Effect of a Bending Stiffness on the Load-Displacement Path of Von Mises Truss

2015 ◽  
Vol 769 ◽  
pp. 43-48
Author(s):  
Martin Psotny ◽  
Jozef Havran
Keyword(s):  
Theoretical Models ◽  
Load Level ◽  
Buckling Analysis ◽  
Iteration Algorithm ◽  
Linear Solution ◽  
Nonlinear Equilibrium ◽  
Von Mises ◽  
Ansys System ◽  
Raphson Iteration ◽  
Linear Buckling Analysis

Von Misses truss is one of the best examples to explain nature of non-linear solution and define the snap-through. Linear buckling analysis and nonlinear finite element approaches are compared in presented paper. At the present time theoretical models for the evaluation of the ultimate load assume a structure with imperfections. The peculiarities of the effect of the magnitude and mode of initial imperfections are investigated. Effect of member stiffness on the load level in critical point of nonlinear solution, as well as the relative position with respect to the critical load from buckling analysis are analyzed. To obtain the nonlinear equilibrium paths, Newton-Raphson iteration algorithm has been used. Obtained results are compared with those gained using ANSYS system.

Effect of a Nonlinear Term in a Strain-Displacement Relationship on the Load-Displacement Path of Von Mises Truss

2015 ◽  
Vol 769 ◽  
pp. 85-90
Author(s):  
Jozef Havran ◽  
Martin Psotny
Keyword(s):  
Load Level ◽  
Iteration Algorithm ◽  
Arc Length ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Total Potential ◽  
Theoretical Approaches ◽  
Newton Raphson ◽  
Von Mises ◽  
Ansys System

Von Misses truss is one of the best examples to explain different theoretical approaches, nature of non-linear solution, define the snap-through, illustrate interactive buckling, etc. The presented paper compares two nonlinear approaches to the problem. Effect of nonlinear terms in strain-displacement relationship on the load level in critical point of nonlinear solution is analyzed. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Custom FEM computer program has been used for analysis. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied. Obtained results are compared with results of the nonlinear analysis using ANSYS system, element type BEAM3 is used. The arc-length method is chosen for analysis, the reference arc-length radius is calculated from the load increment. Only fundamental path of nonlinear solution has been presented.

scholarly journals Slender metal web stability analysis: Impact of initial imperfection on the mode of buckling

2020 ◽  
Vol 313 ◽  
pp. 00006
Author(s):  
Martin Psotný
Keyword(s):  
Initial Imperfection ◽  
Iteration Algorithm ◽  
Initial Shape ◽  
Aspect Ratios ◽  
Nonlinear Approach ◽  
Linearized Problem ◽  
Nonlinear Equilibrium ◽  
Post Buckling ◽  
Ansys System ◽  
Raphson Iteration

The post buckling of a rectangular slender web in compression has been analyzed. Shapes of a buckling area obtained from the nonlinear analysis have been compared with buckling modes from the linearized problem for various aspect ratios. Effects of initial shape imperfections upon the analysis have been investigated using nonlinear approach. To trace the complete nonlinear equilibrium curves, specialized code based on FEM was created. The Newton-Raphson iteration algorithm was used, load versus displacement control was changed during the process of calculation. Obtained results were verified using Ansys system, in this case arc-length method was activated for overcoming critical points.

Stability Analysis of an Imperfect Slender Web Subjected to the Shear Load

2016 ◽  
Vol 837 ◽  
pp. 52-57
Author(s):  
Martin Psotny
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

The stability analysis of an imperfect slender web subjected to the shearing load is presented, a specialized code based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

scholarly journals Buckling And Postbuckling Of An Imperfect Plate Subjected To The Shear Load

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Shear Load ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of an imperfect plate subjected to the shear load is presented. To solve this problem, a specialized computer program based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

scholarly journals Nonlinear Analysis of Buckling & Postbuckling

2014 ◽  
Vol 14 (1) ◽  
pp. 75-80
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Iteration Algorithm ◽  
Nonlinear Finite Element Method ◽  
Buckling Mode ◽  
Initial Imperfections ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.

scholarly journals Snap-Through of the Very Shallow Shell with Initial Imperfection

2016 ◽  
Vol 16 (2) ◽  
pp. 43-48
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Analysis ◽  
Shallow Shell ◽  
Initial Imperfection ◽  
Limit Load ◽  
External Pressure ◽  
Load Level ◽  
Nonlinear Equilibrium ◽  
Load Displacement ◽  
Ansys System

Abstract Elastic shallow shell of translation subjected to the external pressure is analysed in the paper numerically by FEM. Nonlinear equilibrium paths are calculated for the different boundary conditions. Special attention is paid to the influence of initial imperfection on the limit load level of fundamental load-displacement path of nonlinear analysis. ANSYS system was used for analysis, arclength method was chosen for obtain fundamental load-displacement path of solution.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

Linear Buckling Analysis Considering No-compression Property of Metal Grid Shells Stiffened by Tension Braces

2021 ◽  
Vol 62 (3) ◽  
pp. 195-205
Author(s):  
Kenji Yamamoto ◽  
Hayato Utebi
Keyword(s):  
Geometrical Nonlinearity ◽  
Buckling Analysis ◽  
Nonlinear Buckling ◽  
Compression Property ◽  
Buckling Behavior ◽  
Metal Grid ◽  
Linear Buckling ◽  
Nonlinear Buckling Analysis ◽  
Linear Buckling Analysis ◽  
Lattice Shells

In order to analyze the buckling behavior of lattice shells stiffened by cables or slender braces without pre-tension, it is necessary to consider the no-compression property of braces. This paper proposes an innovative method of linear buckling analysis that considers the no-compression property of braces. Moreover, in order to examine the proposed method's validity, its results are compared with the results from a nonlinear buckling analysis with geometrical nonlinearity and material nonlinearity to express the no-compression property of braces. The results show that the proposed method can well-predict the buckling behaviors of lattice shells stiffened by tension braces.

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