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.

scholarly journals Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects

2021 ◽  
pp. 109442812199190
Author(s):  
Mikko Rönkkö ◽  
Eero Aalto ◽  
Henni Tenhunen ◽  
Miguel I. Aguirre-Urreta
Keyword(s):  
Generalized Linear Model ◽  
Functional Form ◽  
Nonlinear Models ◽  
Nonlinear Effects ◽  
Recent Past ◽  
Organizational Research ◽  
Common Practices ◽  
Individual Variables ◽  
The Individual ◽  
The Relationship

Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the recent past. In this article, we point out a few misconceptions about transformations and propose a set of eight simple guidelines for addressing them. Our main argument is that transformations should not be chosen based on the nature or distribution of the individual variables but based on the functional form of the relationship between two or more variables that is expected from theory or discovered empirically. Building on a systematic review of six leading management journals, we point to several ways the specification and interpretation of nonlinear models can be improved.

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