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GATE 2021 CE (CE1) – Question 52

Solid Mechanics · Simple stress and strain relationships · 2 marks · Numerical answer

A square plate of side 1 m deforms with straight edges. Horizontal corner displacements are O:0, P:20 mm, Q:−10 mm, R:0; the figure also gives vertical corner movements. Find horizontal displacement at the centre in mm to one decimal.

see the reproduced source diagram and its labels.

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Correct answer: 2.4 to 2.6

Explanation

The horizontal displacement field interpolates the straight-edged deformation. At the centre of the square, the four bilinear corner shape functions each equal 1/4. Thus $u=(0+20-10+0)/4=\mathbf{2.5}$ mm. The vertical corner movements do not enter this horizontal component.