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Free Sample
301022 Advanced Computer Aided Engineering
Solution.pdf301022 Advanced Computer Aided Engineering
TUTORIAL ASSIGNMENT 2
You must finish each question individually with a step-by-step manner to clearly show your problem solving procedure. Microsoft EXCEL is encouraged to be utilised to replace hand calculation. Only .ANSYS Workbench can be used for conducting any FEA in this unit. Note that q is the last three digits of your student identification number.
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, = 0.3), and its thickness t = 0.1 mm.
Figure 2-1: 2-D Four-node Plane Finite Element
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
u v u v
? ?
? ?
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).
Tutorial Assignment 2 (100 marks, weighted 10%)
Question 2: 2-D Four-node Plane Finite Element Method – Equivalent Nodal Forces (20
marks)
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.
Figure 2-2 Equivalent Nodal Forces of 2-D Four-node Plane Finite Element
Question 3: 2-D Three-node CST Element Method – Finite Element Analysis Procedure
(50 marks)
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 ? are 210 GPa and 0.3, respectively.
Figure 2-3Equivalent Nodal Forces of 2-D Four-node Plane Finite Element
You are required to only use two CST elements to create a finite element model of this cantilever beam and
finish two tasks:
+ 0.q kN
+ 0.q kN
+ q/1000 cm + q/1000 cm
(0 + 0.q, 4)
(0 + 0.q, 0)
Tutorial Assignment 2 (100 marks, weighted 10%)
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.
