Consider a quadratic element whose endpoints anx1e 1 and x2

Consider a quadratic element, whose endpoints anx_1^e = -1 and x_2^e = 1, but whose middle node at xi= 0 Determine x (xi) Determine the Jacobian. Notice that now this is not a constant but varies along the length of the bar. For a constant force per unit length f(x) = f along the length of the element, determine the element force vector

Solution

c)Compute f e for a constant-metric (CM) 10-node tetrahedron if the body forces bx and by vanish, while bz = g (g is the acceleration of gravity) is constant over the element. Use the 4-point Gauss rule to evaluate the integral that gives the consistent node force expression

f e = e NT b d e , in which b = 0 0 g , (E10.1) using the exact expressions for = (5 + 3 5)/20 and = (5 5)/20 in the 4-point rule, and V Ve. You need to list only the z force components. Check that the sum of the z force components is g Ve. The result for the corner nodes is physically unexpected.