2. The quadratic shape functions N = =5(5-1) 2 N = (1+)(1 ) N3 N =...

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2. The quadratic shape functions N = =5(5-1) 2 N = (1+)(1 ) N3 N = (+1) 2 are depicted graphically below in terms of a local coordinate system for a three-node bar element. The nodes in the bar are located at = -1, 0, and +1. 0.5 0 N 0.5 N3 N 0.5 0 -0.5 -0.5 -0.5 0 0 1 a) Are the polynomial shape functions linearly independent? b) Are the polynomial shape functions orthogonal? 2. The quadratic shape functions N = =5(5-1) 2 N = (1+)(1 ) N3 N = (+1) 2 are depicted graphically below in terms of a local coordinate system for a three-node bar element. The nodes in the bar are located at = -1, 0, and +1. 0.5 0 N 0.5 N3 N 0.5 0 -0.5 -0.5 -0.5 0 0 1 a) Are the polynomial shape functions linearly independent? b) Are the polynomial shape functions orthogonal?