2 What are the deflection and stress at the center of a very thin square plate i

Question

2 What are the deflection and stress at the center of a very thin square plate ides 2b due to a uniform load poper unit surface area (Fig. 10.5)? The displacements u. v, and of sid taken to be zero at the edges. The plate under consideration may be regarded as flexible EXAMPLE 1 2b due to a u e having no resistance to bending action. Solution ng that the origin of coordinates x, y is placed at the center of the plate, the displacement may be represented by Wao CosO 2b 2b u=co sin-b.cos 2w Figure 10.5 Uniformly loaded very thin square plate or membrane.

Explanation / Answer

As it is given in the problem statement that the plate under consideration behaves in a flexible manner and there is zero resistance to bending, the restoring energy due to bending will also be zero. Therefore, calculating or considering the bending energy will ultimately have no effect.

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