A typical point P at coordinates (x, y) in a flat plate moves through small displacements u(x, y) and v(x, y) in the x direction and the y direction, respectively. Using the definition of extensional strain, Eq. 2.35, and using the “before deformation” and “after deformation” sketches in Fig. P2.12-16, show that the formula for the extensional strain in the x direction, ϵx (x, y), is the partial differential equation

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