A unified approach to the Timoshenko 3D beam-column element tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations

2021 ◽  
Vol 222-223 ◽  
pp. 111003
Author(s):  
Marcos Antonio Campos Rodrigues ◽  
Rodrigo Bird Burgos ◽  
Luiz Fernando Martha
Keyword(s):  
Stiffness Matrix ◽  
Strain Tensor ◽  
Higher Order ◽  
Unified Approach ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Large Rotations ◽  
Higher Order Terms ◽  
Column Element

Elememt Stiffness Matrix of Members of Reticulated Shell with End Springs

2011 ◽  
Vol 94-96 ◽  
pp. 289-292
Author(s):  
Xing Wang
Keyword(s):  
Axial Force ◽  
Stiffness Matrix ◽  
Single Layer ◽  
Displacement Function ◽  
Axial Stiffness ◽  
Analysis Model ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Higher Order Terms ◽  
Column Element

In this paper, a tangent stiffness matrix of members with end springs of reticulated shell is derived on the basis of Timoshenko’s beam-column theory. In this matrix, joint’s axial stiffness and bending stiffness are considering together, non-linear beam-column element with end springs and rigid ends is taken as the analysis model of members of reticulated shell. In this matrix, not only coupling effects of bending in two axes but also joint’s stiffness and joint’s size are considered, not only the effect of axial force on bending but also the effect of axial force on torsion are considered. Higher order terms in the displacement function are considered. So this matrix is perfect and more precise than Oran’s tangent stiffness matrix. An example of a single layer reticulated shell is provided, which verified the correctness and good accuracy of the present model, and this model can be suited to the non-liner stablity analysis of reticulated shell.

Tangent Stiffness Matrix of Single-Layer Reticulated Shell’s Members with Rigid Ends

2012 ◽  
Vol 479-481 ◽  
pp. 1997-2000 ◽  
Author(s):  
Fan Wang ◽  
Xing Wang
Keyword(s):  
Axial Force ◽  
Stiffness Matrix ◽  
Single Layer ◽  
Displacement Function ◽  
Axial Stiffness ◽  
Analysis Model ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Non Linear ◽  
Column Element

In the paper, the axial stiffness and bending stiffness of single-layer reticulated shell’s joint are considering together, non-linear beam-column element with rigid springs and rigid ends is taken as the analysis model of members of single-layer reticulated shell, a tangent stiffness matrix of members of single-layer reticulated shell considering joint’s stiffness is derived on the basis of the beam-column theory. In this matrix, not only coupling effects of bending in two axes but also joint’s stiffness and joint’s size are considered, not only the effect of axial force on bending but also the effect of axial force on torsion are considered. All higher order terms in the displacement function are considered. So this matrix is perfect and more precise than the tangent stiffness matrix from C.Oran, and this model can be suited to the non-linear stablity analysis of single-layer reticulated shell.

DESIGN OF LATERAL BRACES FOR COLUMNS CONSIDERING CRITICAL IMPERFECTION OF BUCKLING

2004 ◽  
Vol 04 (01) ◽  
pp. 69-88 ◽  
Author(s):  
J. TAKAGI ◽  
M. OHSAKI
Keyword(s):  
Stiffness Matrix ◽  
Load Condition ◽  
Buckling Modes ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Total Potential ◽  
Column Type ◽  
Global Buckling ◽  
Imperfect System ◽  
Allowable Stress Design

The present paper discusses the design of column-type structures, which are composed of columns and lateral braces attached perpendicular to the columns. Buckling of the braces of this kind of structures directly leads to global buckling of the columns. The brace-buckling modes are successfully detected by considering higher-order geometrically nonlinear relations and by introducing Green's strain into the total potential energy of the structure. Sensitivity analysis of the eigenvalues of the tangent stiffness matrix under fixed load condition is carried out with respect to imperfections of the nodal locations. Furthermore, the critical imperfection that most drastically reduces the eigenvalues are calculated and buckling loads of the imperfect systems are evaluated. The numerical results show that the second or higher eigenmode of the tangent stiffness matrix of the perfect system should be sometimes used for estimating the buckling load of the imperfect system. Design examples are presented using the proposed method, and they are compared with those in accordance with an allowable-stress design standard. The results show a possibility of reducing the sizes of the brace sections.

Sign in / Sign up

Export Citation Format

Share Document