Assignment1

Assignment 1 (Part A)

Drop to the Assignment Box in the third floor next to the student common room

(5pm, Friday 24 August 2011)

Q1. (a) For the following stress tensor, draw the stress status in the infinitesimal cubes given; and go on to calculate the principal stresses and the direction cosines of each principal plane by

Upper part of bone

Lower part of bone

Coating Implants

Q2 (FEA Mini-Project). The cantilever beam, determine the stress state at Point A by using (1) engineering beam theory and (2) finite element method (FEM) in ANSYS. Hand in a short report to discuss

? The difference between these two solutions and why?

? Calculate the principal stresses and principal directions using AMME2301 method and eigenvalue/eigenvector method. Compare them with the FEM results in ANSYS.

? Derive the stress functions σxx , σxy . And compare them with the stress σxx , σxy contours plotted from ANSYS.

x

Assignment 1 (Part B)

Drop to the Assignment Box in the third floor next to the student common room

(5pm, Friday 24 August 2011)

Q3. The displacement functions are given inside a cube as shown as follows:

()

()()

z y x = w , yz + x = v , xz y x = u 10

4 0110 4 2 810 62 + 6y 3332???×?×?×?

(1) Determine the strain tensor at points (x , y , z ) = (0, 0, 0) and (1, –1, 0); (2) Calculate the principal strains at point (x , y , z ) = (1, 0, 0);

(3) Determine the maximum magnitude of “volume strain” and justify whether it is a “net compression” or “net tension”.

(4) Plot the normal strain (εxx , εyy , εzz ) distribution in line AB, as shown in the figure.

Q4. For the storage bin design, the engineers decided to perform a strain gauge test to validate the FEA results. The strain gauge rosette was arranged as shown in the figure below. The test results were 4102?×=A ε, 4102?×=B ε and 4101?×=

C ε at point O. Assume that only the in-plane stresses are considered in this point (i.e. 0===yz zx zz σσσ). The valve is made of mild steel with Young’s modulus E=200GPa and Poisson’s ratio ν=0.3. Determine: (1) the strain tensor; (2) the stress tensor; (3) the

characteristic Eigen equation: 032213=?+?I I I σσσ; and (4) the principal stresses.

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