NONLINEAR STABILITY ANALYSIS OF THIN-WALLED FRAMES USING UL–ESA FORMULATION

2004 ◽  
Vol 04 (01) ◽  
pp. 45-67 ◽  
Author(s):  
GORAN TURKALJ ◽  
JOSIP BRNIĆ
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Displacement Field ◽  
Plastic Material ◽  
Plastic Hinge ◽  
Element Formulation ◽  
Nonlinear Stability Analysis ◽  
Perfectly Plastic ◽  
Straight Beam ◽  
Thin Walled

This work presents a one-dimensional finite element formulation for nonlinear analysis of spaced framed structures with thin-walled cross-sections. Within the framework of updated Lagrangian formulation, the nonlinear displacement field of thin-walled cross-sections, which accounts for restrained warping as well as the second-order displacement terms due to large rotations, the equations of equilibrium are firstly derived for a straight beam element. Due to the nonlinear displacement field, the geometric potential of semitangential moment is obtained for both the torsion and bending moments. In such a way, the joint moment equilibrium conditions of adjacent non-collinear elements are ensured. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends and for this a corresponding plastic reduction matrix is determined. The interaction of element forces at the hinge and the possibility of elastic unloading are taken into account. The effectiveness of the numerical algorithm discussed is validated through the test problem.

UPDATED LAGRANGIAN FORMULATION FOR NONLINEAR STABILITY ANALYSIS OF THIN-WALLED FRAMES WITH SEMI-RIGID CONNECTIONS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250013 ◽  
Author(s):  
GORAN TURKALJ ◽  
JOSIP BRNIC ◽  
DOMAGOJ LANC ◽  
STOJAN KRAVANJA
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Nonlinear Stability ◽  
Plastic Hinge ◽  
Test Problems ◽  
Element Formulation ◽  
Nonlinear Stability Analysis ◽  
Straight Beam ◽  
Thin Walled ◽  
Updated Lagrangian

This paper presents a one-dimensional (1D) finite element formulation for the nonlinear stability analysis of framed structures with semi-rigid (SR) connections. By applying the updated Lagrangian incremental formulation and the nonlinear displacement field of thin-walled cross sections, the equilibrium equations of a straight beam element are first developed. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends. To account for the SR connection behavior, a special transformation procedure is developed. The effectiveness of the numerical algorithm discussed is validated through the test problems.

Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections

1999 ◽  
Vol 66 (4) ◽  
pp. 904-912 ◽  
Author(s):  
J. H. Kim ◽  
Y. Y. Kim
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Distortion Function ◽  
Element Formulation ◽  
Numerical Work ◽  
New Approach ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
Thin Walled ◽  
The One

This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

scholarly journals Non-Linear Buckling Analysis of Axially Loaded Column with Non-Prismatic I-Section

2019 ◽  
Vol 5 (3) ◽  
pp. 263
Author(s):  
Adrian Pramudita Dharma ◽  
Bambang Suryoatmono
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Plastic Material ◽  
Slenderness Ratio ◽  
Buckling Load ◽  
Coefficient Of Determination ◽  
Average Cross Section ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In order to use material efficiently, non-prismatic column sections are frequently employed. Tapered-web column cross-sections are commonly used, and design guides of such sections are available. In this study, various web-and-flange-tapered column sections were analysed numerically using finite element method to obtain each buckling load assuming the material as elastic-perfectly plastic material. For each non-prismatic column, the analysis was also performed assuming the column is prismatic using average cross-section with the same length and boundary conditions. Buckling load of the prismatic columns were obtained using equation provided by AISC 360-16. This study proposes a multiplier that can be applied to the buckling load of a prismatic column with an average cross-section to acquire the buckling load of the corresponding non-prismatic column. The multiplier proposed in this study depends on three variables, namely the depth tapered ratio, width tapered ratio, and slenderness ratio of the prismatic section. The equation that uses those three variables to obtain the multiplier is obtained using regression of the finite element results with a coefficient of determination of 0.96.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending

2007 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Material Behavior ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Perfectly Plastic ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load of a structure employing an elastic-perfectly-plastic material behavior was previously developed and successfully applied to a long radius 90-degree pipe bend. The pipe bend is subjected to constant internal pressure and cyclic bending. The cyclic bending includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full cyclic loading finite element simulations or conventional iterative elastic techniques. In the present paper, the simplified technique is further modified to handle structures employing elastic-plastic material behavior following the kinematic hardening rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the kinematic hardening shift tensor, responsible for the translation of the yield surface. The outcomes of the simplified technique showed very good correlation with the results of full elastic-plastic cyclic loading finite element simulations. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes. The generated shakedown diagrams are compared with the ones previously generated employing an elastic-perfectly-plastic material behavior. These indicated conservative shakedown limit moments compared to the ones employing the kinematic hardening rule.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Finite Element Formulation and Vibration Frequency Analysis of a Fluid Filled Pipe

2005 ◽  
Author(s):  
Yi Jia ◽  
Reinaldo E. Madeira ◽  
Frederick Just-Agosto
Keyword(s):  
Finite Element ◽  
Coriolis Force ◽  
Frequency Analysis ◽  
Cross Sections ◽  
Vibration Frequency ◽  
Dynamic Performance ◽  
Element Model ◽  
Piping System ◽  
Element Formulation ◽  
Variable Cross

This paper presents the formulation of a finite element model and vibration frequency analysis of a fluid filled pipe having variable cross sections. The finite element method with consideration of Coriolis force developed in [1] was adopted for frequency analysis of a pipe in this study. The stiffness matrix, the c-matrix (Coriolis force) and mass (for dynamic analysis) matrix that contain all parameters of the fluids properties and flow conditions have been developed. The numerical model was employed to simulate the dynamic performance of the piping system with the specific configurations for an application. A critical relationship between the natural frequencies and pipe geometry has been established. The results of frequencies analysis of the piping system gave us an insight whether a resonance frequency might occur.

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