Lecture 17-->

Question 1

What are superconvergent points

Answer 1

Points where the order of convergence of displacement and stresses is at leas one order higher than the convergence rate anticipated from the polynomial order of the shape functions

Question 2

Best accuracy for the gradient or stresses is obtained at

Answer 2

Gauss point corresponding to a quadrature rule one order lower than full integration

Question 3

What are the coordinates r and s used for?

Answer 3

Used when interpolating Gauss point stresses.
r = square(3) xi
s = square (3) eta

Question 4

Element smoothing is done to

Answer 4

To obtain improved stresses as to have accurate stresses within each element

Question 5

Nodal averaging

Answer 5

Method to obtain improved stresses. Average stress at a node is the sum of the FE stress components computed at node “a” in element “e”, divided by number of elements

Question 6

What is global smoothing

Answer 6

Nodal values of the smoothed stress field is determined by a least-squares fit, minimising the square of the difference between the smoothed stress field and the discontinuous FE stress field

Question 7

What is superconvergent patch recovery?

Answer 7

Local smoothing based kn stresses sampled at superconvergent points. The smoothed stress field is expressed as a polynomial.

Question 8

Why is the unsmoothed FE stress field sometimes better when assessing the accuracy

Answer 8

The amount of discontinuity gives a measure of the accuracy if the FE solution

Question 9

How many displacement patterns does the Q4 element have?

Answer 9

8
3 rigid body
3 constant strain
2 bending

Question 10

Bending deformation of the Q4 element always displays

Answer 10

spurious shear strains as well as the expected bending

Question 11

Does the Q4 exhibit shear locking behaviour?

Answer 11

Yes

Question 12

What is the parasitic shear effect?

Answer 12

The reason behind shear locking. Absorbs strain energy. If the Q4 element is exposed to bending deformation, the bending moment needed to produce it is larger than the correct value

Question 13

What is the remedy for the overly stiff Q4 element when bent?

Answer 13

Adding two additional modes, referred to as incompatible displacement modes. Allow edges of the element to become curved.
—> Q6

Question 14

How many shape functions do the Q6 element have?

Answer 14

6 shape functions

Question 15

Why is Q6 called incompatible?

Answer 15

Because overlap or gaps may appear between adjacent elements

Question 16

What is the QM6 element?

Answer 16

A modified version of Q6, that satisfies the strong form of the patch test and thus converges much faster

Question 17

Can the QM6 represent pure bending exactly?

Answer 17

Yes, but only if the element is rectangular

Question 18

What is reduced integration

Answer 18

Integration with a quadrature rule of less than full order

Question 19

What can reduced integration lead to in regards to the rank?

Answer 19

It may lead to a rank-deficient k, which means that the rank of k is less than its order minus the possible rigid body modes. Will exist one or more spurious modes

Question 20

What are spurious modes?

Answer 20

Deformations that may be activated without any increase in the strain energy. Also called zero-energy modes

Question 21

For n Gauss point, rank (k) =

Answer 21

Min {3n, ndof-nr}

Question 22

Can selective integration avoid shear locking behavior?

Answer 22

Yes, by applying reduced integration to the shear part of the strain only

Question 23

What can you say about the CST element and bending?

Answer 23

Bending deformation of the CST element always displays spurious shear strains.
The CST element exhibit shear locking behaviour

Question 24

What can you say about the LST element and bending?

Answer 24

The LST element can represent pure bending exactly

Question 25

The ___ element cannot model the linearly varying normal stress, neither the quadratic varying sheer stress

Answer 25

CST

Question 26

The ___ element can exactly model the normal stress, but not the quadratic varying shear stress

Answer 26

LST

Question 27

The ___ element can model both stresses exactly

Answer 27

QST

Question 28

CST and bending

Answer 28

The constant strain tetrahedron is poor at representing fields of bending or twisting strains

Question 29

LST and bending

Answer 29

Unless the element edges become curved, the linear strain tetrahedron can exactly represent fields of pure bending exactly

Question 30

Does the tri-linear hexahedron (H8) exhibit shear locking?

Answer 30

Yes

Question 31

H11 element is what?

Answer 31

The H8 with added incompatible displacement modes. Passes patch test, and may represent bending fairly well