Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection

Yin-Ping Li,Gui-Lin She,Lei-Lei Gan,Hai-Bo Liu 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.46 No.5

Although some scholars have studied the thermal post-buckling of graphene platelets strengthened metal foams (GPLRMFs) plates, they have not considered the influence of initial geometrical imperfection. Inspired by this fact, the present paper studies the thermal post-buckling characteristics of GPLRMFs plates with initial geometrical imperfection. Three kinds of graphene platelets (GPLs) distribution patterns including three patterns have been considered. The governing equations are derived according to the first-order plate theory and solved with the help of the Galerkin method. According to the comparison with published paper, the accuracy and correctness of the present research are verified. In the end, the effects of material properties and initial geometrical imperfection on the thermal post-buckling response of the GPLRMFs plates are examined. It can be found that the presence of initial geometrical imperfection reduces the thermal post-buckling strength. In addition, the present study indicates that GPL-A pattern is best way to improve thermal post-buckling strength for GPLRMFs plates, and the presence of foams can improve the thermal post-buckling strength of GPLRMFs plates, the Foam- II and Foam- I patterns have the lowest and highest thermal post-buckling strength. Our research can provide guidance for the thermal stability analysis of GPLRMFs plates.

Finite Element Analysis on Axial Compressive Behaviors of High-Performance Steel Stiff ened Plates in Bridge Application

Yongxuan Li,Yuqing Liu,Rong Liu 한국강구조학회 2019 International Journal of Steel Structures Vol.19 No.5

In order to investigate the mechanical behavior, the buckling performance and failure reason of stiff ened high performance steel (HPS) plates, three-dimensional fi nite element (FE) models considering initial imperfections and residual stresses are compressed with axial force. Various infl uential factors such as element size, constitutive relations, second order eff ects of structure and membrane eff ects in buckling area were discussed to achieve a better validation with experimental data. As load increasing, the plastic strain in the U-rib near the end stiff ener increases gradually under the infl uence of initial imperfections and stress concentration. Local buckling occurs after yielding of the whole section. With the refi ned model, the sensitivity of stiff ened structure to the residual stresses and imperfections are investigated, and parametric studies on the material properties, geometric dimensions are conducted. The results show that the initial imperfections have a major infl uence on the ultimate capacity while the residual compressive stresses govern the elastic capacity and the ductility. Proper values of the imperfections and residual stresses are suggested for FE stiff ened plate simulations. HPS stiff ened plates with short length is more sensitive to initial imperfections. The eff ects of length, thickness and spacing are similar to the ordinary steel plates. Both equations in American and Chinese standards are used to evaluate the ultimate capacity of stiff ened HPS plates, and formulas in AASHTO provide a more accurate estimate on capacity and failure mode, while Chinese specifi cation is more conservative comparatively

제형 및 사인형 주름 강판의 초기 불완전 형상을 고려한 전단 좌굴 특성 비교

서건호,손수덕,이승재,Seo, Geonho,Shon, Sudeok,Lee, Seungjae 한국공간구조학회 2021 한국공간구조학회지 Vol.21 No.4

This paper conducted a comparative analysis of the shear buckling characteristics of trapezoidal and sinusoidal corrugated steel plates considering of their initial imperfection. Initial imperfection refers to the state where the shape of the corrugated plate is initially not perfect. As such, an initially imperfect shape was assumed using the eigen buckling mode. To calculate the buckling stress of corrugated steel plates, the linear buckling analysis used a boundary condition which was applied to the plate buckling analysis. For the comparison of trapezoidal and sinusoidal corrugation, the shape parameters were assumed using the case where the length and slope of each corrugation were the same, and the initial imperfection was considered to be from 0.1% to 5% based on the length of the steel plate. Here, for the buckling analysis, ANSYS, a commercial FEA program, was used. From the results of buckling analysis, the effect of overall initial imperfection showed that the larger the initial imperfection, the lower the buckling stress. However, in the very thin model, interaction or local buckling was dominant in the perfect shape, and in this case, the buckling stress did not decrease. Besides, the sinusoidal model showed higher buckling stress than the trapezoidal one, and the two corrugation shapes decreased in a similar way.

Explicit incremental matrices for the postbuckling analysis of thin plates with small initial curvature

Jayachandran, S. Arul,Gopalakrishnan, S.,Narayanan, R. Techno-Press 2001 Structural Engineering and Mechanics, An Int'l Jou Vol.12 No.3

The postbuckling behaviour of thin plates is an important phenomenon in the design of thin plated structures. In reality plates possess small imperfections and the behaviour of such imperfect plates is of great interest. To numerically study the postbuckling behaviour of imperfect plates explicit incremental or secant matrices have been presented in this paper. These matrices can be used in combination with any thin plate element. The secant matrices are shown to be very accurate in tracing the postbuckling behaviour of thin plates.

Computational analysis of the nonlinear vibrational behavior of perforated plates with initial imperfection using NURBS-based isogeometric approach

VeisiAra Abdollah,Mohammad-Sedighi Hamid,Reza Arash 한국CDE학회 2021 Journal of computational design and engineering Vol.8 No.5

In this article, an isogeometric analysis through NURBS basis functions is presented to study the nonlinear vibrational behavior of perforated plates with initial imperfection. In this regard, the governing equations of plate dynamics, as well as the displacement–strain relations, are derived using the Mindlin–Reissner plate theory by considering von Karman nonlinearity. The geometry of the structure is formed by selecting the order of NURBS basis functions and the number of control points according to the physics of the problem. Since similar basis functions are utilized to estimate the accurate geometry and displacement field of the domain, the order of the basic functions and the number of control points are optimized for the proper approximation of the unknown field variables. By utilizing the energy approach and Hamilton principle and discretizing the equations of motion, the vibrational response of the perforated imperfect plate is extracted through an eigenvalue problem. The results of linear vibrations, geometrically nonlinear vibrations, and nonlinear vibrations of imperfect plates are separately validated by considering the previously reported findings, which shows a satisfactory agreement. Thereafter, a coefficient of the first mode shape is considered as the initial imperfection and the vibrational analysis is reexamined. Furthermore, the nonlinear vibrations of the perforated plate with initial imperfection are analysed using an iterative approach. The effects of the perforated hole, initial imperfection, and geometric nonlinearity are also addressed and discussed.

Stability analysis of multi-layered plates subjected to partial edge compression with and without initial imperfection

Tran, Loc V.,Kim, Seung-Eock Elsevier 2018 COMPOSITE STRUCTURES -BARKING THEN OXFORD- Vol.205 No.-

<P><B>Abstract</B></P> <P>This paper studies buckling and post-buckling behaviours of multi-layered plates under in-plane compression based on Reissner-Mindlin plate theory. The governing equations are derived from a kinematic nonlinearity based on the von-Kármán assumptions and are thereafter discretized by isogeometric analysis (IGA), which utilizes the NURBS basis functions. For the symmetrically laminated plates, stability analysis consists of three steps: pre-buckling, buckling and post-buckling analyses. In fact, the pre-buckling stresses must be first determined in the pre-buckling analysis and become an important factor in accurate estimation of the critical buckling and post-buckling loads. Otherwise, in the imperfect or unsymmetrically stacked plates, there is no buckling bifurcation phenomenon. The Newton-Rapshon method is hence adopted to solve the geometrically nonlinear problem. Numerical examples are supplied to investigate the effect of an initially geometrical imperfection, which is possible imperfection type such as sine-type, global-type or local-type imperfection, on the post-buckling response of the plates.</P>

Free vibration of various types of FGP sandwich plates with variation in porosity distribution

Aicha Kablia,Rabia Benferhat,Tahar Hassaine Daouadji,Rabahi Abderezak 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.1

The use of functionally graded materials in applications involving severe thermal gradients is quickly gaining acceptance in the composite mechanics community, the aerospace and aircraft industry. In the present study, a refined sandwich plate model is applied to study the free vibration analysis of porous functionally graded material (FGM) sandwich plates with various distribution rate of porosity. Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the sandwich plate. The number of unknowns and equations of motion of the present theory is reduced and hence makes them simple to use. In the analysis, the equation of motion for simply supported sandwich plates is obtained using Hamilton’s principle. In order to present the effect of the variation of the porosity distribution on the dynamic behavior of the FGM sandwich plates, new mixtures are proposed which take into account different rate of porosity distribution between the ceramic and the metal. The present method is applicable to study the dynamic behavior of FGM plates and sandwich plates. The frequencies of two kinds of FGM sandwich structures are analyzed and discussed. Several numerical results have been compared with the ones available in the literature.

Dynamic of behavior for imperfect FGM plates resting on elastic foundation containing various distribution rates of porosity: Analysis and modeling

Kablia, Aicha,Benferhat, Rabia,Tahar, Hassaine Daouadji Techno-Press 2022 Coupled systems mechanics Vol.11 No.5

During the manufacture of FGM plates, defects such as porosities can appear. Those can change the entire behavior of these plates. This paper aims to investigate the free vibration characteristics of porous functionally graded (FG) plates resting on elastic foundations. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power-law formulation, and the Poisson ratio is held constant. Different types of porosity distribution rates are considered. To examine the accuracy of the present formulation, several comparison studies are investigated. Effects of variation of porosity distribution rate, foundation parameter, power-law index and thickness ratio on the fundamental frequency of plates have been investigated.

Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

Zhaoting Chen,Ronghui Wang,Li Cheng,Chunguang Dong 대한기계학회 2016 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.30 No.8

This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening

Ghannadpour, S. Amir M.,Kiani, Payam Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.66 No.5

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.