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3 ) Consider a small Ax by Ay material element in a thin plate. The state...

Question:

3 ) Consider a small Ax by Ay material element in a thin plate. The state of stress in the plate is specified by four components ơxx, Ơyy and Ơxy-o,r, and the state of strain is specified by Exx. Eyy and Exy Eyx. The other components are zero. Let the x-component of the body force acting on the body be Fx, show that the equation of equilibrium for the element in the x-direction is (ii) Given the constitutive relation between the stress tensor and the strain tensor and that the displacement of the point (x, y) in the plate is given by u(x, y) in the x-direction and v(x, y) in the y-direction, show that the equation of equilibrium derived above can be written as

3 ) Consider a small Ax by Ay material element in a thin plate. The state of stress in the plate is specified by four components ơxx, Ơyy and Ơxy-o,r, and the state of strain is specified by Exx. Eyy and Exy Eyx. The other components are zero. Let the x-component of the body force acting on the body be Fx, show that the equation of equilibrium for the element in the x-direction is (ii) Given the constitutive relation between the stress tensor and the strain tensor and that the displacement of the point (x, y) in the plate is given by u(x, y) in the x-direction and v(x, y) in the y-direction, show that the equation of equilibrium derived above can be written as

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