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Question: 4 the weakform expression for the onedimensional axial deformation...

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4 () The weak-form expression for the one-dimensional (axial deformation, u(x), of a loaded bar of circular cross-section over the range 0 3 x < e is given by Jo dx where A(x) is the cross-sectional area at x, E is the elastic constant, F(x) is the total force acting on the cross-section at x, f(x) is the body force per unit length at x and w(x)is some suitably chosen weight function. For simplicity, it is decided to use a single element with two nodal points, X1-0, x2 = 1, and two shape functions, NI(x), Ng (x), satisfying N1 (0)- 1, NI (1) = 0 and N (0)-0, N (1) = 1, to model the problem. Using a suitable notation, write down the trial function, U(x) (x), in terms of these shape functions and show how, by a suitable choice of the weight function, w(x), we can approximate equation (1) above by the system of linear equations where and dN () Given that A(x) and f(x) are both constant, and that the shape functions are chosen as N2x give the explicit form of equation (2). above.

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