Evaluation of bending and post-buckling behavior of thin-walled FG beams in geometrical nonlinear regime with CUF

2021 ◽  
pp. 114408
Author(s):  
Erasmo Carrera ◽  
M. Didem Demirbas
Keyword(s):  
Nonlinear Regime ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Post Buckling ◽  
Thin Walled

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 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.

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.

Post-buckling and Snap-Through Behavior of Inclined Slender Beams

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Jian Zhao ◽  
Jianyuan Jia ◽  
Xiaoping He ◽  
Hongxi Wang
Keyword(s):  
Large Deflection ◽  
Buckling Modes ◽  
Strongly Nonlinear ◽  
Elastic Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Slender Beams ◽  
Post Buckling ◽  
Inclined Beam ◽  
Good Agreement

Based on the geometrical nonlinear theory of large deflection elastic beams, the governing differential equations of post-buckling behavior of clamped-clamped inclined beams subjected to combined forces are established. By using the implicit compatibility conditions to solve the nonlinear statically indeterminate problems of elastic beams, the strongly nonlinear equations formulated in terms of elliptic integrals are directly solved in the numerical sense. When the applied force exceeds the critical value, the numerical simulation shows that the inclined beam snaps to the other equilibrium position automatically. It is in the snap-through process that the accurate configurations of the post-buckling inclined beam with different angles are presented, and it is found that the nonlinear stiffness decreases as the midpoint displacement is increased according to our systematical analysis of the inward relations of different buckling modes. The numerical results are in good agreement with those obtained in the experiments.

The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams

1987 ◽  
Vol 54 (3) ◽  
pp. 558-562 ◽  
Author(s):  
I. Sheinman ◽  
M. Adan
Keyword(s):  
Finite Difference ◽  
Shear Deformation ◽  
Nonlinear Differential Equations ◽  
Kinematic Model ◽  
Transverse Shear Deformation ◽  
Shear Effect ◽  
Laminated Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Post Buckling

A geometrical nonlinear theory of composite laminated beams is derived with the effect of transverse shear deformation taken into account. The theory is based on a high-order kinematic model, with the nonlinear differential equations solved by Newton’s method and a special finite-difference scheme. A parametric study of the shear effect involving several kinematic approaches was carried out for isotropic and anisotropic beams.

scholarly journals Post-buckling Behavior of Non-shallow Thin-walled Cylindrical Shells

1998 ◽  
Vol 1 ◽  
pp. 65-72
Author(s):  
Kouichi KOHNO ◽  
Kaoru YOKOYAMA ◽  
Masatoshi NAKAZAWA ◽  
Tetsuo IWAKUMA
Keyword(s):  
Cylindrical Shells ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

A New Concept of the Effective Shear Modulus for a Plate Buckled in Shear

1995 ◽  
Vol 39 (01) ◽  
pp. 70-75
Author(s):  
Jeom Kee Paik
Keyword(s):  
Shear Modulus ◽  
Theoretical Background ◽  
Effective Width ◽  
Ultimate Shear Strength ◽  
Effective Shear Modulus ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled ◽  
Strength Formula

A new concept of the effective shear modulus is suggested for describing stiffness and strength of a plate in edge shear. This concept has quite similar advantages to the effective width, which has been recognized as an efficient approach for analysis of the post-buckling behavior of thin-walled members in compression. The theoretical background of the new idea is described, and based on results of the series analysis an empirical formula of the effective shear modulus for a simply supported rectangular plate is derived taking into account initial deflection effects. Using this formula, an ultimate shear strength formula of a plate is also suggested. The validity of the proposed formula is checked by comparison with the numerical results. It is concluded that the proposed idea will be quite useful if an effective shear modulus formula is successfully developed.

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