research

I want to numerical calculate vibration of a closed shell of revolution with double layers. There exists Coefficient cot(θ) in the governing equation, where θ is angle between the revolving axle and normal line. Therefore, cot(θ) will incline to infinity when θ is close to zero for the vertex point on the revolving axle. How to deal with the singularity? Can you give me some advices or reference article? Thanks.

Buckling of stiff thin films on compliant substrates has many important applications ranging from stretchable electronics to precision metrology and sensors.  John Hutchinson, Zhiggang Suo, Rui Huang, Xi Chen et al. have developed nice theories for stiff thin film buckling on soft substrate.

I am working on the problem of interacting cracks in piezoelectric materials. Due to the interaction of cracks, I found a non-intuitive phenomenon that the electric displacement intensity factor of the crack for some interacting profiles may be negative under some loading conditions (a tensile stress and an applied electric displacement). However, under the same loading conditions, the electric displacement intensity factor can never be negative for a single crack problem.