scholarly journals New Formula for Geometric Stiffness Matrix Calculation

2016 ◽  
Vol 04 (04) ◽  
pp. 733-748 ◽  
Author(s):  
I. Němec ◽  
M. Trcala ◽  
I. Ševčík ◽  
H. Štekbauer
Keyword(s):  
Stiffness Matrix ◽  
Geometric Stiffness ◽  
New Formula ◽  
Matrix Calculation

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

A Study on the Simulation of Flexible Link Mechanics Based on FEM

1997 ◽  
Author(s):  
Koichi Honke ◽  
Yoshio Inoue ◽  
Eiko Hirooka ◽  
Naoki Sugano
Keyword(s):  
Stiffness Matrix ◽  
Large Displacement ◽  
Dynamics Analysis ◽  
Flexible Link ◽  
Finite Rotation ◽  
Fem Model ◽  
Elastic Vibrations ◽  
Link Structure ◽  
Geometric Stiffness ◽  
Inertia Matrix

Abstract The dynamics analysis of link structure, including elastic vibrations, is presented. The two nodes element including large displacement is developed. This element is based on the theory of finite rotation, and includes geometric stiffness. The stiffness matrix and the inertia matrix are obtained from the FEM model by the theory of Guyan’s reduction including large displacement motion. In this paper, we explain the theory of this element and show some examples of analysis.

scholarly journals Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Emir Gülümser ◽  
Uğur Güdükbay ◽  
Sinan Filiz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
Nonlinear Fem ◽  
Calculation Technique ◽  
Stiffness Matrices ◽  
Matrix Calculation ◽  
Element Method

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.

Kinematic analysis of linkages based in finite elements and the geometric stiffness matrix

2008 ◽  
Vol 43 (8) ◽  
pp. 964-983 ◽  
Author(s):  
R. Avilés ◽  
A. Hernández ◽  
E. Amezua ◽  
O. Altuzarra
Keyword(s):  
Finite Elements ◽  
Kinematic Analysis ◽  
Stiffness Matrix ◽  
Geometric Stiffness

scholarly journals A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities

1992 ◽  
Vol 45 (1) ◽  
pp. 155-163 ◽  
Author(s):  
P.A. Bosela ◽  
D.G. Fertis ◽  
F.J. Shaker
Keyword(s):  
Rigid Body ◽  
Stiffness Matrix ◽  
Geometric Stiffness

scholarly journals A Spinning Finite Beam Element of General Orientation Analyzed With Rayleigh/Timoshenko/Saint-Venant Theory

1994 ◽  
Author(s):  
Thomas J. S. Abrahamsson ◽  
Jan Henrik Sällström
Keyword(s):  
Stiffness Matrix ◽  
Axial Load ◽  
Angular Speed ◽  
Beam Element ◽  
Shape Functions ◽  
Geometric Stiffness ◽  
General Orientation ◽  
Linear Vibrations ◽  
Fixed Axis ◽  
And Performance

Linear vibrations are studied for a straight uniform finite beam element of general orientation spinning at a constant angular speed about a fixed axis in the inertial space. The gyroscopic and circulatory matrices and also the geometric stiffness matrix of the beam element are presented. The effect of the centrifugal static axial load on the bending and torsional dynamic stiffnesses is thereby accounted for. The Rayleigh/Timoshenko/Saint-Venant theory is applied, and polynomial shape functions are used in the construction of the deformation fields. Non-zero off-diagonal elements in the gyroscopic and circulatory matrices indicate coupled bending/shearing/torsional/tensional free and forced modes of a generally oriented spinning beam. Two numerical examples demonstrate the use and performance of the beam element.

scholarly journals Stability analysis of steel frames with semirigid connections and semirigid connections with rigidzones

2001 ◽  
Vol 23 (3) ◽  
pp. 134-148 ◽  
Author(s):  
Vu Quoc Anh
Keyword(s):  
Stiffness Matrix ◽  
Axial Load ◽  
Steel Frames ◽  
Beam Element ◽  
Force Distribution ◽  
Joint Flexibility ◽  
Geometric Stiffness ◽  
Semirigid Connections ◽  
Plane Frames ◽  
Insight Into

To obtain an accurate insight into the behavior of most realistic steel frames, joint flexibility should be allowed for in the analysis since connection flexibility affects both force distribution and deformation in beams and columns of the frames. This paper proposes a method to establish the geometric stiffness matrix and stiffness matrix for semirigid beam element and semirigid beam element with rigidzones. The proposed method can also applied to analyse frame stability with rigid, semirigid and simple connections with rigidzones or without rigidzones. In addition, an approach that evaluates the effective lengthμ factor, thecritical axial load of column in plane frames with rigid, semirigid, and simple connections is also presented.

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