Reference no: EM132365042

Assignment Questions -

Question 1: 2-D Four-node Plane Finite Element Method - Interpolation Functions

Consider a first-order four-node rectangular plane element shown in Figure 2-1, made of steel (E = 207 GPa, ν = 0.3), and its thickness t = 0.1 mm.

The coordinates of each node in mm are:

(x₁, y₁) = (1.0 + 0.q, 1.0 + 0.q) (x₂, y₂) = (5.0 + 0.q, 1.0 + 0.q)

(x₃, y₃) = (5.0 + 0.q, 3.0 + 0.q) (x₄, y₄) = (1.0 + 0.q, 3.0 + 0.q)

The displacements at each node are found in the FEA as follows:

(u₁, v₁) = (0.001, 0.0005) mm (u₂, v₂) = (0.0015, 0.0006) mm

(u₃, v₃) = (0.0012, 0.0008) mm (u₄, v₄) = (0.0025, 0.001) mm

You are required to

a) Determine its B matrix of this element and;

b) Determine the displacements at a point with its coordinates (3 + 0.q, 2 + 0.q).

Question 2: 2-D Four-node Plane Finite Element Method - Equivalent Nodal Forces

For the four-node linear plane element shown in Figure 2-2 with a uniform surface traction along its side 2-3.

You are required to evaluate the force matrix by using the energy equivalent nodal forces. Let the thickness of the element be t = 2 + 0.q mm.

Question 3: 2-D Three-node CST Element Method - Finite Element Analysis Procedure

A cantilever is 200 + q/1000 cm long, 30 cm high and 5 + q/1000 cm thick, and it is attached to a wall with full fixity at its left end (i.e., no rotations allowed). The figure below shows an elevation and cross section view of a cantilever beam subject to an end moment couple of 10 + 0.q kN forces, spaced at 30 cm centres. The beam is made of steel and its modulus of elasticity E and Poisson's ratio ν are 210 GPa and 0.3, respectively.

You are required to only use two CST elements to create a finite element model of this cantilever beam and finish two tasks:

A) Compute by hand or use MS EXCEL to determine:

a) The nodal displacements at each node;

b) The reactions at the support;

c) The strain and stress in each element;

B) Conduct this finite element analysis employing ANSYS Workbench to do a 2-D FEA and report the results compared to the solutions obtained in Part A.