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In this paper, the mechanical buckling load on a simply supported plate made of Functionally Graded Materials (FGM) with linearly varying thickness is considered. The material properties are assumed to vary as a power law though the plate thickness. Based on higher–order theory assumptions, the equilibrium, stability equations and the relations for pre-buckling loads of the plate under mechanical load are obtained by using a variational formulation. The equations are based on Love-Kirchhoff hypothesis and the Sanders non-liner strain-displacement relations. The closed form solution for the buckling load is obtained and the result is verified against known case i.e. a plate with constant thickness. The buckling load is derived by employing the weighted residual approach. Finally, different plots indicating the variation of buckling load vs. different FGM materials, geometries and loading conditions were obtained.

A method named interval analysis method, which solves the buckling load of composite laminate with uncertainties, is presented. Based on interval mathematics and Taylor series expansion, the interval analysis method is used to deal with uncertainties. Not necessarily knowing the probabilistic statistics characteristics of the uncertain variables, only little information on physical properties of material is needed in the interval analysis method, that is, the upper bound and lower bound of the uncertain variable. So the interval of response of the structure can be gotten through less computational efforts. The interval analysis method is efficient under the condition that probability approach cannot work well because of small samples and deficient statistics characteristics. For buckling load of a special cross-ply laminates and antisymmetric angle-ply laminates with all edges simply supported, calculations and comparisons between interval analysis method and probability method are performed.

An experimental study was performed to obtain the data about the buckling strength of the columns using structural steel(SN490B) at high temperature. Two kinds of experiments under the centrally compressive load with rectangular cross-sections of thickness 10mm X width 26mm, (1)tests at constant high temperature, and (2), tests at increasingly higher temperature under a constant axial load. By the tests(1), the buckling loads of column models which were enforced axial edge compression at a constant-high temperature were examined. And, by the tests(2), the collapse temperatures of the column models at increasingly higher temperature under a constant load were examined. The results of these tests were compared on a chart of buckling curves, and the effect of creep strain on the buckling strength of the column models was investigated. Furthermore, numerical simulations of the tests were performed. And the results of the calculations clearly show that numerical analysis can be used to provide accurate predictions of the buckling characteristics of columns at high temperatures, when an appropriate mechanical model and data of steel materials at high temperature are used. Comparing the results of tests and analyses, the effects of creep strain (time effect) on the buckling characteristics of steel columns at high temperature are shown.

This paper progresses the implementation of a simplified computational model for predicting buckling load Pcr for slender beam ‒ type structures with transverse cracks. The work presents an upgrade of the finite element model that has already successfully proved itself as being capable of producing applicable results by exhibiting considerably good agreement with those values from more precise and complex computational models. The major handicap of the previously applied finite element was the absence of a clear analytical form as it was presented (due to its complex form) only by the main steps of the numerical procedure. For that reason, the main advance of the presented finite element lies in its clear analytical form. In order to achieve this improvement the location of the crack was limited to the mid ‒ span position. Although both (old and new) cracked beam ‒ column finite elements are derived at on the basis of a fairly accurate approximation of the governing differential equation’s solution (GDE), the novel finite element even produces slightly better results. It further allows for flexible utilization and also yields a small compact computational model, thus exhibiting itself as very suitable for inverse identification problems. Numerical examples covering several structures with different boundary conditions are briefly presented in order to confirm the competence of the newly derived finite element. The results obtained using the presented finite element are further compared with corresponding values from references thus clearly proving the quality of the newly derived finite element., Ovaj rad poboljšava uporabu pojednostavljenog komputacijskog modela u predviđanju sile izvijanja Pcr-za vitke konstrukcije grednog tipa s poprečnom pukotinom. Rad predstavlja nadogradnju modela konačnog elementa za koji je već uspješno dokazano da daje primjenjive rezultate pokazujući dobro slaganje s vrijednostima dobivenih preciznijim i složenijim komputacijskim modelima. Glavni nedostatak prethodno primijenjenog konačnog elementa je nepostojanje jasnog analitičkog oblika, jer je (zbog složenosti) predstavljen samo po glavnim koracima numeričkog postupka. Iz tog razloga, glavna prednost predstavljenog konačnog elementa leži u jasnom analitičkom obliku. Da bi se postiglo to poboljšanje mjesto pukotine je ograničeno na sredinu elementa. Iako su oba konačna elementa (stari i novi) za napuknuti stup izvedena na osnovi prilično točne aproksimacije rješenja diferencijalne jednadžbe za poprečne pomake, novi daje i nešto bolje rezultate. To dodatno omogućuje fleksibilnu uporabu i daje mali kompaktni komputacijski model, zbog čega je vrlo pogodan za probleme inverzne identifikacije. Numerički primjeri koji obuhvaćaju nekoliko konstrukcija s različitim rubnim uvjetima ukratko su prikazani kako bi potvrdili učinkovitost novo izvedenog konačnog elementa. Ovaj rad poboljšava uporabu pojednostavljenog komputacijskog modela u predviđanju sile izvijanja Pcr-za vitke konstrukcije grednog tipa s poprečnom pukotinom. Rad predstavlja nadogradnju modela konačnog elementa za koji je već uspješno dokazano da daje primjenjive rezultate pokazujući dobro slaganje s vrijednostima dobivenih preciznijim i složenijim komputacijskim modelima. Glavni nedostatak prethodno primijenjenog konačnog elementa je nepostojanje jasnog analitičkog oblika, jer je (zbog složenosti) predstavljen samo po glavnim koracima numeričkog postupka. Iz tog razloga, glavna prednost predstavljenog konačnog elementa leži u jasnom analitičkom obliku. Da bi se postiglo to poboljšanje mjesto pukotine je ograničeno na sredinu elementa. Iako su oba konačna elementa (stari i novi) za napuknuti stup izvedena na osnovi prilično točne aproksimacije rješenja diferencijalne jednadžbe za poprečne pomake, novi daje i nešto bolje rezultate. To dodatno omogućuje fleksibilnu uporabu i daje mali kompaktni komputacijski model, zbog čega je vrlo pogodan za probleme inverzne identifikacije. Numerički primjeri koji obuhvaćaju nekoliko konstrukcija s različitim rubnim uvjetima ukratko su prikazani kako bi potvrdili učinkovitost novo izvedenog konačnog elementa. Dobiveni rezultati dalje se uspoređuju s odgovarajućim vrijednostima iz literature čime se jasno dokazuje postignuta kvaliteta.

Since mid 30s (Theory of Elastic Stability, Timoshenko, 1936) up to now, buckling of plates subjected to in plane combined loadings has been a matter of concern for many investigators in structural engineering. When buckling occurs, there is a sudden change in deformation state, which occurs at the critical load. Being able to determine the critical stress for a given loading condition is of remarkable importance in aeronautical industry. There are some areas at which it is of paramount importance to know under which load the structure buckles, to design it appropriately. In some other areas, like the skins of aerodynamic surfaces, buckling needs to be avoided so as not to change the geometry of the aerodynamic surface. This phenomena occurs, among other structures, in plates, such as fuselage or wing skin panels. Those panels or sheets in the wing, fuselage or other parts are subjected to combination of complex loadings. For instance, the upper surface of an aircraft wing in flight may be subjected to combined shear and compressive stress. Wing panels are delimited by spanwise stiffeners and chordwise ribs. Note that the panels in the wing are not flat but slightly curved. The buckling load of those panels can be computed assuming they are flat, because it is a conservative estimate (curved panels have greater buckling loads). To solve flat plates buckling problems for different loadings and boundary conditions, currently two different methods are used; the analytical method and the Finite Element Method. This work will compare the flat plates combined loadings buckling results obtained analytically with those obtained from Finite Element Method. Ingeniería Aeroespacial

© 2015, Allerton Press, Inc. A new approach to solving the task of stability for a circular cylindrical shell under axial compression is presented, taking into account the dynamic buckling. The modification of the algorithm for solving the known problem by the Ritz method is also proposed that allows investigating the effect of geometrical factors on the buckling load.

An experimental study was performed to obtain the data about the buckling strength of the columns using fire resistant steel (NSFR490A) at high temperature. Two kinds of experiments under the centrally compressive load with rectangular cross-sections of thickness 10mm×width 26mm, (1) tests at constant high temperature, and (2). tests at increasingly higher temperature under a constant axial load. By the tests (1), the buckling loads of column models which were enforced axial edge compression at a constant high temperature were examined. And, by the tests (2), the collapse temperatures of the column models at increasingly higher temperature under a constant load were examlned. The results of these tests were compared on a chart of buckling curves, and it is observed that the influence of the strain rate and P-Delta effect caused by creep strain on the buckling strength of the column models was very small. Furthermore, in order to explain this result, numerical analyses were carried out.

The present study focuses on the determination of the buckling load and post-buckling behaviour of simply supported laminated composite rectangular panels loaded in shear. The nonlinear structural response is studied with a non-linear finite element approach. In order to determine the accuracy of the procedure, several tests have been performed comparing the finite element solutions for isotropic and laminated composite rectangular panels with existing ones, adopting different sequences of lamination and different length to width ratios. The analysis then considers the behaviour of laminates produced with innovative thermoplastic matrix composites developed in the frame of a national research program.

An experimental study was performed to obtain the data about the buckling strength of the column models using new metallic structural material (SA440B) at high temperature. Two kinds of experiments under the centrally compressive load with rectangular cross-sections of thickness lOmm X width 26mm, (1)tests at constant high temperature, and (2), tests at increasingly higher temperature under a constant axial load. By the tests (1), the buckling loads of column models which were enforced axial edge compression at a constant high temperature were examined. And, by the tests (2), the collapse temperatures of the column models at increasingly higher temperature under a constant load were examined. The results of these tests were compared on a chart of buckling curves, and it is observed that the buckling load of the tests(2) was larger than the tests(1) in the region of small slenderness ratio, and the result was reverse in the region of large slenderness ratio. Furthermore, in order to explain this result, numerical analyses were carried out, and the influence of the strain rate and P-Delta effect on the buckling strength of the column models under the elastic-plastic-creep behavior were confirmed.

An experimental study was performed to predict the effects of high temperature and creep strain on the buckling strength of steel columns at high temperature. In order to satisfy the purpose of this study, two kinds of experiments, (1)tests at constant high temperature and (2)tests at increasing high temperature under constant axial load were performed using the steel columns (SM490 J1S grade) with rectangular cross-section. In the tests at constant high temperature, the buckling strength at constant high temperature of SM490 steel column was clarified. The experimental result at constant high temperature and the computed result based on the nonlinear buckling theory showed good agreement. The results of two kinds of buckling tests were compared on a chart of buckling curves mutually, and the effect of creep strain on the buckling strength of steel column at increasing high temperature was evaluated.

A seismic isolation pad produced by utilizing the scrap tire rubber which contains interleaved steel reinforcing cords has been proposed. The steel cords are expected to function similar to the steel plates used in conventional laminated rubber bearings. The scrap tire rubber pad (STRP) isolator is intended to be used in low rise residential buildings of highly seismic areas of the developing countries. Experimental investigation was conducted on unbonded STRP isolators, and test results provided useful information including stiffness, damping values and an eventual instability of the isolation unit. Finite element analysis (FE analysis) of STRP isolator was carried out on properly bonded samples. These types of isolators provide positive incremental force resisting capacity up to shear strain level of 155%. This paper briefly discusses the force deformation behavior of bonded STRP isolators including stability of the isolation unit., {"references":["James M. Kelly, Dimitrios Konstantinidis. Low-cost seismic isolators for\nhousing in highly-seismic developing countries. 10th World Conference\non Seismic Isolation, Energy Dissipation and Active Vibrations Control\nof Structures, Istanbul, Turkey, May 28-31, 2007","James M. Kelly. Seismic isolation system for developing countries,\nEarthquake Spectra, 2002, Vol. 18, issue 3:385-406.","Hamid Toopchi-Nezhad, Michael J. Tait, Robert G. Drysdale. Testing\nand modeling of square carbon fiber-reinforced elastomeric seismic\nisolators. Structural Control and Health Monitoring, 2008, 15: 876-900.","Ahmet Turer and Bayezid Ozden. Seismic base isolation using low-cost\nScrap Tire Pads (STP). Material and Structures, Vol. 41, 2008, 891-908.","Hamid Toopchi-Nezhad, Michael J. Tait, Robert G. Drysdale. Bonded\nversus unbonded strip fiber reinforced elastomeric isolators: Finite\nelement analysis. Composite Structures, 93(2011):850-859.","Y.J. Arditzoglou, J. A. Yura and A. H. Haines. Test methods for\nelastomeric bearing on bridges. Research Report 1304-2, Texas\nDepartment of Transportation","H. Holcher, M. Tewes, N. Botkin, M. Lohndorf, K. H. Hoffmann, E.\nQuandt. Modeling of pneumatic tires by a finite element model for the\ndevelopment of a tire friction remote sensor. Center of Advanced\nEuropean studies and Research (Caesar), (2004), 40.","Jong She Lee and Long Won Oh. Stability of rubber bearings for seismic\nisolation. Transactions of the 15th International Conference on Structural\nMechanics in reactor technology, Seol, Korea, August 15-20, 1999.","Gabriela Ferraro, Giuseppe Oliveto and Nicholas D. Oliveto. On the\nstability of elastomeric bearings. Department of Civil and Environmental\nEngineering, University of Catania, Italy.\n[10] Ian Buckle, Sathish Nagarajaiah and Keith Ferrell. Stability of\nelastomeric isolation bearings: Experimental Study. Journal of Structural\nEngineering, vol. 128, No. 1, January 2002.\n[11] R. Lo Frano and G. Forasassi. Evaluation of instability of Laminated\nRubber Bearings under dynamic loading. Proceeding of ICAPP -10-, San\nDiego, USA, 2010.\n[12] Farzad Naeim, James M. Kelly. Design of seismic isolated structures\nfrom theory to practice. John Willey and sons, Inc. 1999, chapter 6.\n[13] ASCE-7. Minimum design loads for building and other structures,\nASCE/SEI 7-05. New York, American Society of Civil Engineers, 2005.\n[14] MSC Software (2010), MSC Marc 2010 and MSC Marc Mentat 2010,\nSanta Ana, California\n[15] Eurocode 8. Design of structures for earthquake resistance. 2004"]}

The exact closed-form solution for the vibration modes and the eigen-value equation of the Euler–Bernoulli beam-column in the presence of an arbitrary number of concentrated open cracks is proposed. The solution is provided explicitly as functions of four integration constants only, to be determined by the standard boundary conditions. The enforcement of the boundary conditions leads the exact evaluation of the vibration frequencies as well as the buckling load of the beam-column and the corresponding eigen-modes. Furthermore, the presented solution allows a comprehensive evaluation of the influence of the axial load on the modal parameters of the beam. The cracks, which are not subjected to the closing phenomenon, are modelled as a sequence of Dirac’s delta generalised functions in the flexural stiffness. The eigen-mode governing equation is formulated over the entire domain of the beam without enforcement of any further continuity condition. The influence of the axial load on the vibration modes of beam-columns with different number and position of cracks, under different boundary conditions, has been analysed by means of the proposed closed-form expressions. The presented parametric analysis highlights some abrupt changes of the eigen-modes and the corresponding frequencies.

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2010, Bu çalışmada, yaklaşık taşıma matrisi yöntemi ile çift duvarlı ve iki ucu basit mesnetli bir karbon nanotüpün burkulma yükü hesaplanmıştır. Öncelikle nanoteknoloji ve karbon nanotüpler hakkında bilgiler verilmiştir. Stabilite ve burkulma problemi açıklanmış ve ele alınacak problemler tanıtılmıştır. Problem çözümlerinde kullanılan yöntemlerden biri olan başlangıç değerler metodu açıklanmış ve yöntemin işleyişi gösterilmiştir. Kesin taşıma matrisi ve yaklaşık taşıma matrisi ile burkulma problemlerinin çözümü ele alınmıştır. Kesin taşıma matrisi ve yaklaşık taşıma matrisi ile dört farklı şekilde mesnetlenmiş sabit ve değişken kesitli çubuk elemanları için burkulma yükü hesaplanmıştır. Karşılaştırmalar yaparak yaklaşık taşıma matrisinin kullanışlılığı gösterilmiştir. İki ucu basit mesnetli, çift duvarlı bir karbon nanotüpün burkulma yükü hesaplanmıştır. Nanotüpler arası çekim kuvvetinin burkulma yüküne etki etmemektedir. Sonuç olarak, yaklaşık taşıma matrisi ile problem çözümünün mühendislik açısından yeterli yakınsaklığı sağladığı görülmüştür., In this study buckling load of a double walled and simply supported carbon nanotube is calculated with approximate transfer matrix method. Primarily, informations about nanotechnology and carbon nanotubes are given. Stability and buckling problem are explained and the problems, which will be discussed, are introduced. As a procedure used during the problem solution, initial values method is explained and the process of the method is shown. Buckling problem solutions with the principal matrix and the approximate transfer matrix are approached. Buckling loads for constant and inconstant sectioned frame elements, which are supported in four different forms, are calculated with the principal matrix method and approximate transfer matrix method. Usefulness of approximate transfer matrix method is shown with comparisons. Buckling load of a double walled and simply supported carbon nanotube is calculated. Gravitational force between the nanotubes does not affect the buckling load. As a result, problem solution with the approximate transfer matrix was in a good agreement., Yüksek Lisans, M.Sc.

Shear walls are used in most of the tall buildings for carrying the lateral load. When openings for doors or windows are necessary to be existed in the shear walls, a special type of the shear walls is used called "coupled shear walls" which in some cases is stiffened by specific beams and so, called "stiffened coupled shear walls". In this paper, a mathematical method for geometrically nonlinear analysis of the stiffened coupled shear walls has been presented. Then, a suitable formulation for determining the critical load of the stiffened coupled shear walls under gravity force has been proposed. The governing differential equations for equilibrium and deformation of the stiffened coupled shear walls have been obtained by setting up the equilibrium equations and the moment-curvature relationships for each wall. Because of the complexity of the differential equation, the energy method has been adopted for approximate solution of the equations., {"references":["A. Coul, L. Bensmil, \"Stiffened Coupled Shear Walls,\" Journal of\nStructural Engineering ASCE, vol. 117, no. 8, 1991, pp. 2205-2223.","H. C. Chan, J. S. Koung, \"Elastic Design charts for Stiffened Coupled\nShear Walls,\" Journal of Structural Engineering ASCE, vol. 115, no. 2,\n1989, pp. 247-267.","H. C. Chan, J. S. Koung, \"Stiffened Coupled Shear Walls,\" Journal of\nEngineering Mechanics ASCE, vol. 115, no. 4, 1989, pp. 689-703.","R. Rosman, \"Stability and Dynamics of shear-wall Frame Structures,\"\nBuilding Science, vol. 9, 1974, pp. 55-63.","E. Grzelak, \"The Approximate Free Vibration and Stability Analysis of\nShear- Flexure Cantilevers,\" M.Sc. Project report, Dept. Civ. Eng.,\nMcGill Univ., Montreal.","H. Khosravi, \"Geometrically Nonlinear Analysis of Stiffened Coupled\nShear Walls,\" M.Sc. thesis, Dept. Civ. Eng., Islamic Azad Univ.,\nKerman-Iran, 2005."]}

In the present paper the topological optimal design of isotropic/orthotropic thin structures performed via genetic algorithms is shown. Examples involving structural weight minimization under compressive load or buckling load maximization are presented. A modified finite strip method was developed and used to analyze parametric structures arranged in form of plates or stiffened panels with almost arbitrary cross-section shapes. Specific design variables were defined to assure a robust control over geometrical and topological features. In particular, a semi-analytical formulation for the determination of eigenvalues and eigenvectors was adopted in order to reduce computational efforts requested by the optimization task. A mesh-independent solver, involving a reduced number of degrees of freedom, was implemented and interfaced with a genetic optimizer for the purpose. The optimization procedure was based on a specific bit-masking oriented genetic algorithm, able to handle in parallel different genetic operators expressly conceived to process with proper metrics discrete and continuous design variables. As preliminary example, the buckling load maximization of a metallic plate with an arbitrary grid-shaped cross-section is described first. Then a topological optimization concerning the weight minimization of a composite stiffened panel subject to constraint about buckling load is illustrated and discussed in detail about parametric model definition and genetic procedure.

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2002, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2002, Bu çalışmada, öncelikle P-delta kavramının anlaşılmasına yönelik geometrik rijitlik, burkulma yükü gibi kavramlar açıklanmıştır. Daha sonra P-delta etkilerinin yapı analizinde hesaba nasıl dahil edileceği konusunda büyütme katsayısı yöntemi, iteratif yöntem, iteratif ağırlık yükü yöntemi, direkt yöntem ve negatif rijitlikli fiktif eleman yöntemi gibi hesap yöntemleri açıklanmıştır. Bu yöntemler genelde iteratif hesaba dayanmakta, bu iteratif hesap da uzun ve zaman alıcı olduğu için pek tercih edilmemekle birlikte, negatif rijitlikli fiktif eleman yöntemi problemi lineerleştirerek çözümde kolaylık sağlar. Bunun yanında asimetrik yapılardaki p-delta etkilerinin hesabı anlatılmıştır. Ayrıca bu çalışmada P-delta etkilerinin deprem ve tasarım yönetmelikleri çerçevesinde nasıl göz önünde bulundurulduğu hususu üzerinde durulmuştur. Son olarak da 22 katlı bir yapı p-deltalı ve p-deltasız yöntemle çözülüp sonuçlar karşılaştırılmıştır., In this study, firstly, some notion like that geometrical stiffness and buckling load were explained to understand P-Delta concept. After that some method about how P-delta effects include construction analyse were explained such as amplification factor method, iterative method, iterative gravity load method, direct method, negative property fictitious member method. Usually, these methods are based on iterative calculation . Since, these methods are large and time consuming, it is not preferred. But as a ease of use, We can use negative property fictitious member method to lineerize this problem. Beside, P-Delta analyse on assymetric structures were explained. Additionally, in this study, how P-Delta effects considered in the seismic codes were explained. Finally, 22 stories building were analysed either with P-delta effects or without P-Delta effects and compared results., Yüksek Lisans, M.Sc.

The bending of the shock-absorber rod calls for a second order analysis as it is a rather slender bar subjected to a considerable axial compressive load. The second order deflection analysis of the according mechanical model produces the theoretical moment amplification factor. The expression for the design moment amplification factor expressed by the theoretical buckling load is established. The diagrams of the buckling load are plotted.

This work addresses an accurate and detailed axial static load dependence linearly elastic free vibration analysis of cylindrical helical springs based on the theory of spatially curved bars and the transfer matrix method. For a continuous system, governing equations comprise coupled vibration modes namely transverse vibrations in two orthogonal planes, torsional and axial vibrations. The axial and shear deformation effects together with the rotatory inertia effects are all considered based on the first order shear deformation theory and their effects on the frequencies are investigated. The effects of the initial stress resultants on the frequencies are also studied. After buckling, forward-shifting phenomenon of higher frequencies is noticeably demonstrated. It is also revealed that a free/forced vibration analysis with an axial static load should not be performed individually without checking buckling loads. © 2016 Brazilian Association of Computational Mechanics. All rights reserved.