Question 2-[20 Marks] For a 4-noded quadrilateral element, the shape functions may be expressed in terms of a natural coordinate system (§. n), where all symbols have their usual meanings. N₁ = (1-5)(1-7) N₁ =(1+5)(1-1) N₁ = (1+5)(1+77) N₁ = (1-5)(1+7) (a) Show that these shape functions for the 4-noded quadrilateral element satisfy the following criteria for forming a proper set of shape functions: ΣΝ = 1. [6 marks] (b) Consider the distributed load applied to the 4-noded quad shown in Figure Q2. The distributed load acts at an angle of a = 60° to the x- axis and the thickness of the element is 1mm. Calculate the equivalent nodal forces on nodes x and y. [14 marks] t=5 N/mm (5,6) (2,5) (5,2) (2,1) Figure Q2 x