Nonlinear analysis of frames using low-order mixed finite elements

2010 ◽  
pp. 111-115
Author(s):  
J Petrolito ◽  
K Legge
Keyword(s):  
Finite Elements ◽  
Nonlinear Analysis ◽  
Mixed Finite Elements ◽  
Low Order

Stabilization of Low-order Mixed Finite Elements for the Stokes Equations

2006 ◽  
Vol 44 (1) ◽  
pp. 82-101 ◽  
Author(s):  
Pavel B. Bochev ◽  
Clark R. Dohrmann ◽  
Max D. Gunzburger
Keyword(s):  
Finite Elements ◽  
Stokes Equations ◽  
Mixed Finite Elements ◽  
Low Order

A mesh-dependent norm analysis of low-order mixed finite element for elasticity with weakly symmetric stress

2014 ◽  
Vol 24 (11) ◽  
pp. 2155-2169 ◽  
Author(s):  
Mika Juntunen ◽  
Jeonghun Lee
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Finite Elements ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Mixed Finite Elements ◽  
Complex Approach ◽  
Weakly Symmetric ◽  
Rectangular Element ◽  
Low Order

We consider mixed finite elements for linear elasticity with weakly symmetric stress. We propose a low-order three-dimensional rectangular element with optimal O(h) rate of convergence for all the unknowns. The element is a rectangular analogue of the simplified Arnold–Falk–Winther element. Instead of the elasticity complex approach, our stability analysis is based on new mesh-dependent norms.

Nonlinear Analysis of Frames with Shear Deformation using Higher-Order Mixed Finite Elements

2021 ◽  
pp. 2141009
Author(s):  
J. Petrolito ◽  
D. Ionescu
Keyword(s):  
Finite Elements ◽  
Nonlinear Analysis ◽  
Shear Deformation ◽  
Large Deflection ◽  
Nonlinear Models ◽  
Mixed Finite Elements ◽  
Nonlinear Effects ◽  
Accurate Analysis ◽  
Codes Of Practice ◽  
Deflection Analysis

Until recently, linear analysis has been considered sufficient for the static analysis of structural frames. Nonlinear effects, if included, have tended to be considered at the element level rather than at the complete structure level. However, recent changes in codes of practice have been introduced that require a more complete nonlinear analysis to be performed. While these requirements should lead to a more accurate analysis, there has been little guidance given to the type and implementation of such an analysis. Moreover, different implementations have been adopted by various commercial software. In this paper, we discuss the use of mixed finite elements for the large deflection analysis of two-dimensional frames including shear deformation. In particular, we develop a family of elements that can be combined with different nonlinear models and discuss the effects of various assumptions and approximations that are commonly used to simplify the analysis. Examples are given to illustrate the various issues discussed.

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