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1

Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment

Zenkour A. M., Radwan A. F.

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 4

198--220

EN

The present paper deals with the effect of exponential temperature and moisture concentration on the bending and buckling analysis of functionally graded plates resting on two-parameter elastic foundations via a four-variable exponential shear deformation theory. The mechanical properties of the plates are assumed to vary through the thickness. The equations of equilibrium are derived using Hamilton’s principle. The present solutions are derived using Navier’s method. Using Navier’s solution the numerical results are presented and compared well with those available in the literature. Discussions are made to show how the foundation stiffness, hygrothermal loading and other parameters have a significant influence on the bending and buckling analysis of FG plates under hygrothermal and mechanical loading.

2

The effect of material gradient on the static and dynamic response of layered functionally graded material plate using finite element method

Vasiraja N., Nagaraj P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 4

827--838

EN

This article focuses on the finite element analysis (FEA) of the nonlinear behavior of a layered functionally graded material (FGM) plate as concerns displacement, stresses, critical buckling load and fundamental frequency. The material properties of each layer in an FGM plate are assessed according to a ceramic based simple power law distribution and the rules of mixture. The finite element model of a layered FGM plate is developed using ANSYS®15.0 software. The developed finite element model is used to study the static and dynamic responses of an FGM plate. In this paper, the effects of power law distribution, thickness ratio, aspect ratio and boundary conditions are investigated for central displacement, transverse shear stress, transverse normal stress, critical buckling load and fundamental frequency, and the obtained FEA results are in sound agreement with the literature test data results. Since the FGM is used in a high temperature environment, the FE analysis is performed for the FGM plate under a thermal field and then correlated. Finally, the FGM plate is analyzed under a thermomechanical load by using the current FE concept.

3

Finite element study on thermal buckling of functionally graded piezoelectric beams considering inverse effects

Nasirzadeh R., Behjat B., Kharazi M.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 4

1097--1108

EN

In this article, the buckling behavior and bifurcation point of Functionally Graded Piezoelectric (FGP) beams are investigated based on Euler-Bernoulli beam theory. The finite element method is employed to model the beam in thermal environment. The material properties of the beam are considered to vary gradually in the thickness direction and the beam is subjected to electrical and thermal loading. In this paper, direct and inverse piezoelectric effects are considered and buckling of the beam in the sensor state is investigated. By solving the eigenvalue problem, the buckling load of the FGP beam is obtained and the effect of various parameters such as power law index, temperature, applied voltage and beam aspect ratio on the buckling load are investigated. The results show that the boundary conditions are the main factor that affects the buckling load of the FGP beam.

4

Investigation of boundary condition effects on the stability of FGP beams in thermal environment

Nasirzadeh R., Behjat B., Kharazi M., Khabazaghdam A.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

1003--1014

EN

In this paper, stability and instability of Functionally Graded Piezoelectric (FGP) beams is investigated based on the Timoshenko beam theory. The material properties of the beam are considered to change gradually through thickness of the beam by a simple power law. By using the principle of minimum total potential energy, governing equations of the beam are derived. Stability behavior of the beam is predicted by solving the governing equations of the FGP beam. The results show that the homogeneity of boundary conditions plays a critical role in the stability of the FGP beam. While non-homogeneous boundary conditions lead to stable behavior of the FGP beam; homogeneous boundary conditions cause instability in the beam. By solving the eigenvalue equation of the FGP beam, the buckling load of the beam is obtained for the beams that have unstable behavior. Finally, the effects of various parameters on the buckling load of the unstable beam, such as power law index, temperature, applied voltage and aspect ratio are investigated, and the results are compared with the Euler-Bernoulli beam theory.

5

Comparative analysis of buckling load of circular and corrugated tubes by utilizing key performance indicators

Rahim M. R., Akhtar S., Bharti P. K.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 3

789--797

EN

The performance of buckling load of tubular structures under quasi-static axial loading is quite appreciable, numerous tubes of various cross-section have been extensively investigated and corrugated sections have been designed to further improve the performance. In this paper, a carefully designed set of key performance indicators (KPIs) is utilized to assess and compare the buckling load of circular and corrugated tubes. A series of diagrams related to KPIs with various parameters of tubes are presented to demonstrate the influence of sectional configuration on the performance of tubes as well as the effect of the material on the potential of the same. The work is inestimable to engineering designs and applications, and further studies on the buckling load of other configurations.

6

Stability of an innovative cold-formed GEB section

Łukowicz A., Krajewski M.

Engineering Transactions

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2017

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Vol. 65, iss. 1

45--51

EN

This paper is focused on the numerical analysis and experimental test of stability of the cold-formed profile with an innovative GEB cross-section. For the shell model of the axially compressed member, the linear buckling analysis and the nonlinear static analysis were carried out. In the numerical research, the buckling load and the limit load for variable section heights were obtained. Some of the results were compared with the GEB member bearing capacity calculated on the basis of PN-EN 1993-1-1 Eurocode 3 requirements.

7

Experimental and numerical analysis of compression thin-walled composite plates weakened by cut-outs

Falkowicz K.

Archives of Civil Engineering

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2017

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Vol. 63, nr 4

161--172

EN

Buckling and postbuckling response of thin-walled composite plates investigated experimentally and determinated analytically and numerically is compared. Real dimension specimens of composite plates weakened by cut-out subjected to uniform compression in laboratory buckling tests have been modelled in the finite element method and examined analytically based on P-w2 and P-w3 methods. All results were obtained during the experimental investigations and the numerical FEM analysis of a thin-walled composite plate made of a carbon-epoxy laminate with a symmetrical eight-layer arrangement of [90/-45/45/0]s. The instrument used for this purpose was a numerical ABAQUS® program.

PL

W pracy zajmowano się oryginalną koncepcją płytowego elementu cienkościennego z centralnym wycięciem, do zastosowania jako element sprężysty. Badania obejmowały liniową i nieliniową analizę numeryczną konstrukcji z wykorzystaniem metody elementów skończonych oraz eksperymentalną weryfikację obliczeń MES. Przedmiot badań stanowiła cienkościenna płyta z centralnym prostokątnym wycięciem, wykonana z kompozytu węglowo-epoksydowego. Struktura laminatu złożona była z 8 warstw o jednakowej grubości wynoszącej 0.131 [mm] w symetrycznym układzie warstw względem płaszczyzny środkowej pakietu. Badania prowadzono na płycie kompozytowej o konfiguracji warstw kompozytu [90/-45/45/0]s. Zakres pracy obejmował badania eksperymentalne na rzeczywistej konstrukcji oraz wykonanie symulacji numerycznej z wykorzystaniem metody elementów skończonych. Analizowano stan krytyczny ściskanej osiowo cienkościennej płyty kompozytowej z centralnym prostokątnym wycięciem, podpartej przegubowo na obydwu końcach oraz rozwiązanie zagadnienia nieliniowej stateczności, w którym obliczenia prowadzono na modelach z zainicjowaną imperfekcją geometryczną odpowiadającą wyższej, giętno-skrętnej postaci wyboczenia konstrukcji.

8

Buckling Analysis of Cold Formed Silo Column

Rejowski K., Iwicki P.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 2

109--120

EN

The paper is devoted to stability analysis of different models of steel cold formed silo column. The steel cylindrical silos are often composed of corrugated walls and vertical open-sectional columns uniformly placed along the silo circumference. Both the whole 3D silo, a simplified model consisting of one column with a part of the silo walls, and a single column resting on elastic foundation provided by the silo walls were analyzed. Linear buckling analyses were carried out using commercial FE package ABAQUS. Axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1 were considered. The calculated buckling loads of 1D column model were compared with the permissible one given by Eurocode 3 and with results found for the whole silo and a single column on elastic foundation modeled by shell elements.

9

Stability of an imperfect truss loaded by wind

Krajewski M., Iwicki P.

Engineering Transactions

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2016

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Vol. 64, iss. 4

509--516

EN

The present paper is devoted to the numerical research of stability of a truss loaded by wind and stiffened by elastic supports located at the top chord. The lateral braces or lateral and torsional braces were taken into account. In this paper, the linear buckling analysis results for the beam and shell model were presented. Two different shapes of initial geometric imperfections were considered in the non-linear static analysis performed for the shell model of the structure. As a result, the truss buckling and the limit load were found to be related to the truss bracing stiffness and the threshold bracing condition, necessary to provide maximum buckling resistance of the truss, was obtained.

10

A new approach for buckling analysis of axially functionally graded beams

Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 2

95--102

EN

The object of considerations are axially functionally graded (FG) beams, which are loaded by an axial force varying along the length of the beam. The main idea presented here is to approximate FG beams by an equivalent beam with piecewise exponentially varying material properties, geometrical properties and axial load. Numerical solutions of the buckling analysis are obtained for four various types of boundary conditions associated with pinned and clamped ends. The usefulness of the proposed method is confirmed by comparing numerical results with those available for graded beams of special polynomial non-homogeneity.

11

Analysis of brace stiffness influence on stability of the truss

Krajewski M., Iwicki P.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 1

97--108

EN

The paper is devoted to the numerical and experimental research of stability of a truss with side elastic supports at the top chord. The structure is a model of a real roof truss scaled by factor ¼. The linear buckling analysis and non-linear static analysis were carried out. The buckling length factor for the compressed top chord was calculated and the limit load for the imperfect truss shell model with respect to brace stiffness was obtained. The relation between brace normal force and loading of the truss is presented. The threshold stiffness of braces necessary to obtain the maximum buckling load was found. The truss load bearing capacity obtained from numerical analysis was compared with Eurocode 3 requirements.

12

Stability and load bearing capacity of a bars with built up cross section and elastic supports

Krajewski M.

Civil and Environmental Engineering Reports

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2015

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No. 16

95--104

EN

The present paper is devoted to the numerical analysis and experimental tests of compressed bars with built–up cross section which are commonly used as a top chord of the roof trusses. The significant impact on carrying capacity for that kind of elements in case of out-of-plane buckling is appropriate choice of battens which are used to provide interaction between separate members. Linear buckling analysis results and nonlinear static analysis results, with material and geometrical nonlinearity, are presented for the bar with built-up cross section which was used as the top chord of the truss made in reality. Diagonals and verticals which are supports for the top chord between marginal joints were replaced by the elastic supports. The threshold stiffness (minimum stiffness) for the intermediate elastic supports which ensures maximum buckling load was appointed for the beam and shell model of the structure. The magnitude of limit load depended on length of the battens was calculated for models with initial geometric imperfections. The experimental tests results for the axially compressed bars with built-up cross section and elastic support are presented.

PL

Niniejsza praca poświecona jest analizom numerycznym i badaniom doświadczalnym ściskanych prętów złożonych, które są często stosowane, jako pasy górne kratownic dachowych. Istotny wpływ na nośność tego typu elementów, przy założeniu wyboczenia z płaszczyzny układu, ma odpowiedni dobór przewiązek zapewniający współpracę poszczególnych gałęzi. W pracy przedstawiono rezultaty liniowych analiz stateczności oraz fizycznie i geometrycznie nieliniowych analiz statycznych dla pręta złożonego, z którego zbudowany jest pas górny kratownicy wykonanej w rzeczywistości. Słupki i krzyżulce podpierające pas między węzłami skrajnymi zastąpiono podporami sprężystymi. Wyznaczono graniczną (minimalna) sztywność sprężystych podpór pośrednich zapewniającą maksymalną wartość obciążenia krytycznego dla modelu prętowego i powłokowego konstrukcji. Podano wartości obciążenia granicznego zależnego od długości zastosowanych przewiązek dla modeli konstrukcji ze wstępnymi imperfekcjami geometrycznymi. Zaprezentowane zostały rezultaty badań doświadczalnych osiowo ściskanych prętów złożonych z podporą sprężystą.

13

Optimal design of bar structures with their supports in problems of stability and free vibrations

Bojczuk D., Rębosz-Kurdek A.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 2

533--546

EN

The problem of maximization of the buckling load and the problem of maximization of the natural vibration frequency under a condition imposed on the global cost is discussed. Cross-sectional areas of bar structures and number of elastic supports, their positions and stiffnesses (or the number and positions of rigid supports) are selected as design parameters. The proposed here algorithm of optimization of bar structures with their supports is applied for analysis of some optimization problems. Illustrative examples confirm applicability of the proposed approach.

14

Buckling of imperfect thick cylindrical shells and curved panels with different boundary conditions under external pressure

Alashti R. A., Ahmadi S. A.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 1

25--36

EN

In this paper, the effects of initial imperfections on the buckling behavior of thick cylindrical shells and curved panels are investigated. It is assumed that the shell has an axisymmetric and periodic initial imperfection in the axial direction. The shell is assumed to have different boundary conditions and subjected to pure external pressure loading. Governing differential equations are developed on the basis of the second Piola-Kirchhoff stress tensor and are re- duced to a homogenous linear system of equations using the differential quadrature method. The effects of different boundary conditions, geometric ratios, curvature and imperfection parameter on the buckling behavior of isotropic thick cylindrical shells and curved panels are carefully discussed. The results obtained by the present method are verified with finite element solutions and those reported in the literature.

15

Buckling analysis of axially functionally graded beams

Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 4

103--108

EN

In this paper critical buckling loads for axially functionally graded (FG) beams are studied. It is assumed that material properties of the beam vary exponentially through the axial direction. Solutions are derived for three types of boundary conditions: a beam that is clamped at both ends, pinned at both ends and a beam that is clamped at one end and pinned at the other.

16

3D Buckling Analysis of a Truss with Horizontal Braces

Iwicki P., Krajewski M.

Mechanics and Mechanical Engineering

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2013

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Vol. 17, nr 1

49–-58

EN

The present research is devoted to the study of out–of–plane buckling of a truss with horizontal braces. The truss is a model of real roof truss scaled by factor 1/4. A linear buckling and a non–linear analysis with geometric and material non–linearity were carried out. The truss buckling and limit load for different stiffnesses and number of braces are found. Numerical analysis are verified by experiment. Threshold bracing stiffness condition for full bracing of the truss is proposed.

17

Dynamical analysis of stiffened plates under patch loading

Srivastava A. K. L., Pandey S. R., Kumar A.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 2

537--553

EN

The vibration characteristics of stiffened plates with cutouts subjected to in-plane partial edge loadings at one end at the plate boundaries are studied using the finite element method. Buckling loads and vibration frequencies are determined for different cutout ratios and extent of partial edge loading at one end. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The main elegance of the formulation lies in the treatment of the stiffeners. The stiffeners can be placed anywhere within the plate element, and need not be placed on the nodal lines. The vibration characteristics are discussed and the results are compared with those available in the literature. Numerical results are presented for a range of cutout to plate size from 0 to 0.8.

18

Neural network prediction of buckling load of steel arch-shells

Hasanzadehshooiili H., Lakirouhani A., Sapalas A.

Archives of Civil and Mechanical Engineering

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2012

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Vol. 12, no. 4

477--484

EN

Calculating the buckling load of structures is one of the main aspects of geometric structural instability. With reference to finite element software (ANSYS) and considering the weight of the structure as a constant load, the paper calculates the buckling load of steal arch shells as the main scope. Then, the article makes a prediction for the buckling load of steel arch shells applying 85 datasets prepared by the above mentioned method and using an artificial neural network by means of NeuroSolution 5.0 software. The radius of the periphery cylinder of an arch shell, the thickness of the shell and its internal angel are considered as inputs of construct models. Next, in order to attain an optimum model calculating and comparing the value of Root Mean Squared Error, RMSE, Mean Absolute Error, MAE and the coefficient of correlation, R2, for all 1 and 2-layer constructed models, a model having architecture 3-7-1 was found to be optimum. A high confirmed correlation with calculated buckling loads employing the finite element method and considering the calculated values of RMSE (0.0126), MAE (0.011) and the obtained value R2 (0.998) demonstrated high efficiency of a new developed neural network model.

19

A generalized FE formulation for buckling analysis of solid or built-up columns with nonprismatic section

Li G.-Q., Li J.-J.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

651-663

EN

In this paper, a generalized FE formulation for buckling analysis of nonprismatic columns with various cross-sections is established by using the Chebyshev polynomial approach to the governing differential equation. The proposed formulation includes the effects of shear deformation and is therefore applicable to solid or built-up columns. The change of the sectional properties along the length direction, such as the area and inertia moment, need not be fitted with approximate expressions and can be defined exactly and freely with user-defined functions in programming. Buckling of the three structures, respectively for a tapered mast column with a circular hollow section, a web-tapered I-sectional column and a tapered lattice column, is studied numerically and compared with the results of previous studies. The effects of shear deformation on the buckling loads of those tapered columns are specified.