- Section A Finite Element Analysis Answer Any One Question From The Following Two Questions In Section A 1 A Two Node 1 (105.63 KiB) Viewed 43 times
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SECTION A: FINITE ELEMENT ANALYSIS Answer any ONE QUESTION from the following TWO questions in Section A. 1. A two-node one dimensional linear finite element with its physical (x-y) co-ordinate system and natural (5-1) 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 q and q at node i and j, respectively. [10 Marks] (b) In an analysis using the above element, it is found that the displacement at node iis q = +0.003mm and that at node j is q = -0.005mm. Using the interpolation functions you have developed in part (a) above, calculate the displacement vector u, 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 [k] = [[D]* av where the various terms have their usual meaning. Using the above relationship, develop an explicit expression of [k] for the element is shown in Figure 1. [9 marks] Total [25 marks] -U, + 0,0 0,0 x - 20mm -X - 24mm -- 36mm (b) (a) Figure 1