Finite Element Analysis: Coursework It is required that you provide a printed report with answers, solutions and plots requested in the description of the assessment problems below. The report should be accompanied by a CD with a .log file (containing the ANSYS commands) and a .db database file (containing a model, displacement constraints and loads) for each of the problems solved. Each set of files need to be saved in a separate directory with a name describing the problem, e.g. Problem 1 (or P1), Problem 2 (or P2), etc. All pictures plotted in the report should have a white background. Problem 1. The truss structure shown in Fig.1 is loaded by the force F=250kN. The reference length used in Fig.1 is: L=120cm. All elements of the structure located above level 1200cm have cross-section area A1=40cm2 and the other elements (shown in Fig.1 by bold lines) have cross-section area A2=60cm2. All elements are made of the same material with Youngs modulus 198 GPa and Poissons ratio is 0.3. The stress limit acceptable for this truss structure is 165MPa.

Fig. 1 Use ANSYS in order to: a) Set up a model, consisting of 2-node truss elements and provide a picture with all node and element numbers shown. b) Provide the two coordinate components of the displacement and the total displacement for the point where the force is applied. c) Provide a table of stresses in all finite elements of the structure. d) Check whether stresses are acceptable for the proposed design and comment on possible problems and solutions related to this issue.

[6% + 4% + 5% +5%]

University of Sussex Computer Aided Design and Modelling Dr. E.Petrov Problem 2. The beam structure shown in Fig.2 has the reference length L=0.6m; all beams have a rectangular cross-section 40x80mm (which is oriented by its long side out of the plane of Fig.2a, i.e. as it is shown in Fig.2b). The structure is loaded by two forces as shown in Fig.2a, where F=4.5kN. The beam material properties are: Youngs modulus E =210GPa and Poisson ratio, 0.3.

a) b) Fig. 2

Set up a model in ANSYS consisting of 2-node beam elements with cubic approximation for displacements and determine: a) The values of X & Y displacements for the point k (in the middle of the top beam) and the deformed shape plot. b) The axial forces, shear forces and bending moment diagrams.

[10% + 10%] Problem 3. A thin square plate with a central hole shown in Fig.3 is loaded by pressure 0.02 kN/mm2 applied at two plate sides as shown in this figure. The plate has thickness 12 mm and is made of copper with material properties: Youngs modulus of 121 GPa and a Poissons ratio of 0.364.

Fig.3

a) Construct a quarter-model of the plate (located in the quadrant corresponding to positive values of coordinate x and y) and apply the boundary conditions for displacements and loads. Explain

University of Sussex Computer Aided Design and Modelling Dr. E.Petrov briefly how you did this and provide a picture.

b) Mesh the model using triangular finite elements. Ensure that the mesh is sufficiently refined at the hole and does not have too many elements in the whole model. Describe how you controlled the mesh size. Provide a plot of the mesh you created.

c) Once you have solved the problem, provide contour plots for displacements along X and Y axes;

for stresses x , y and Von Mises stresses.

d) Consider two nodes: (i) the first is located at the plate hole (its coordinates are (0,40mm)) and (ii) the second is located at the right upper corner of the plate (its coordinates are (225mm, 225mm)). For each of these nodes, provide plots of two finite elements attached to these nodes together with the node numbers of these finite elements: the total number of different nodes will be 4. Give a

table of stress values, x , at these four nodes - for each of the two cases considered here. What can

you say about the rate of stress variation in the vicinity of the two points of interest? Is there a need to refine the mesh for any of these two considered nodes? [4% + 4% +6% + 6%] Problem 4. An axisymmetric tank with a hole at the top has geometric sizes shown in Fig.4 where all dimensions are given in millimeters. The tank is rigidly fixed at its base and is subjected to a uniformly distributed pressure of 20 MPa at the top. The tank is made from steel having a Youngs modulus of 195 kN/mm2 and a Poissons ratio of 0.3. Owing to the axial symmetry of the tank and boundary conditions, the finite element model can be created for tank radial cross-section shown in Fig.4b.

a)

b) Fig.4

a) Create the model and mesh it using eight-node quadrilateral elements. Control the element size in the mesh (e.g. setting the global element size). The number of elements in your mesh should be approximately 2000. Provide the mesh plot.

c) Before solving the problem, various displacement constraints have to be imposed on the model. What are these boundary conditions? Describe how to apply the pressure loading to the top surface of the tank. Provide a plot illustrating all boundary conditions and loads you applied.

d) Solve the problem and, provide plots of the computed stresses: (i) axial normal stresses; (ii)

University of Sussex Computer Aided Design and Modelling Dr. E.Petrov radial stresses, and (iii) circumferential stresses.

e) Make the symmetry expansion of the results obtained for the axisymmetric model over the whole structure. Provide contour plots with the symmetry result expansions for: (i) the vector sum of the displacements and (ii) von Mises stresses. [4% + 4% +6% + 6%] Problem 5. A solid model of a cotter was created in CAD software using inches as units of length and saved as an IGES file with a name: cotter.igs. The cotter is made of a material with an elasticity modulus of 210 GPa and a Poisson ratio of 0.3. One area of the cotter model is fixed and a pressure 0.2 MPa is applied on another area, as it is shown in Fig.5a. The finite element analysis of displacements and stresses of this model should be performed using 3D solid finite elements.

a) b)

c) d)

Fig.5 a) Download the file from the course webpages and import it in ANSYS. Pay attention that all

dimensions are given in this file in inches. Apply the displacement constraints and loads. Mesh the cotter and provide a picture displaying the mesh with all boundary constraints and pressure applied.

b) Solve the problem and provide: contour plots for displacements along X, Y and Z directions and a contour plot for a von Mises stresses. Indicate on each of these plots the location where the maximum value is achieved.

c) Display stress distribution inside the three-dimensional body of the cotter, namely provide contour plots of von Mises stresses for: (i) a cross-section of the cotter by a middle plane (as shown in Fig.5b); (ii)-(iii) two cross-sections of the cotter by a plane perpendicular to the axis of the cotter at different locations: one is close to the cotter head and second is in the middle of the cotter, as shown in Figs.5c) & d).

d) Try to prove that the mesh you are using is fine enough to provide sufficiently accurate values for stress distributions and maximum stress levels.

[5% + 5% + 5%+ 5%] [Total: 100%] End of the paper