Stiffness matrix of a 3-d beam element

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.

Download Full-text

Incorporation of Spinal Flexibility Measurements Into Finite Element Analysis

Journal of Biomechanical Engineering ◽

10.1115/1.2891216 ◽

1990 ◽

Vol 112 (4) ◽

pp. 481-483 ◽

Cited By ~ 33

Author(s):

Mack G. Gardner-Morse ◽

Jeffrey P. Laible ◽

Ian A. F. Stokes

Keyword(s):

Experimental Data ◽

Finite Element Analysis ◽

Finite Element ◽

Stiffness Matrix ◽

Beam Element ◽

Technical Note ◽

Element Analysis ◽

Spinal Motion ◽

Spinal Flexibility

This technical note demonstrates two methods of incorporating the experimental stiffness of spinal motion segments into a finite element analysis of the spine. The first method is to incorporate the experimental data directly as a stiffness matrix. The second method approximates the experimental data as a beam element.

Download Full-text

Stiffness Update Procedure in Iterative Global-Local Analysis of Columns

Volume 9: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2015-53331 ◽

2015 ◽

Author(s):

R. Emre Erkmen ◽

Ashkan Afnani ◽

Vida Niki

Keyword(s):

Stiffness Matrix ◽

Beam Element ◽

Global Model ◽

Local Analysis ◽

Element Solution ◽

Computationally Efficient ◽

Embedded Discontinuities ◽

Softening Behaviour ◽

Number Of Iterations ◽

Local Deformations

The purpose of this study is to develop a stiffness update technique to be used in a computationally efficient finite element solution for the analysis of columns undergoing local deformations, within the procedure of iterative global-local analysis. The computational problem that arises is that the stiffness matrix is formulated according to the global model, and as a result, considerably large number of iterations is required when the local deformations are significant. To overcome this difficulty, a stiffness update technique is presented in which the displacement field of the global model is altered at each step to consider the locally induced softening behaviour in order to accelerate the convergence. This goal is achieved by introducing embedded discontinuities in the beam element.

Download Full-text

The Meticulous Analysis of Skew Beam Based on the Space Skew Beam Element Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.578-579.220 ◽

2014 ◽

Vol 578-579 ◽

pp. 220-224

Author(s):

Xiang Feng Xu ◽

Feng Zhang ◽

Guang Zhi Qi

Keyword(s):

Stiffness Matrix ◽

Beam Element ◽

Finite Element Models ◽

Single Beam ◽

Skew Bridge ◽

Proposed Model ◽

Minimum Potential ◽

Space Beam Element ◽

Beam Bridge ◽

Grillage Method

When a skew bridge is analyzed, it is difficult to treat skew boundary conditions with general space beam element in single beam calculation of skew beam bridge. The stiffness of skew bridge cannot be simulated efficiently. In order to improve the accuracy of skew bridge, the stiffness matrix of the space skew beam element is derived based on the principle of minimum potential in this paper, this element is suitable for single beam of skew bridge and grillage method. A corresponding program is completed by Visual C++, the calculated results of different finite element models are compared, so the validity of the proposed model in this paper is validated. This paper can provide reference for plane and space calculation of the skew bridge design.

Download Full-text

Stiffness matrix derivation of space beam element at elevated temperature

Journal of Shanghai Jiaotong University (Science) ◽

10.1007/s12204-010-1038-7 ◽

2010 ◽

Vol 15 (4) ◽

pp. 492-497

Author(s):

Xiu-ying Yang ◽

Jin-cheng Zhao ◽

Jing-hai Gong

Keyword(s):

Elevated Temperature ◽

Stiffness Matrix ◽

Beam Element ◽

Space Beam Element

Download Full-text

A Simple Co-Rotational Finite Planar Beam Element of Geometrical and Material Nonlinearity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.268-270.1163 ◽

2012 ◽

Vol 268-270 ◽

pp. 1163-1167

Author(s):

Song Bai Cai ◽

Da Zhi Li ◽

Chang Wan Kim ◽

Pu Sheng Shen

Keyword(s):

Stiffness Matrix ◽

High Efficiency ◽

Beam Theory ◽

Yield Function ◽

Beam Element ◽

Transformation Matrix ◽

Material Nonlinearity ◽

Beam Deflection ◽

Nodal Force ◽

Tangential Stiffness

A simple geometrical and material nonlinear co-rotational planar beam element of field consistency is proposed. Herein the element which produces a local stiffness matrix of 3 by 3 other than 6 by 6 is developed. Material nonlinearity is taken into account on the base of yield function of element internal forces. By applying static equilibrium relationship of classic beam theory for the transferring of local element nodal force to global element nodal force, a new transformation matrix different from the nodal displacement transformation matrix is established. Although this results in an asymmetric global tangential stiffness matrix, the new transformation is simpler, and gives rise to field consistency and makes it possible to compute very large beam deflection without remeshing of the deformed structure. Computations of numerical example indicates that formulations for the nonlinear beam element are of validation and high efficiency

Download Full-text