Problems for Appendix E

 

Miscellaneous Derivations

 

 

 

 

A.      

E.1     Let  be a time varying tensor.   Show that

 

 

 

 

E.2     Consider a deformable solid.  Let  denote a closed region within the undeformed solid, and let  be the same region of the solid in the deformed configuration.  Let  denote the area of the surface surrounding , and let  denote the area of the same surface after deformation.  Let  denote the position of a material particle in the solid before deformation and let  be the position of the same point after deformation.  Define

 

Show that

 

 

 

 

 

 

(c) A.F. Bower, 2008
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