Question: Consider the gradient elasticity problem under a one-dimensional deformation field of the form u = u(x), v = w = 0. Using constitutive form (15.7.3),

Consider the gradient elasticity problem under a one-dimensional deformation field of the form u = u(x), v = w = 0. Using constitutive form (15.7.3), determine the stress components. Next show that equilibrium equations reduce to dσ_x/
dx = 0, and this will lead to the equation:

1 du c dx du dx4 Finally show that the solution for the displacement is given by h(c). ve) +c4 cosh(

Equation 15.7.3

1 du c dx du dx4 Finally show that the solution for the displacement is given by h(c). e) + C4 cosh( u=c+c2x+c3 sinh = 0 X (JC)

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