Thick-walled anisotropic elliptic tube analyzed via curvilinear tensor calculus

Abstract

After a brief introduction into the tensor calculus, the thick-walled anisotropic elliptic tube is analyzed. A procedure of the analysis is described in a stepwise manner. A choice of the appropriate coordinate systems is the first step. The second step consists of the determination of corresponding metric tensors. Then the elasticity tensor of a local orthotropy is transformed into a global computational coordinate system. Next the appropriate Christoffel symbols of the second kind are determined and the total potential energy of the system is expressed. At the end the solution is approximated by a Fourier series and for given geometrical values and loading the numerical results are obtained and graphically represented. It must be said that throughout the calculation the free software only was used and for the numerical operations an old laptop is sufficient. The author regards both the former and the latter as a great advantage of the demonstrated method.