Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements. Assume that bars can only undergo translation in
x
(1 DOF at each node). Nodes 1 and 4 are fixed. Elements 1, 2 and 3 have Young's Modulus of E1
=100Pa,E2=200Pa,E3=150Pa
. All elements have length of 1 m and cross-sectional area of
2m^(2)
. There is an applied external force acting at Node 2 of 50 N and Node 3 of 30 N .