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.

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.

Comparisons between 1D (Beam) and 2D (Plate/Shell) Finite Elements to Analyze Thin Walled Structures

2014 ◽  
Vol 93 (1-2) ◽  
pp. 3-16 ◽  
Author(s):  
E. Carrera ◽  
M. Cinefra ◽  
M. Petrolo ◽  
E. Zappino
Keyword(s):  
Finite Elements ◽  
Thin Walled Structures ◽  
Thin Walled

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.

Time Response Stress Analysis of Solid and Reinforced Thin-Walled Structures by Component-Wise Models

2020 ◽  
pp. 2043010
Author(s):  
R. Azzara ◽  
E. Carrera ◽  
M. Filippi ◽  
A. Pagani
Keyword(s):  
Stress State ◽  
Complex Stress ◽  
Time Response ◽  
Modeling Technique ◽  
Integration Scheme ◽  
Structural Domain ◽  
Mode Superposition ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Stress States

This paper deals with the evaluation of time response analyses of typical aerospace metallic structures. Attention is focussed on detailed stress state distributions over time by using the Carrera Unified Formulation (CUF) for modeling thin-walled reinforced shell structures. In detail, the already established component-wise (CW) approach is extended to dynamic time response by mode superposition and Newmark direct integration scheme. CW is a CUF-based modeling technique which allows to model multi-component structures by using the same refined finite element for each structural component, e.g. stringers, panels, ribs. Component coupling is realized by imposing displacement continuity without the need of mathematical artifices in the CW approach, so the stress state is consistent in the entire structural domain. The numerical results discussed include thin-walled open and closed section beams, wing boxes and a benchmark wing subjected to gust loading. They show that the proposed modeling technique is effective. In particular, as CW provides reach modal bases, mode superposition can be significantly efficient, even in the case of complex stress states.

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.

Influences of Thermal Loads on Nonlinear Response of Thin-Walled Structures in Thermo-Acoustic Environment

2011 ◽  
Vol 105-107 ◽  
pp. 220-226 ◽  
Author(s):  
Yun Dong Sha ◽  
Zhi Jun Gao ◽  
Fei Xu
Keyword(s):  
High Speed ◽  
Nonlinear Response ◽  
Large Deflection ◽  
Thermal Protection ◽  
Thermal Loads ◽  
Acoustic Response ◽  
Restoring Force ◽  
Acoustic Environment ◽  
Thin Walled Structures ◽  
Thin Walled

Thin-walled structures of future hypersonic flight vehicles will encounter complex loadings and exhibit obvious nonlinear responses. The thermal loads from high speed flow or engine jet flow can cause thermal buckling of thin-walled structures, such as Thermal Protection System (TPS). If the structures are loaded with intense acoustic loads simultaneously, large deflection nonlinear response, including snap-through, can be induced. Snap-through will give rise to large amplitude stress cycles and non-zero mean stress, which can lessen the fatigue life markedly. Starting from Hooker’s Law with thermal components, the large deflection governing equations of motion for simply-supported plate under thermo-acoustic loadings are derived. The partial differential equation (PDE) of motion which is difficult to solve is then transformed with Galerkin’s method to the system of ordinary differential equations (ODE) under modal coordinates. The displacement responses under different combinations of temperature increments and sound pressure levels are calculated by employing Runge-Kutta method. Typical thermo-acoustic responses are predicted: 1) random vibration around pre-buckled equilibrium position, 2) persistent snap-through between post-buckled positions, 3) intermittent snap-through, 4) vibration around one of the two post-buckled positions. By dividing the restoring force term in the equation into linear term and nonlinear one, the evolutions of each term are obtained to illustrate the mechanism of thermo-acoustic response and the contributions of each force, including shear force, thermal force and membrane force. Thus a further insight into thermo-acoustic response has been achieved.

scholarly journals Axial Compression Behavior of Circular Concrete-Filled High-Strength Thin-Walled Steel Tubular Columns with Out-of-Code D/t Ratios

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Jun-Xin Li ◽  
Jian-Tao Wang ◽  
Qing Sun ◽  
Yan-Ru Wu ◽  
Shi-Ming Zhou ◽  
...  
Keyword(s):  
Axial Compression ◽  
Full Range ◽  
High Strength ◽  
Displacement Curve ◽  
Fe Model ◽  
Range Analysis ◽  
Cross Sectional ◽  
Compression Behavior ◽  
Thin Walled ◽  
Cfst Columns

This paper systematically investigated the axial compression behavior of circular concrete-filled high-strength thin-walled steel tubular (CFHTST) columns with out-of-code diameter-to-thickness (D/t) ratios. The axial compression test was first conducted to examine the failure mode, load-displacement curves, and composite mechanism effect. The finite element (FE) model was thereafter established to perform full-range analysis on the load versus displacement curve as well as the interaction behavior, where the parametric study was performed to investigate the influences of the material strengths and geometric sizes. Subsequently, the applicability of typical design methods was evaluated, and a revised equation for determining strain εscy corresponding to ultimate strength was established to assess the plastic deformation capacity of CFHTST columns. Finally, a theoretical model for calculating axial bearing capacity was derived based on unified twin-shear strength theory by considering the influence of intermediate principal stress. The research results indicate that a relatively high confine effect can be guaranteed for CFHTST columns under out-of-code D/t ratios, given that the ratio Nu/Nnom between the measured capacity (Nu) and nominal cross-sectional capacity (Nnom) mainly distributes within 1.179∼1.292; the full-range analysis reflects that the axial load-deformation curve can be distinguished by four various loading stages; the scope b = 0.3∼0.55 of intermediate stress coefficient is generally suggested for predicting axial strength of circular CFST columns within an error of ±5%. The abovementioned study can provide the meaningful design reference for the analysis and application of CFHTST columns.

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