Geometrically Nonlinear Analysis of Shells

R. Levy; Erez Gal

doi:10.4203/ccp.59.9.2

Geometrically Nonlinear Analysis of Shells

Research output: Contribution to conference › Paper › peer-review

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.

Original language	English
Number of pages	8
DOIs	https://doi.org/10.4203/ccp.59.9.2
State	Published - 23 Jun 2021
Externally published	Yes

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title = "Geometrically Nonlinear Analysis of Shells",

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.",

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AB - 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.

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DO - 10.4203/ccp.59.9.2

M3 - Paper

ER -

Geometrically Nonlinear Analysis of Shells

Abstract

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