the submodel’s cut boundaries, which must be placed well away from the region of interest.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct. Statement 3 states the condition too loosely and is the usual error: symmetry of the structure is not enough, the loading must be symmetric too. A symmetric structure under an antisymmetric load can be modelled on half the geometry, but with antisymmetric boundary conditions, and under a general load it cannot be reduced at all without decomposing the load first.