scholarly journals Nonlinear Response of Graphite-Epoxy Composite Thin-Walled Structure under Elevated Thermal Environment

2011 ◽  
Vol 2-3 ◽  
pp. 865-869
Author(s):  
Yun Dong Sha ◽  
Fei Xu ◽  
Zhi Jun Gao
Keyword(s):  
Critical Temperature ◽  
Boundary Conditions ◽  
Nonlinear Response ◽  
Thermal Environment ◽  
Epoxy Composite ◽  
Complex Loading ◽  
Thin Walled Structures ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

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.

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.

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
Keyword(s):  
Boundary Condition ◽  
Lateral Displacement ◽  
Compressive Load ◽  
Elastic Stability ◽  
Knife Edge ◽  
Loading Process ◽  
Thin Walled Structures ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

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.

scholarly journals On the theory and practice of thin-walled structures

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tamaz Vashakmadze
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Complex Analysis ◽  
Theory And Practice ◽  
Linear Case ◽  
Wide Sense ◽  
Partial Differential ◽  
Thin Walled Structures ◽  
Thin Walled

Abstract The basic problem of satisfaction of boundary conditions is considered when the generalized stress vector is given on the surfaces of elastic plates and shells. This problem has so far remained open for both refined theories in a wide sense and hierarchic type models. In the linear case, it was formulated by I. N. Vekua for hierarchic models. In the nonlinear case, bending and compression-expansion processes do not split and in this context the exact structure is presented for the system of differential equations of von Kármán–Mindlin–Reisner (KMR) type, constructed without using a variety of ad hoc assumptions since one of the two relations of this system in the classical form is the compatibility condition, but not the equilibrium equation. In this paper, a unity mathematical theory is elaborated in both linear and nonlinear cases for anisotropic inhomogeneous elastic thin-walled structures. The theory approximately satisfies the corresponding system of partial differential equations and the boundary conditions on the surfaces of such structures. The problem is investigated and solved for hierarchic models too. The obtained results broaden the sphere of applications of complex analysis methods. The classical theory of finding a general solution of partial differential equations of complex analysis, which in the linear case was thoroughly developed in the works of Goursat, Weyl, Walsh, Bergman, Kolosov, Muskhelishvili, Bers, Vekua and others, is extended to the solution of basic nonlinear differential equations containing the nonlinear summand, which is a composition of Laplace and Monge–Ampére operators.

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.

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.

Post-Buckling Analysis of Heavy Columns with Application to Marine Risers

1985 ◽  
Vol 29 (03) ◽  
pp. 162-169
Author(s):  
Theodore Kokkinis ◽  
Michael M. Bernitsas
Keyword(s):  
Boundary Conditions ◽  
Small Strain ◽  
Equilibrium Path ◽  
Drilling Mud ◽  
Tubular Columns ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Combined Action ◽  
Raphson Iteration ◽  
Good Agreement

The post-buckling behavior of heavy tubular columns following static instability under the combined action of weight, tension/compression at the top, and fluid static pressure forces in the gravity field is studied. A two-dimensional nonlinear small-strain large-deflection model of the column is derived, consisting of an integrodifferential equilibrium equation and two end rotation conditions. The equation of equilibrium is discretized using a finite-element method. An approximate solution valid in the neighborhood of the bifurcation point and an incremental solution are used to determine the secondary equilibrium path. The results of both methods are corrected by Newton-Raphson iteration. Conditions for unstable initial post-buckling behavior and existence of limit points on the secondary equilibrium path are presented. The numerical solution is applied to the problem of the elastica and is found to be in good agreement with the analytical solution. The secondary equilibrium path for a 500-m-long (1640 ft) marine drilling riser is calculated for two sets of boundary conditions and various values of the drilling mud density. The effect of the drilling mud density and the boundary conditions on the riser's post-buckling behavior is discussed.

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.

Effects of Friction on Post-Buckling Behavior and Axial Load Transfer in a Horizontal Well

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1104-1118 ◽  
Author(s):  
Guohua Gao ◽  
Stefan Miska
Keyword(s):  
Boundary Conditions ◽  
Critical Load ◽  
Axial Load ◽  
Load Transfer ◽  
Experimental Studies ◽  
Proper Solution ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Helical Buckling ◽  
Lateral Friction

Summary In this paper, the buckling equation and natural boundary conditions are derived with the aid of calculus of variations. The natural and geometric boundary conditions are used to determine the proper solution that represents the post-buckling configuration. Effects of friction and boundary conditions on the critical load of helical buckling are investigated. Theoretical results show that the effect of boundary conditions on helical buckling becomes negligible for a long pipe with dimensionless length greater than 5π Velocity analysis shows that lateral friction becomes dominant at the instant of buckling initiation. Thus, friction can increase the critical load of helical buckling significantly. However, once buckling is initiated, axial velocity becomes dominant again and lateral friction becomes negligible for post-buckling behavior and axial-load-transfer analysis. Consequently, it is possible to seek an analytical solution for the buckling equation. Analytical solutions for both sinusoidal and helical post-buckling configurations are derived, and a practical procedure for modeling of axial load transfer is proposed. To verify the proposed model and analytical results, the authors also conducted experimental studies. Experimental results support the proposed solutions.

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