Differentiation in curvilinear coordinates
Andrey Melnikov (University of Glasgow)
Friday 27th March, 2015 16:00-17:00 Maths 204
In Continuum Mechanics for some forms of deformations it is convenient to use curvilinear coordinates. For example, for problems where cylindrical geometry is maintained it is convenient to use cylindrical polar coordinates and for problems where spherical geometry is preserved – spherical polar coordinates. Cylindrical and spherical polar coordinates are examples of orthogonal curvilinear coordinates. I will talk about differentiation in curvilinear coordinates. I will show derivations for a gradient of a vector field and divergence of a vector and a tensor fields expressed in cylindrical polar coordinates. I will show how this theory works in calculating deformation gradient and divergence of Cauchy stress for the problem of extension and inflation of a thick-walled tube. If time permits I will talk about spherical polar coordinates as well.