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## 301022 Advanced Computer Aided Engineering

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301022 Advanced Computer Aided Engineering

301022 Advanced Computer Aided Engineering

TUTORIAL ASSIGNMENT 2

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 .

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,

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:

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.**

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