This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Formulation and Analysis of Thin Plates”.

1. Which of the following is an assumption in thin plates theory?

a) Normal stresses in a direction transverse to the plate are negligible

b) Normal stresses in a direction perpendicular to the plate are negligible

c) There are no normal stresses acting

d) Shear stresses in a direction perpendicular to the plate are negligible

View Answer

Explanation: In case of thin plates with small deflections, the following assumptions are made –

- Normal stresses in a direction perpendicular to the plate are negligible
- No deformation in the middle plane of the plate
- Points lying on a normal remain unaffected even after bending

2. Stresses in the middle plane of the plate are neglected regardless of the size of deflections.

a) True

b) False

View Answer

Explanation: The given statement is false. When the deflections are small when compared to the thickness, then the stresses in middle plane are neglected. This is in accordance with the theory of thin plates with small deflections. When deflections are large, these plane stresses are to be considered. This is in accordance with theory of thin plates with large deflections, where geometric non-linearity is incorporated.

3. When are the assumptions of thin plate theory not applicable?

a) If thickness to span ratio is more than 1/10th

b) If thickness to span ratio is equal to 1/10th

c) If thickness to span ratio is less than 1/10th

d) Assumptions are applicable always

View Answer

Explanation: If the plate under consideration has a thickness to span ratio lesser than 1/10th, then the assumptions of thin plate theory are not applicable. These plates would require three dimensional analysis. Theory in accordance with such plates may also be referred to as thick plate theory.

4. Which of the following is not a displacement model for plate analysis?

a) C^{2} – Continuity element

b) C^{1} – Continuity element

c) C^{3} – Continuity element

d) C^{0} – Continuity element

View Answer

Explanation: There are three displacement models for plate analysis. They are C

^{0}, C

^{1}, C

^{2}continuity elements. Each of them correspond to second, first and nodal order elements respectively. In C

^{2}continuity element, the second order derivatives of ‘w’ are also nodal unknowns.

5. Which type of displacement model is considered for the rectangular plate element with 12 degrees of freedom?

a) C^{1} type

b) C^{2} type

c) C^{0} type

d) All types can be used

View Answer

Explanation: For the rectangular plate element with 12 degrees of freedom, the C

^{1}type continuity element is considered. These consist of first order continuity elements, in which the highest order of ‘w’ corresponds to 1 only.

6. What are the degrees of freedom considered in case of rectangular plate element with 12 degrees of freedom?

a) w, dw/dx, dw/dy

b) w, du/dx, du/dy

c) w only

d) u only

View Answer

Explanation: There are three degrees of freedom at each node. They are w, dw/dx, dw/dy, which are treated as basic unknowns. As a basic rectangular element possesses 4 nodes, each node corresponds to 3 degrees of freedom; and thus 3 * 4 = rectangular plate with 12 degrees of freedom.

7. What is the advantage of 16 degrees of freedom over 12 degrees of freedom in case of rectangular plate elements?

a) Non conformity is overcome in 16 degrees of freedom

b) Non conformity is overcome in 12 degrees of freedom

c) No advantage

d) Computation time is reduced

View Answer

Explanation: The issue of non conformity of elements that arises in case of the rectangular plate with 12 degrees of freedom is overcome by making use of a rectangular plate with 16 degrees of freedom. This element possesses 4 degrees of freedom at each node of the rectangular plate element.

8. In Mindlin’s Plate theory, rotation and lateral deflections are coupled.

a) True

b) False

View Answer

Explanation: The given statement is false. In this theory, rotation and lateral deflections are decoupled and shear deformations are considered. This theory is considered the extension of Timoshenko beam theory; used for analysis of plates. This theory also helped in development of the C

^{0}type continuity element.

9. What kind of plates can conform to the Mindlin’s plate theory?

a) Thick plates only

b) Thin plates only

c) Thick and thin plates

d) Curved plates only

View Answer

Explanation: Mindlin’s plate theory is applicable majorly to thick plates alone. Even though some of the assumptions of the thin plate theory hold good for this case, Kirchoff’s assumption hasn’t been considered for the same. This theory further helped in making use of isoparametric concept for plate analyses.

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