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ME477 Finite Element Analysis Spring 2020
Calculate the answers to the problems below by hand and Excel. Please submit a pdf file of your
written work along with xls/xlsx files you created when solving the problems.
Consider the set of axially aligned pillars shown below made of a material with an elastic
modulus of E = 200 GPa. The dimensions of the pillars are h1 = 1 m, h2 = 1.5 m, w1 = 0.8 m, w2 =
0.5 m, d1 = 0.7 m, and d2 = 0.5 m. A pressure, P1 = 275 MPa, is applied to the top surface of the
upper most pillar and a pressure, P2 = 100 MPa, is applied to the upper surface of the bottom pillar.
Model this system using three axial elements and determine the axial displacement at each node,
the stress in each element and any reaction forces. Consider the bottom surface of the lowermost
pillar to be fixed.
Consider the beam below which is made of a material with an elastic modulus of E = 200
GPa and is fixed at both ends. The length of the beam is L = 5 m and the dimensions of its cross
section are w = 10 cm and h = 50 cm. Two ramp loads have been applied to either half of the top
of the beam. The maximum of the left ramp load is P1 = 7.5 kN/m and the maximum of the right
ramp load is P2 = 5 kN/m. The magnitude of the downward point load is F = 10 kN. Model this
system using two beam elements and determine the vertical displacement and rotation at each node
as well as any reaction forces or moments.
Consider the frame below which is made of a made of a material with an elastic modulus
of E = 200 GPa and whose left most member is fixed at its left end. Each member of this frame
has length, L = 3 m and a square cross section with area, A = 100 cm2. The angle between the two
members is θ = 135 degrees. The left most member is subjected to a uniform distributed load with
magnitude, P = 2.5 kN/m and a point load, F = 1 kN is applied at the end of the right most member
in a direction perpendicular to its long axis. Model this system using two frame elements and
determine the displacements and rotation at each node as well as any reaction forces or moments.
Evaluate the 2D integral below analytically and using 2-point Gauss-Legendre quadrature.
Compute the percent error between the exact solution and that obtained using the Gauss-Legendre
Consider the polygon shaped plate below which is fixed at node i and made of a material
with an elastic modulus, E = 200 GPa and Poisson’s ratio, v = 0.3. The positions of the corners
(nodes) of the plate are given below and the plate’s thickness is t = 1 cm. Three forces are applied
to the plate; the force F1 = 1 kN is applied vertically downward at node n, the force F2 = 1.5 kN
is applied horizontally to the right at node m, and the force F3 = 0.5 kN is applied horizontally to
the right at node j. Assuming plane stress conditions, model the plate using a 4-node quadrilateral
element and determine the displacements of each node, any reaction forces, and the stress and
strain at the center of the plate.