Geometric Imperfection Distributions of Existing Reticulated Shells: Theoretical and Experimental Analysis

Wu Jun,Luo Yongfeng,Wang Lei 한국강구조학회 2020 International Journal of Steel Structures Vol.20 No.5

Geometric imperfection is one of the most disadvantageous factors that impair mechanical behaviors of existing reticulated shell structures. However, the available consistent mode methods and statistical methods which usually applied in designing structures can hardly estimate the actual geometric imperfection distribution for existing structures, because these methods use the assumed imperfections. In this paper, a Markov Random Field (MRF) theoretical model of existing reticulated shells is established by introducing the theory of probabilistic graphical model. The unit of graphic model named node clique are proposed to deduct the geometric state function of reticulated shells, based on the local Markov property. Then the inversion function along with its iterative equation is established to predict geometric imperfection distribution of existing reticulated shells. The MRF method makes the predicted distribution of the numerical model as consistent as possible with its corresponding actual structure, and only a few measurement nodes are needed as known conditions. An experimental structure of K6 single-layer reticulated shell is built to verify the proposed theory by comparing the calculated geometric imperfection distribution results with the actual measured data. Meanwhile, the signifi cance level of the calculated results between MRF and traditional stochastic method is analyzed, which shows MRF method can eff ectively predict the geometric imperfections of single layer reticulated shells.

Prediction of Ultimate Behaviors in Cold-formed Steel Bolted Connection by the Introduction of Initial Geometric Imperfection in FE Modeling

Kim, Tae Soo,Kuwamura, Hitoshi,Cho, Taejun The Iron and Steel Institute of Japan 2008 ISIJ international Vol.48 No.5

<P>Experimental research and nonlinear finite element analysis for the structural behaviors of single shear test on bolted connections fabricated with cold-formed stainless steel have been conducted. Failure criteria for prediction of failure mode of bolted connections under static shear and out-of-plane deformation, <I>i.e.</I>, curling criteria were proposed based on experimental data for calibration of FE modeling. Failure mode and ultimate strength predicted by recommended FEA procedures with solid element showed a good correspondence with those of previous test results and the validation of FEA method was verified. The previous numerical analyses of bolted connection were carried out on geometrically perfect specimens. However, it has been known that geometric imperfection of thin-walled members must be considered in a FE model to simulate the actual shape of specimen. Therefore, in this paper, parametric studies were carried out based on the validity of numerical modeling of bolted connections in cold-formed stainless steel so that authors investigated the influence of initial geometric imperfection of connected plate on its structural behavior. Solid element and shell element with reduced integration were introduced as an element type and included two types of geometric imperfection. Consequently, FE modeling technique of cold-formed stainless steel bolted connection introducing initial imperfection to compensate the function of shell element and to induce the curling was proposed.</P>

Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites

Khalaf, Basima Salman,Fenjan, Raad M.,Faleh, Nadhim M. Techno-Press 2019 Advances in materials research Vol.8 No.3

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

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.

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

S. Amir M. Ghannadpour,Payam Kiani 국제구조공학회 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.

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.

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.

Isogrid 패널의 초기 형상 불완전성에 관한 연구

이종웅(Jong Woong Lee),유준태(Joon Tae Yoo),윤종훈(Jong Hoon Yoon),장영순(Young Soon Jang),이영무(Yenong Moo Yi) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.11

There are many methods to reinforce the cylindrical structure for light weight design. Isogrid is one of the reinforced structures to improve buckling load. To make Isogrid panel, trigngle shape grid is removed by mechanical milling and it is curved-shaped by roll bending which is one of the plastic forming. When the Isogrid panel is shaped by roll bending, initial geometrical imperfection is occurred and becomes the reason which diminish the buckling load. In this paper, ANSYS is used for non-linear FE analysis and analysis results are compare with manufactured Isogrid panel about dimension of initial geometrical imperfection.

Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects

Laith A. Hassan Kunbar,Luay Badr Hamad,Ridha A. Ahmed,Nadhim M. Faleh 국제구조공학회 2020 Smart Structures and Systems, An International Jou Vol.25 No.5

This paper studies nonlinear free vibration characteristics of nonlocal magneto-electro-elastic (MEE) nanobeams resting on nonlinear elastic substrate having geometrical imperfection by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All of previously reported studies on MEE nanobeams ignore the influences of geometric imperfections which are very substantial due to the reason that a nanobeam cannot be always perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric constituent in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam are dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and geometrical imperfection.