## Abstract

A basic ingredient to the success of a FE analysis of shells undergoing large rotations is the geometric stiffness matrix. The geometric stiffness matrix for is usually derived by discretizing the nonlinear governing equations that include large strains in the formulations.

This paper derives the geometric stiffness matrix somewhat differently. The equilibrium equations for a flat element that can take both membrane stretching and bending are first perturbed following Levy and Spillers to yield the in-plane geometric stiffness matrix. Out-of-plane considerations finally provide an additional geometric stiffness matrix that together with the elastic stiffness matrix and the in-plane geometric stiffness matrix defines the tangential stiffness matrix.

This paper derives the geometric stiffness matrix somewhat differently. The equilibrium equations for a flat element that can take both membrane stretching and bending are first perturbed following Levy and Spillers to yield the in-plane geometric stiffness matrix. Out-of-plane considerations finally provide an additional geometric stiffness matrix that together with the elastic stiffness matrix and the in-plane geometric stiffness matrix defines the tangential stiffness matrix.

Original language | English |
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Number of pages | 8 |

DOIs | |

State | Published - 23 Jun 2021 |

Externally published | Yes |