Dynamic Post-Buckling Behavior of Thin-Walled Structures With Flexible Knife-Edge Supports

1993 ◽  
Vol 46 (11S) ◽  
pp. S148-S155 ◽  
Author(s):  
M. A. Souza

The paper discusses the influence that changes of the simply supported boundary condition during the loading process have on the dynamic post-buckling behavior of elastic thin-walled structures. Of special interest is the knife-edge type of support which is associated to the free-to-rotate boundary condition. The results presented show how changes of the free-to-rotate condition during the loading process can dramatically alter the response of thin-walled structures. This fact is highlighted by the equilibrium paths and the characteristic curves presented. The former relate the applied compressive load and the lateral displacement, whereas, the latter relate the compressive load and the square of the corresponding natural frequency of vibration. The importance of an adquate design of the supports is stressed in view of the observed dramatic changes. The work is done in the scope of the elastic stability and damping is not included in the analysis.

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4742
Author(s):  
Tomasz Kopecki ◽  
Przemysław Mazurek ◽  
Łukasz Święch

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.


2011 ◽  
Vol 2-3 ◽  
pp. 865-869
Author(s):  
Yun Dong Sha ◽  
Fei Xu ◽  
Zhi Jun Gao

Composite materials thin-walled structures are widely used as skin panel in flight vehicles in recent years. These structures will encounter severe complex loading conditions, which may be a combination of mechanical, aerodynamic, thermal and acoustic loads. Thin-walled structures subjected to this kind of loadings will exhibit nonlinear response; as a result, fatigue failure will occur. High temperature may cause large thermal deflection and stress, for some special conditions, may cause thermal buckling. Once the thermal buckling appears, the stiffness will change correspondingly, it will cause significant influence on the dynamic response and fatigue failure. Accordingly, it is important to research the nonlinear response of this kind of structures under elevated thermal environment. Nonlinear response and thermal pre-buckling/post-buckling behavior of a Graphite-Epoxy composite plate subjected to server thermal loading is numerically investigated in this paper. A composite laminated plate with clamped-clamped boundary conditions is chosen as simulated body, nonlinear finite element model is developed using the first-order shear deformable plate theory, Von Karman strain-displacement relations, and the principle of virtual work. The thermal load is assumed to be a steady-state with different predefined temperature distribution. The thermal strain is stated as an integral quantity of the thermal expansion coefficient with respect to temperature. Then the modes of the plate are analyzed, the nature frequencies and modal shapes are obtained. The critical temperature of buckling is calculated. The static nonlinear equations of motions are solved by the Newton-Raphson iteration technique to obtain the thermal post-buckling deflection. The Riks method is used to analyze static post-buckling behavior. In the numerical examples, four types of situations are studied, which include i) the buckling behaviors for different initial imperfections, ii) the buckling behaviors for different thickness to width ratios, and iii) The buckling behaviors for different width to length ratios; The critical temperature, the static thermal post-buckling deflection and the load to displacement relation are presented respectively. The influences of different boundary conditions on the buckling behaviors of the plate are achieved as well. The simulation method and results presented in this paper can be valuable references for further analysis of the nonlinear responses of thin-walled structures under complex loading conditions.


2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo

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.


2020 ◽  
Author(s):  
E. Carrera ◽  
◽  
A. Pagani ◽  
R. Augello

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.


2018 ◽  
Vol 22 (6) ◽  
pp. 1910-1930 ◽  
Author(s):  
Tran Minh Tu ◽  
Le Kha Hoa ◽  
Dang Xuan Hung ◽  
Le Thanh Hai

The nonlinear buckling and post-buckling response of imperfect porous plates is investigated analytically in this paper. The porous materials with elastic moduli are assumed to vary through the thickness of the plate according to two different distribution types. Governing equations are derived based on the classical shell theory taking into account Von Karman nonlinearity and initial geometrical imperfection. Explicit relations of load–deflection curves for rectangular porous plates are determined by applying stress function and Galerkin’s method. The accuracy of present theoretical formulation is verified by comparing it with available results in the literature. The effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate are studied in detail. A parametric study is carried out to investigate the effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate. The results show that the critical buckling loads decrease with increasing porosity coefficient and the post-buckling curves for nonlinear symmetric porosity distribution are always higher than those for nonlinear non-symmetric porosity.


2018 ◽  
Vol 149 ◽  
pp. 01089
Author(s):  
Mahi Imene ◽  
Djafour Naoual ◽  
Djafour Mustapha

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.


2016 ◽  
Vol 08 (03) ◽  
pp. 1650028
Author(s):  
Youhong Sun ◽  
Baisheng Wu ◽  
Yongping Yu

This paper is concerned with thermal post-buckling of uniform isotropic beams with axially immovable spring-hinged ends. The ends of the beam with elastic rotational restraints represent the actual practical support conditions and the classical hinged and clamped conditions can be achieved as the limiting cases of the rotational spring stiffness. The governing differential–integral equation is solved by assuming suitable admissible function for lateral displacement and by employing the Galerkin method. A brief and explicit analytical approximate formulation is established to predict the thermal post-buckling behavior of the beam. The present analytical approximate expressions show excellent agreement with the corresponding numerical solutions based on the shooting method. This confirms the effectiveness and verifies the accuracy of the formulas established.


1988 ◽  
Vol 55 (3) ◽  
pp. 635-640 ◽  
Author(s):  
Izhak Sheinman ◽  
Yeoshua Frostig

An analytical-numerical procedure is applied to investigate the post-buckling behavior of a composite laminated stiffened panel. The panel is modeled by plate elements for which the nonlinear equations are derived (via a variational principle) in terms of the lateral displacement and Airy stress function, and treated by resolving the variables into eigenfunctions in conjunction with a finite-difference scheme.


Sign in / Sign up

Export Citation Format

Share Document