In: Mechanical Engineering
For the elastic body defined in Question 1 (below), define the boundary conditions in terms of displacement, assuming the boundary surface at the point in question has direction cosines with respect to x and y and z equal to l=0.8 and m=0.6 and n=0 . Consider the case when the change in volume is negligible.
Are all the compatibility equations satisfied for the Plane Stress conditions? If not, which equations are not satisfied? Explain the case for the Plane Strain conditions?
Question 1:
Write down the equilibrium equations for a three-dimensional isotropic material in terms of displacements. Assume that the material modulus of elasticity, Poisson ratio and density are, and that the body forces are due to the material weigh and the constant gravitational accelerations applied in z-direction.