MT4271 Elasticity: Corrections to Handouts

Corrections:

• Solutions for example sheet 1 (Oct. 1, 1998): The solution to problem 2c was (obviously!) wrong.
• Handout for chapter 2: Page 5 under (2.12): `The principal axes are formed by the normalised eigenvectors'. Also: `The normalised eigenvectors form the rows of the transformation matrix...'. The word normalised had been ommitted.
• Example sheet 2 (Oct. 8, 1998): In problem 2, replace theta by d.
• Solutions to example sheet 2 (Oct. 8, 1998): In the solution to problem (1a), a factor 2 was missing in the change in angle between n_1 and n_2. The correct result is -14/25 epsilon, not -7/25 epsilon.
• Solutions to example sheet 3 (Oct. 15, 1998): In the solution to problem (2), the third line should read du_i/dx_j + du_j/dx_i = 0 (rather than du_i/dx_j = 0). The calculation following this statement is carried out using the correct expression.
• Handout for chapter 5: In equation (5.8), the right hand side is missing. It is (of course) = 0.
• Solutions to example sheet 3 (Oct. 15, 1998): In the solution to problem 3 on page 4, the equation should read |x x y| = 2A, not 1/2 A. The subsequent calculations (and the result) are not affected by this since the factor 4 is missing everywhere.
• Solutions to example sheet 3 (Oct. 15, 1998): In the solution to problem 4, the sign of b was wrong. This also changes the sign of d; furthermore, the plus sign in the brackets in the result for c should be a minus.
• Solutions to example sheet 5 (Oct. 29, 1998): In the solution to problem 1, the sign of the traction and the normal vectors on the top and bottom surfaces of the cylinder is wrong. So, luckily they just cancel and the rest of the calculation is correct...
• Handout for chapter 6: There's an error in the last row of the table in section 6.6.2. The correct entries are: tau_{xx} = 0 and tau_{yy} = 6 a_{30} x.
• Example sheet 8 (Dec. 17, 1998): Add: `There is no body force.'

If you spot any other problems, please see me in my office (18.07), contact me by email (M.Heil@maths.man.ac.uk) or catch me after the lecture. Thanks.