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(a) Which three properties do FE basis functions have? (b) Why do we call Bar Theory a "One Dimensional Reduction Technique"? (c) Given an arbitrary bilinear form B(u, v) and an arbitrary load functional F(v), and you were to apply Galerkin's method, what are the expressions for the coefficients of the stiffness matrix and load vector? (d) Explain how to post process the distribution of normal force in an arbitrary bar element . (e) Given a FE approximation uh (x) of the displacement of a bar neutral axis based on linear polynomial approximations. What can you say about the distribution of the normal strain sh(x) at element interfaces? (f) (10 points) Derive the variation of the following expression: du du = [" ( (u) + () + tan (2) () dz ({ dx J(u) {