scholarly journals TANGENT STIFFNESS MATRIX OF 3D BEAM-COLUMN ELEMENT AT APEX OF YIELD SURFACE FOR GENERALIZED PLASTIC HINGES

2008 ◽  
Vol 73 (634) ◽  
pp. 2129-2134
Author(s):  
Noriko TAKIYAMA ◽  
Yoshikazu ARAKI ◽  
Koji UETANI
Keyword(s):  
Yield Surface ◽  
Stiffness Matrix ◽  
Plastic Hinges ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Column Element

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.

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.

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.

scholarly journals On the co-rotational method for geometrically nonlinear topology optimization

2020 ◽  
Vol 62 (5) ◽  
pp. 2357-2374
Author(s):  
Peter D. Dunning
Keyword(s):  
Topology Optimization ◽  
Stiffness Matrix ◽  
Optimization Problems ◽  
Geometrically Nonlinear ◽  
Tangent Stiffness ◽  
Tangent Stiffness Matrix ◽  
Simplified Method ◽  
Nonlinear Topology Optimization ◽  
Consistent Method ◽  
Rotational Method

Abstract This paper investigates the application of the co-rotational method to solve geometrically nonlinear topology optimization problems. The main benefit of this approach is that the tangent stiffness matrix is naturally positive definite, which avoids some numerical issues encountered when using other approaches. Three different methods for constructing the tangent stiffness matrix are investigated: a simplified method, where the linear elastic stiffness matrix is simply rotated; the consistent method, where the tangent stiffness is derived by differentiating residual forces by displacements; and a symmetrized method, where the consistent tangent stiffness is approximated by a symmetric matrix. The co-rotational method is implemented for 2D plane quadrilateral elements and 3-node shell elements. Matlab code is given in the appendix to modify an existing, freely available, density-based topology optimization code so it can solve 2D problems with geometric nonlinear analysis using the co-rotational method. The approach is used to solve four benchmark problems from the literature, including optimizing for stiffness, compliant mechanism design, and a plate problem. The solutions are comparable with those obtained with other methods, demonstrating the potential of the co-rotational method as an alternative approach for geometrically nonlinear topology optimization. However, there are differences between the methods in terms of implementation effort, computational cost, final design, and objective value. In summary, schemes involving the symmetrized tangent stiffness did not outperform the other schemes. For problems where the optimal design has relatively small displacements, then the simplified method is suitable. Otherwise, it is recommended to use the consistent method, as it is the most accurate.

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