The Development of an Axisymmetric Shell Finite Element with a Rigid End Surface Option for Solving Static and Modal Analysis Problems of Thin-Walled Structures

Despite the rapid growth of computing power, the task of reducing computational costs by developing effective mathematical models remains topical. In this paper, an algorithm for obtaining matrices of stiffness and mass for a two-node axisymmetric shell finite element with asymmetric deformation and a rigid end face option is developed and tested. The rigid end face option makes one of the nodal sections of the finite element absolutely rigid. The developed element is based on the conical shell finite element under asymmetric deformation. To test the element, various test problems are solved (determination of displacements under static loading of the shell, determination of the natural frequencies of the conical shell and a shell with arbitrary form of the generator). The possibility of creating a rigid end face is realized as the element option by reducing the stiffness and mass matrices of the element without the rigid end face. It eliminates the need to use Lagrange multipliers that always increase the dimensionality of the system of equations and impair its properties.

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