301000 Computer Aided Engineering

Subject Code :
301000
Country :
AU
University :
Western Sydney University

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, Q= 0.3), and its thickness t = 0.1 mm.

1 1 2 2

3 3 4 4

The coordinates of each node in mm are:

( , ) (1.0+ 0.q, 1.0+ 0.q) ( , ) (5.0+ 0.q, 1.0+ 0.q)

(x , y ) (5.0+ 0.q, 3.0 + 0.q) ( , ) (1.0+ 0.q, 3.0 + 0.q)

The dispalcements at each node are found in

x y x y

x y

1 1 2 2

3 3 4 4

the FEA as follows:

( , ) (0.001,0.0005) mm ( , ) (0.0015, 0.0006) mm

( , ) (0.0012,0.0008) mm ( , ) (0.0025, 0.001) mm

u v u v

You are required to 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.

(0 + 0.q, 4)

(0 + 0.q, 0)

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 Q are 210 GPa and 0.3, respectively.

+ 0.q kN

+ q cm

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.

Posted on : December 24th, 2019

301000 Computer Aided Engineering

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