a) Derive the elements N), N, and B1, B2 of the interpolation matrix [M] and strain to displacement matrix [B] for the 3

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A Derive The Elements N N And B1 B2 Of The Interpolation Matrix M And Strain To Displacement Matrix B For The 3 1 (50.92 KiB) Viewed 38 times

a) Derive the elements N), N, and B1, B2 of the interpolation matrix [M] and strain to displacement matrix for the 3-node bar element with parabolic shape functions of Figure Q3a. 2 E = constant 3 L/2 1/2 k Figure Q3a b) The uniform bar of Figure Q3b with Young's modulus E and cross-section area A is fixed only at end 3 and carries a linear distributed axial load q = 10x along its full length, L. Determine the displacement and stress at points 1 and 2 of the bar using the 3-node bar element with parabolic shape functions of Figure Q3a. Recall that the stiffness matrix [k] of the 3-node bar element with parabolic shape functions of Figure Q3a is given by: [k] 7 EA -8 3L 1 -8 16 -8 1 -8 7 q=10 EA = constant 2 T L/2 L/2 Figure Q5b Answer: = 4BEA (3) Call {0}x=0 = {0}r=/2 =- 512 ЗА 6A'