20. A linearly varying pressure p is applied along the edge of the four-node element shown in the figure. The finite element method converts the distributed force into an equivalent set of nodal forces {Fc} such that uTTdS= {q(<')}7'{Fw}

s where T is the applied traction (force per unit area) and u is the vector of displacements. Since the applied pressure is normal to the surface (in the jc-direction), the traction can be expressed as T = { p, 0}r where p can be expressed as p = po(f + l)/2, t = — 1 at Node 1 and t = +1 at Node 4. The length of the edge is L. Integrate the left-hand side of the above equation to com¬

pute the work-equivalent nodal forces {F^'j when {q^'} = {«i, V\, 112, vj, 113, V3, 114, V4}.

it 4

L 1 2