Using the results from Exercise 2.20, determine the two-dimensional strains e r , e , e

Using the results from Exercise 2.20, determine the two-dimensional strains e_r, e_θ, e_rθ for the following displacement fields:

a. 

b. 

c. 

where A, B, and C are arbitrary constants.

Data from exercise 2.20

Consider the plane deformation of the differential element ABCD defined by polar coordinates r, θ as shown in the following figure. Using the geometric methods outlined in Section 2.2, investigate the changes in line lengths and angles associated with the deformation to a configuration A^′B^′C^′D^′, and develop the strain displacement relations:

Transcribed Image Text:

Ur A r Ug = B cos 0