scholarly journals Coupled Static and Dynamic Buckling Modelling of Thin-Walled Structures in Elastic Range Review of Selected Problems

2016 ◽  
Vol 10 (2) ◽  
pp. 141-149 ◽  
Author(s):  
Zbigniew Kołakowski ◽  
Andrzej Teter
Keyword(s):  
Numerical Method ◽  
Cross Sections ◽  
Bending Moment ◽  
Dynamic Buckling ◽  
Equilibrium Path ◽  
Compression Load ◽  
Thin Walled Structures ◽  
Post Buckling ◽  
Plates And Shells ◽  
Thin Walled

AbstractA review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.

Bend Flexibility Factors of Piping Elbows and Piping Elbows With Trunnion Attachments Using the Boundary Element Method

2009 ◽  
Author(s):  
Manuel Martinez ◽  
Johane Bracamonte ◽  
Marco Gonzalez
Keyword(s):  
Boundary Element Method ◽  
Numerical Method ◽  
Bending Moment ◽  
Piping System ◽  
Thin Walled Structures ◽  
Out Of Plane ◽  
Thin Walled ◽  
Plane Bending ◽  
Flexibility Factor ◽  
Element Method

Flexibility Factor is an important parameter for the design of piping system related to oil, gas and power industry. Elbows give a great flexibility to piping system, but where a trunnion is attached to an elbow in order to support vertical pipe sections, the piping flexibility is affected. Generally, determination of elbow flexibility factors has been performed by engineering codes such as ASME B31.3 or ASME B31.8, or using the Finite Element Method (FEM) and Finite Difference Method (FDM). In this work, bend flexibility factors for 3D models of piping elbows and piping elbows with trunnion attachments using the Boundary Element Method (BEM) are calculated. The BEM is a relatively new numerical method for this kind of analysis, for which only the surface of the problem needs to be discretized into elements reducing the dimensionality of the problem. This paper shows the simulation of 9 elbows with commercially available geometries and 29 geometries of elbows with trunnion attachments, 10 of them using commercial elbow dimensions, with applied in-plane and out-of-plane bending moments. Structured meshes are used for all surfaces, except the contact surface of elbow-trunnion joints, and no welded joints are simulated. The results show smaller values of flexibility factors of elbow and elbow–trunnion attachments in all loading cases if are compared to ASME B31.3 or correlations obtained from other works. The results also indicate that flexibility factor for elbow-trunnion attachment subjected to in-plane bending moment is greater than flexibility factor for out-of plane bending moment. Accuracy of BEM’s results were not good when flexibility characteristic values are lesser than 0.300, which confirm the problems of this numerical method with very thin-walled structures. The method of limit element could be used as tool of alternative analysis for the design of made high-pitched system, when the problem with very thin-walled structures is fixed.

scholarly journals Eigenproblem Versus the Load-Carrying Capacity of Hybrid Thin-Walled Columns with Open Cross-Sections in the Elastic Range

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3468
Author(s):  
Zbigniew Kolakowski ◽  
Andrzej Teter
Keyword(s):  
Cross Sections ◽  
Carrying Capacity ◽  
Ultimate Load ◽  
Equilibrium Path ◽  
Load Carrying Capacity ◽  
Nonlinear Buckling ◽  
Elastic Range ◽  
Load Carrying ◽  
Thin Walled ◽  
Ultimate Load Carrying Capacity

The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

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.

Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia
Keyword(s):  
Energy Absorption ◽  
Cross Section ◽  
Cross Sections ◽  
Peak Load ◽  
Circular Cross Section ◽  
Absorption Capacity ◽  
Energy Absorption Capacity ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

scholarly journals Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

2020 ◽  
Author(s):  
E. Carrera ◽  
◽  
A. Pagani ◽  
R. Augello
Keyword(s):  
Finite Elements ◽  
Large Deflection ◽  
Nonlinear Problems ◽  
Structural Domain ◽  
Fe Model ◽  
Efficient Manner ◽  
Cross Sectional ◽  
Thin Walled Structures ◽  
Post Buckling ◽  
Thin Walled

AbstractIn the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.

scholarly journals Study of Local and Distortional Stability of Thin-Walled Structures

2018 ◽  
Vol 149 ◽  
pp. 01089
Author(s):  
Mahi Imene ◽  
Djafour Naoual ◽  
Djafour Mustapha
Keyword(s):  
Design Method ◽  
Global Mode ◽  
Thin Walls ◽  
Thin Walled Structures ◽  
Post Buckling ◽  
Steel Sections ◽  
Resistance Curves ◽  
Thin Walled ◽  
The Stability ◽  
Hot Rolled

Thin-walled structures have an increasingly large and growing field of application in the engineering sector, the goal behind using this type of structure is efficiency in terms of resistance and cost, however the stability of its components (the thin walls) remains the first aspect of the behavior, and a primordial factor in the design process. The hot rolled sections are known by a consequent post-buckling reserve, cold-formed steel sections which are thin-walled elements also benefit, in this case, it seems essential to take into account the favorable effects of this reserve in to the verification procedure of the resistance with respect to the three modes of failures of this type of structure. The design method that takes into account this reserve of resistance is inevitably the effective width method. The direct strength method has been developed to improve the speed and efficiency of the design of thin-walled profiles. The latter mainly uses the buckling loads (for Local, Distortional and Global mode) obtained from a numerical analysis and the resistance curves calibrated experimentally to predict the ultimate load of the profile. Among those, the behavior of a set of Cshaped profiles (highly industrialized) is studied, this type of section is assumed to be very prone to modes of local and distortional instability. The outcome of this investigation revealed very relevant conclusions both scientifically and practically.

scholarly journals The Impact of 3D Printing Parameters on the Post-Buckling Behavior of Thin-Walled Structures

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4742
Author(s):  
Tomasz Kopecki ◽  
Przemysław Mazurek ◽  
Łukasz Święch
Keyword(s):  
3D Printing ◽  
Numerical Solutions ◽  
Structure Mapping ◽  
Thin Walled Structures ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled ◽  
The Impact ◽  
Printing Direction ◽  
Bearing Structure

This study presents the results of experimental research and numerical calculations regarding models of a typical torsion box fragment, which is a common thin-walled load-bearing structure used in aviation technology. A fragment of this structure corresponding to the spar wall was made using 3D printing. The examined system was subjected to twisting and underwent post-critical deformation. The research was aimed at determining the influence of the printing direction of the structure’s individual layers on the system stiffness. The experimental phase was supplemented by nonlinear numerical analyses of the models of the studied systems, taking into account the details of the structure mapping using the laminate concept. The purpose of the calculations was to determine the usefulness of the adopted method for modeling the examined structures by assessing the compliance of numerical solutions with the results of the experiment.

Crashing Behaviour Analysis of TWB Tubular Structures with Different Cross-Sections

2013 ◽  
Vol 814 ◽  
pp. 159-164
Author(s):  
Vlad Andrei Ciubotariu
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Fuel Efficiency ◽  
Tubular Structures ◽  
Tailor Welded Blanks ◽  
Thin Walled Structures ◽  
Prediction And Control ◽  
Thin Walled ◽  
Crushing Behavior ◽  
Bimetallic Structures

The present paper investigates the crashing behavior and energy absorption characteristics of thin-walled (tubular) structures with different cross-sections made from tailor welded blanks (TWB) which were subject of axial quasistatic loadings. Resulted data were obtained by using explicit nonlinear finite element code LS_Dyna V971. Implementing the TWB into the auto industry was an efficient method to decrease the general weight of different structures. By far, these kind of bimetallic structures are largely utilized in auto and naval industries because it led to important decrease of scarp quantities and general manufacturing costs, improved material use and probably the most important, great fuel efficiency. After reviewing the literature it was concluded that proper combination between mechanical characteristics of sheet metals, different thicknesses and cross-section shapes into the same thin-walled structure is far too little researched and understood. The aims of this study are better understandings of the crashing behavior regarding thin-walled structure with various cross-sections made from TWB blanks subject to quasistatic loadings. The non-linear finite element platform LS_Dyna V971 was used for the numerical analysis of the crushing behavior regarding the thin-walled structures. Having two materials constituting the thin-walled structures, the crashing behavior changed during the quasistatic loading. Thus, the crashing inertia of the structure is somehow limited and controlled. It is noted that material ratio should not be randomly chosen due to the unexpected crashing mode which could aggravate the prediction and control of the crashing behavior of the thin-walled structure.

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