Application of Groebner Basis Methodology to Nonlinear Static Cable Analysis

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Y. Jane Liu ◽  
George R. Buchanan ◽  
John Peddieson
Keyword(s):  
Nonlinear Analysis ◽  
Analytical Solutions ◽  
Geometrically Nonlinear ◽  
Large Deflections ◽  
Groebner Basis ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Exact Analytical Solutions ◽  
Highly Nonlinear ◽  
Nonlinear Static

The governing equations for large deflections of cables have a highly nonlinear and coupled nature, which precludes exact analytical solutions except in a few simplified cases. The present study demonstrates the utility of Groebner Basis methodology in facilitating the construction of approximate analytical and semianalytical Galerkin solutions in the geometrically nonlinear analysis of cable statics.

Application of Groebner Basis Methodology to Nonlinear Analysis of an Underwater Cable

2011 ◽  
Author(s):  
Y. Jane Liu ◽  
George R. Buchanan
Keyword(s):  
Galerkin Method ◽  
Nonlinear Analysis ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Geometrically Nonlinear ◽  
Groebner Basis ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Highly Nonlinear ◽  
The Galerkin Method

The governing equations for a large deflection cable analysis have a highly nonlinear and coupled nature. As a result, analytical solutions are unavailable or limited to a few simplified cases. The present study is to apply the Groebner Basis methodology combined with the Galerkin method to a geometrically nonlinear analysis of an underwater cable as an example.

Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhi Li ◽  
Song Cen ◽  
Chenfeng Li
Keyword(s):  
Nonlinear Analysis ◽  
Linear Elasticity ◽  
Analytical Solutions ◽  
Geometrically Nonlinear ◽  
Governing Equations ◽  
Geometrically Nonlinear Analysis ◽  
Content Type ◽  
Solid Element ◽  
Key Innovation ◽  
Updated Lagrangian

Purpose The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis. Design/methodology/approach Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions. Findings Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements. Originality/value The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

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