A Hybrid formulation in the stress analysis of curved pipes - Madureira, Luísa (2000)
Describes a hybrid formulation solution based on variational techniques, where unknown functions are combined with a set of Fourier trigonometric expansions. The unknown functions refer to the toroidal shell distortion in the longitudinal direction when the shell is submitted to generalised in-plane forces in the linear-elastic stress field. This set of functions is solved from a system of differential equations, having calculated the eigenvalues and corresponding eigenvectors in the complex field from the system equations matrix. For this purpose the MAPLE1 mathematical solver was used. This module led to an analytical solution, which is exact for each Fourier term used in the global solution. The final results agree very well with finite element method or other solutions obtained using a total expansion of trigonometric functions in the longitudinal and meridional directions.