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The distribution of the internal forces corresponding to the individual buckling modes of lip-channel (LC) beams is investigated using the Semi Analytical Method (SAM) and the Finite Element Method (FEM). Channel section beams made of 8-layered GFRP (Glass Fiber Reinforced Polymer) laminate with three different layer arrangements were considered. T...
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... on these results, it can be concluded that the layer arrangement of the LC-1 beam is the least favourable for the considered instances due to the value of the critical loads. In Table 5, the values of the critical moment M min corresponding to the lowest critical load for each of the three instances, and also those corresponding to the M min angle of rotation at the support α min are listed. Comparing the three applied methods (FEM BC I, FEM BC II and SAM), a very high result accuracy was obtained for the two FE models. ...Similar publications
Compression testing of continuous fiber reinforced materials is challenging, because a great number of competing failure modes and instabilities on different length scales have to be considered. In comparison to tensile testing, the results are more affected by the chosen test set-up. Effects introduced by the test set-up as well as the type of dam...
Citations
... Using experimental research and finite element methods, the authors presented the impact of honeycomb design parameters as well as core and lining material properties on the mechanical properties of lightweight laminated panels. Many works deal with theoretical considerations in terms of the analysis of the stability of composite structures [28][29][30][31]. ...
The article presents continued considerations presented in a prior publication on the development of a model for calculating the bending stiffness BS of cellular honeycomb paperboards, applying the strength properties of paper raw materials used for the production of paperboard and the geometric parameters of cellular board. The results of BS calculations obtained by using the analytical model presented in the prior publication were significantly overestimated in relation to the value obtained by measurements. The calculation error in relation to the measurement value for the tested group of paperboards in the case of bending stiffness in the machine direction MD was within the range from 23% to 116%, and the average error was 65%, while in the cross direction CD, it was within the range from 2% to 54%, and the average error was 31%. The calculation model proposed in this work based on the physical properties of cellular paperboard reduces the error values for bending stiffness in both the machine and cross directions. The value of the average error for both main directions in the paperboard plane was 10%. The method enables more accurate determination of BS in the machine direction MD and in the cross direction CD at the paperboard design stage. In order to validate the proposed analytical model, the calculation results were compared with the results of BS laboratory measurements performed using the four-point bending method and, in order to expand the group of tested paperboards, with the measurement results presented in the prior article for cardboards with different raw material composition and different geometric parameters.
... In the literature, one can find many experimental studies on composite panels, such as those described in [9][10][11][12][13][14][15][16][17][18]. Theoretical work on the analysis of the stability of composite structures has also been presented in the literature [19][20][21][22]. However, these studies do not concern the analysis of a board's strength. ...
This article analyzes the influence of the initial deflection of the flat layers on the bending stiffness (BS) of honeycomb paperboards and presents two methods for its calculation. Both methods allow for the determination of BS in the main directions in the plane of the paperboard, i.e., the machine direction (MD) and the cross direction (CD). In addition, they have been verified by comparing the calculation results with the results of the BS measurements. The first method allowed for the calculation of the BS of cellular paperboard based on the mechanical properties of the paper used for its production. The second method allowed for the estimation of the BS of cellular paperboard based on the bending stiffness of other honeycomb paperboards with the same raw material composition and the same core cell size but with different thicknesses. In the first analytical method for the calculation of the bending stiffness of cellular paperboard, which does not include the deflections of the flat layers, the calculation results significantly differ from the measurement results, and they are overestimated. The second of the presented BS calculation methods allowed for a much more accurate assessment of paperboard’s bending stiffness depending on its thickness.
... There are not enough works in the world-wise literature focusing on the non-linear stability of channel cross-section beams under pure bending. A deep literature review and theoretical background are shown in the following papers [15][16][17][18][19]. Due to the nature of the work, the authors decided to focus on documents directly connected with the presented research. ...
... During the initial experimental tests, the vertical and horizontal rotation angles at the support were investigated, and those rotations were explained by global lateral-distortional buckling mode. The results of theoretical works [15][16][17][18][19] show that in the case of the load-carrying capacity in medium length beams, the most crucial is the initial imperfection corresponding to the secondary global buckling mode. ...
... In the following article, the Semi-Analytical Method (SAM), deeply explained in [17,19,25], was used to investigate the problem. SAM is the lower boundary estimation method, which means that the post-buckling curves are less inclined (less stiff) than in the case of the Finite Element Method (FEM) [25,30]. ...
Presented research aims to prove the appearance of lateral-distortional buckling mode by observing the beams' deflection characteristics. Eight-layer channel and lip-channel cross-section glass fibre reinforced polymer (GFRP) beams subjected to pure bending in the web plane were discussed. The Finite Element Method and the Semi-Analytical Method were used to perform all calculations. Deflection angles at the beams' ends show that the lateral deflection sharply increases from load close to critical one and in the post-buckling range. It was observed that for simply supported beams subjected to bending, the lateral-distortional global buckling mode is accompanied by rotation at support in the flange plane.
In the FEM approach, the lowest buckling mode is usually considered in beams subjected to bending, and the angle of rotation in the load plane corresponding to the critical bending moment is only analysed. However, in the interactive buckling analysis, the horizontal rotation at the supports is accompanied by the global mode, and its impact is often neglected due to its high bifurcation value compared to the lowest mode. Moreover, in the paper, the influence of this mode on the equilibrium paths, the critical buckling load, the load-carrying capacity, distributions of internal membrane forces, and vertical and horizontal angle of rotation was investigated.
... Yong et al. in paper [15] investigated the stress state in frame-truss composite wall by using Abaqus software to simulate the places of the cracks in structures. In the literature, one can distinguish papers devoted to an analysis of composite plate [3], plate structures [4,13], beams [9,16,17] and cylindrical structure [8]. Authors of these papers studied the stress state in single structures taking into account both experimental tests and numerical approach based on finite element method (FEM). ...
The paper concerns numerical study of the ultra-light seat frame serving transported patients in ambulance. The structure of seat was designed to be built of the carbon fibers, aluminium and steel. The present prototype distinguishes itself with low mass and high strength. During modelling, the stress state and displacement state were verified based on requirements according to regulation ECE14. In simulation, solid, beam and connection elements were employed to consider all the parts of structures. The analysis of the stress state verification based on the assumptions of boundary conditions close to regulation ECE14. The isotropic materials were considered to be in elastic range. In case of composite materials, TSAI-WU (TSW) criterion for assessment of strength was taken into account. Five different variants of seat were taken into consideration to indicate the differences between them. The paper includes the results of analysis of composite structure under static loads which were shown and discussed.
... The authors of [25] investigated the flexural damage of honeycomb paperboard based on FEM and experimental tests. On the other hand, the research on composite material structures within a buckling and a postbuckling state were carried out numerically in [26][27][28][29] and/or experimentally in [30][31][32][33][34][35][36][37]. Progressive failure analysis in numerical computations was considered in papers [38][39][40], among others. ...
This paper concerns the analysis of five-layer corrugated paperboard subjected to a four-point bending test. The segment of paperboard was tested to determine the bending stiffness. The investigations were conducted experimentally and numerically. The non-damaging tests of bending were carried out in an elastic range of samples. The detailed layers of paperboard were modelled as an orthotropic material. The simulation of flexure was based on a finite element method using Ansys® software. Several material properties and thicknesses of papers in the samples were taken into account to analyse the influence on general stiffness. Two different discrete models based on two geometries of paperboard were considered in this study to validate the experimental stiffness. The present analysis shows the possibility of numerical modelling to achieve a good correlation with experimental results. Moreover, the results of numerical estimations indicate that modelling of the perfect structure gives a lower bending stiffness and some corrections of geometry should be implemented. The discrepancy in stiffness between both methods ranged from 3.04 to 32.88% depending on the analysed variant.
... Martins et al. [13,14] focused on the distortional behaviour of beams under uniform bending. The deep research was performed by Kolakowski et al., in his works, he focused on the interactive buckling [15][16][17], the influence of internal forces [18] and distortional buckling mode on the post-buckling behaviour [19]. ...
... In previous authors' works [15][16][17][18][19], based on observations that the lateral deflection (measured as deflection angle α 2 at support) grows for loads close to the buckling load, it was stated that the load corresponding to a high increase of α 2 could be treated as the buckling load. ...
The presented results of the research aimed to experimentally investigate the influence of boundary conditions applied in the four-point bending test on the distortion buckling and lateral post-buckling behaviour of thin-walled C – section beams made of Glass Fibre Reinforced Polymer (GFRP). Two types of boundary conditions have been realised using specially designed grips (the newly developed and the old one – presented in earlier authors’ papers), allowing to perform a four-point bending test for channel section beams. Compared to the old one, the new grip enables the application of the load and support in the desired location on the beam and allows deflection between the support and load. The results of experimental investigations for beams under bending mounted in both grips have been compared. Eight-layer beams with three different layer arrangements were considered. The influence of laminate layup on post-buckling behaviour and failure load was also investigated. The tests have been performed using the INSTRON® universal testing machine, and the beam behaviour was tracked using the Digital Image Correlation (DIC) ARAMIS® system. The relations between boundary conditions on lateral deflection, buckling load, and postbuckling behaviour have been found and described.
... With steel C-section and top-hat columns subject to compression, a catastrophic unexpected influence of the sec-ondary global distortional mode on the load-carrying capacity of the structure was indicated as well [3]. In [9], attention was paid to an effect of the distribution of inner forces, in particular, the global distortional longitudinal force, on an interaction of buckling modes and the load-carrying capacity of composite structures under bending. An influence of the secondary global mode on the load-carrying capacity of C-section beams of medium length under bending, made of a step-variable gradient material, was analyzed as well [10]. ...
... However, it should be remembered that eigenvalues are determined with an accuracy up to a certain constant. In [9], the key role of inner longitudinal forces corresponding to global distortional modes and of local distortional buckling modes was pointed out. These modes rarely correspond to the lowest bifurcational values of thin-walled structures [3,[6][7][8][9][10][11]. ...
... In [9], the key role of inner longitudinal forces corresponding to global distortional modes and of local distortional buckling modes was pointed out. These modes rarely correspond to the lowest bifurcational values of thin-walled structures [3,[6][7][8][9][10][11]. An effect of distortional modes on post-buckling equilibrium paths and the load-carrying capacity of structures was also investigated in [12][13][14][15][16][17][18]. ...
The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.
... In the literature there are many papers which involve the analysis of the buckling and the post-buckling state of the thin-walled structures. Experimental and numerical studies on structures built of different material are widely described in papers [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Authors of these papers focused on the strength and the stability of structures. ...
The paper deals with an examination of the behaviour of glued Ti-Al column under compression at elevated temperature. The tests of compressed columns with initial load were performed at different temperatures to obtain their characteristics and the load-carrying capacity. The deformations of columns during tests were registered by employing non-contact Digital Image Correlation Aramis® System. The numerical computations based on finite element method by using two different discrete models were carried out to validate the empirical results. To solve the problems, true stress-logarithmic strain curves of one-directional tensile tests dependent on temperature both for considered metals and glue were implemented to software. Numerical estimations based on Green–Lagrange equations for large deflections and strains were conducted. The paper reveals the influence of temperature on the behaviour of compressed C-profile Ti-Al columns. It was verified how the load-carrying capacity of glued bi-metal column decreases with an increase in the temperature increment. The achieved maximum loads at temperature 200 °C dropped by 2.5 times related to maximum loads at ambient temperature.
... Theoretical approaches involving thermal buckling of functionally graded structures can be found in [24][25][26][27]. Among others, the failure of thin-walled plate structures relied upon theoretical and experimental approach was also analyzed in papers [28][29][30][31][32][33]. These works are strictly associated with phenomenon of stability occurring in thinwalled structures. ...
The paper deals with numerical and experimental investigations of the channel section column subjected to heating and compression at elevated temperature. The analyzed columns were made of titanium alloy (Grade 2) and simply supported on both ends. The research procedure involved initial compression of the column (i), heating the preloaded column (ii) and compression of the column at elevated temperature to failure (iii). The tests were performed at temperatures from 23 °C to 300 °C. Numerical calculations were carried out in the Ansys® software and involved the application of bilinear and multilinear isotropic hardening. It has been revealed that the temperature increase in a statically indeterminate system causes a decrease in the load-carrying capacity of the profile. An increase in temperature by 27 °C causes a reduction of the load-carrying capacity by 10%, while compression at temperature 300 °C reduces the nominal load-carrying capacity of the profile by half. Most of the proposed numerical procedures allowed for accurate estimation of reaction forces during heating and maximum compressive forces recorded during compression at elevated temperatures. The correctness of the determined material characteristics and the suitability of shell models for estimation of the response of a thin-walled structure subjected to thermomechanical loading was confirmed.
... There are many papers based on theoretical approach of thermal analysis on structures whose accomplishments are included in [23][24][25][26][27][28][29]. Theoretical or/and experimental studies involving the pre-and post-buckling state of thin-walled structures were widely discussed in [30][31][32][33][34][35][36][37][38][39]. These works concern mainly the structures built of plane plates where the phenomenon of stability was under investigation. ...
The analysis of structures under higher temperature is important for predicting the ultimate strength of a structure. Therefore, many experimental tests on samples should be undertaken to observe their behaviour and to determine ultimate load. The present work includes the study on a thin-walled C-column made of titanium compressed in an elevated temperature. The phenomenon of buckling and the post-buckling state of columns were investigated during heating or compressing in higher temperature. The tests of compression were conducted for several temperature increments by assuming the same preload to determine the load-carrying capacity. The deformations of columns until total damage were measured by using the non-contact Digital Image Correlation Aramis® System (DICAS). The numerical calculations based on the finite element method (FEM) were performed to validate the empirical results. The full characteristics of one-directional tension tests were taken into account in order for them to be constant or dependent on the temperature change. Numerical computations were conducted by employing Green-Lagrange equations for large deflections and strains. Based on our own experiment, the thermal property of titanium as a linear expansion coefficient was stable up to 300 °C in contrast to its mechanical properties. The paper shows the influence of varying material properties as a function of temperature on the behaviour and load-carrying capacity of columns. These aspects cause thin-walled columns made of titanium to endure, in elevated temperatures, significantly smaller maximum loads. Moreover, the critical buckling loads for several types of stiff supports were compared to the maximum loads of columns. The results obtained indicate that the temperature rise in columns by 175 K with regard to ambient temperature brings about the decrease of the maximum load by a half.
