Problem 8 (a) Explain the concepts of an "isotropic" and an "inhomogeneous" material. Write the most general form of the

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Problem 8 A Explain The Concepts Of An Isotropic And An Inhomogeneous Material Write The Most General Form Of The 1 (96.31 KiB) Viewed 16 times

Problem 8 (a) Explain the concepts of an "isotropic" and an "inhomogeneous" material. Write the most general form of the linear elastic stress-strain law for each of the following four cases, making sure to explicitly show the influence of anisotropy and/or inhomogeneity in each case: (i) isotropic and homogeneous (ii) isotropic and inhomogeneous (iii) fully anisotropic and homogeneous (iv) fully anisotropic and inhomogeneous (b) St. Venant Principle: (i) State, and briefly explain the significance and use of, the St. Venant principle. (ii) A bar of square cross-section with side a (i.e., a 3D geometry) made of a linearly elastic homogeneous and isotropic material is loaded in tension with traction I applied to a portion of its cross section as shown in the figure below (with T extending along the entire cross-section in the through-thickness direction). 1. What are the exact boundary conditions for this problem? 2. Find the net axial force and bending moment(s) on the end faces. 3. What is the stress state in the bar? State all assumptions that have been used (explicitly or implicitly) in the derivation of this stress state. T Ta/2 L a