Abstract:

In this study, a general higher-order one-dimensional model for large deformation analysis of 3-D solids is developed.   The displacement vector of the cross-section or slices of a 3-D body are approximated in the reference frame using  general basis functions in polar coordinates. For the basis in theta-direction, Fourier bases is used as shown in the equation below and in the radial direction Taylor expansion in radius is used.  Using the principle of virtual displacements, we obtain the governing equations of motion for large deformation. Further, we develop weak-form finite element model of the theory. The finite element model is used to obtain solutions for cylindrical shells under internal pressure and pinching point forces. The solution obtained for the cylindrical shell under internal pressure from this one-dimensional analysis have been compared with the solutions obtained with the 7-parameter shell theory. The results are found to be in good agreement, even though one-dimensional model is used.

Numerical examples:  

Three examples of cylindrical and semi-cylindrical shell under pressure and point load based on this theory are presented below. The numerical results are also compared with 7-parameter shell theory and ANSYS. The results from this study are found to be in very good agreement with 7-parameter shell theory. 

Quasi-static analysis of pinched cylinder and half cylinder (animating video):

 Arbind, A., and J. N. Reddy. "A general higher-order one-dimensional model for large deformation analysis of solid bodies." Computer Methods in Applied Mechanics and Engineering 328 (2018): 99-121.