B1. A two-node one dimensional linear finite element with its physical (x-y) co-ordinate system and natural (s-n) co-ord

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B1 A Two Node One Dimensional Linear Finite Element With Its Physical X Y Co Ordinate System And Natural S N Co Ord 1 (120.11 KiB) Viewed 46 times

B1. A two-node one dimensional linear finite element with its physical (x-y) co-ordinate system and natural (s-n) co-ordinate system is shown in Figure 1(a) and 1(b), respectively. The element has a uniform cross-sectional area A and the Young's modulus of its material is E. (a) Using any logical method of your choice, develop expressions for interpolation functions in the natural space associated with displacements qi and gi at node i and j, respectively. [10 Marks] (b) In an analysis using the above element, it is found that the displacement at node i is qi = +0.003mm and that at node j is gi = -0.005mm. Using the interpolation functions you have developed in part (a) above, calculate the displacement vector up at generic point P on the element. [6 marks] (c) The general expression of stiffness matrix for a solid continuum finite element is given by [*1 = [ATAT AV V where the various terms have their usual meaning. Using the above relationship, develop an explicit expression of [k] for the element shown in Figure 1. [9 marks] Total [25 marks] 91 Up -4 0,0 X; - 20mm 1-5 P - 1 0,0 +1 -X = 24mm -X; - 36mm (b)