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1

Influence of Size of Open Hole on Stability of Compressed Plate Made of Carbon Fiber Reinforced Polymer

Wysmulski Paweł, Mieczkowski Grzegorz

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no 2

238--247

EN

This manuscript concerns the investigation of the influence of the open hole on stability of the compression plate made of carbon-epoxy composite. Experimental tests carried out on the real plate resulted in a postcritical path from which the critical load value was determined using appropriate approximation method. In parallel, an independent study was carried out based on a numerical analysis using the finite element method (FEM). Investigations were conducted in terms of a linear eigenproblem analysis, from which the value of the bifurcation load was determined for the FEM model of the plate. Its values resulting from the numerical analyses were validated against the experimental results, thus confirming the adequacy of the designed FEM model of the plate. The paper shows that the incremental increase of the hole in the plate monotonically influences the decrease in the critical load of the plate. The largest decrease was observed for the specimen with the largest hole analysed and was 13.5% compared to a plate without a hole. The newness of the paper is the application of interdisciplinary investigation methods to describe the influence of the open hole compression (OHC) on the stability of composite plates. ABAQUS® was used as the tool with which the numerical analyses were realised.

2

Niejednoznaczność określania długości wyboczeniowych słupów stalowych ram portalowych

Studziński Robert, Ordziniak Paweł

Inżynieria i Budownictwo

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2023

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R. 79, nr 3-4

191--196

PL

W artykule omówiono różne sposoby wyznaczania długości wyboczeniowej słupów stalowych ram portalowych. Rozważania ograniczono do wyboczenia ramy w płaszczyźnie, w której jest ona układem przechyłowym. Przedstawiono i porównano ze sobą łącznie trzy sposoby określania długości wyboczeniowej. Na koniec przeprowadzono uproszczoną ocenę wpływu wielkości długości wyboczeniowej na poziom wytężenia słupa ramy portalowej.

EN

The article discusses various ways of determining the column buckling length of steel portal frames. Considerations were limited to in-plane buckling of the frame in which the frame is characterized as a sway. A total of three methods of determining the buckling length are presented and compared. Finally, a simplified evaluation of the effect of buckling length on the utilization ratio of the column was carried out.

3

Analytical investigation of a beam on elastic foundation with nonsymmetrical properties

Wstawska Iwona, Magnucki Krzysztof, Kędzia Piotr

Engineering Transactions

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2022

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Vol. 70, iss. 1

77--93

EN

The subject of presented analytical and numerical investigation is the stability of an axially compressed beam on an elastic foundation. The shape function of the foundation was assumed. The formula was supplemented with the offset parameter. The critical values of loads were calculated and presented as a function of geometric and mechanical properties of the beam and nonsymmetrical properties of the elastic foundation. The highest values of critical loads can be obtained for the highest values of shape parameter and the lowest values of amplitudes of shape function. The values of critical loads increase with the increase of the value of the offset parameter.

4

The Influence of Composite Lay-Up on the Stability of a Structure with Closed Section

Różyło Patryk, Dębski Hubert

Advances in Science and Technology. Research Journal

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2022

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Vol. 16, no 1

260--265

EN

This paper presents a study on the stability of a composite structure with a closed section. The research was carried out solely based on numerical simulations using the finite element method. ABAQUS software was used to conduct numerical simulations, which allowed to determine the values of critical loads, as well as the corresponding forms of buckling. As part of the research, the influence of composite material arrangement of layers on the stability of the structure was analyzed. The study was conducted on a composite material, which is a carbon-epoxy composite (CFRP). The obtained research results will be verified in subsequent studies by the results of experimental tests.

5

The Influence of Composite Lay-Up and the Shape of the Closed Section on the Stability of the Structure

Czajka Błażej, Różyło Patryk

Advances in Science and Technology. Research Journal

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2022

|

Vol. 16, no 2

216--224

EN

Stability tests of a thin-walled composite structure with a closed section are presented in this paper. The purpose of this paper is to conduct preliminary studies in the context of numerical simulations of critical and slightly post-buckling states. The tests were conducted based only on numerical simulations by the finite element method. Numerical simulations were conducted using ABAQUS software, which allowed to determine the values of critical loads and their corresponding buckling forms. The influence of layer arrangement on the stability of the structure was studied. Carbon-epoxy laminate (CEL) was used in the tests. It is shown that there are composite lay-ups that show more than 1.3 times higher stiffness than the other cases. The paper demonstrates the dependence of the influence of the arrangement of layers on the stability of the structure, which will provide the basis for planned experimental studies (the results require experimental verification, which will be carried out in subsequent studies).

6

Obciążenie krytyczne niestężonych ram stalowych

Krystosik Przemysław

Inżynieria i Budownictwo

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2021

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R. 77, nr 5-6

232--234

PL

Omówiono zagadnienia dotyczące stateczności ram stalowych, ze szczególnym zwróceniem uwagi na problem określania obciążenia krytycznego w tych ramach. Przedstawiono propozycję algorytmu wyznaczania obciążenia krytycznego. Zamieszczono przykłady liczbowe.

EN

The paper presents the stability issue of unbraced steel frames with special attention paid to the problem of determining the value of critical load in these frames. In the paper was presented an algorithm of the critical load determination, and then it was used to calculate of certain steel frames.

7

Geometric Characteristic of a Sewing Needle Applied in Clothing Manufacture Technology with Reference to Elastic Critical Statically Balance Loads – A Comparative Study

Hashima Wael A.

Fibres & Textiles in Eastern Europe

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2021

|

Vol. 29, no. 3 (147)

86--90

EN

In this work a sewing needle of an industrial commercial sewing machine is investigated from the different points of view of geometrical and critical elastic statistical balance. The dimensions of the sewing needle are l = 60 mm, and ϕ = 2.5 mm and 1.45 mm diameter for the two stepped needle. The needle is treated as a fixed – free end column, with two sections: Ι0 (Ι1) = 1.9615 (Ε – 12) m4 and (Ι2) = 2.0516 (Ε – 13) m4. The upper partial lenght a = 31.2 mm, while the lower partial lenght b = 28.2 mm. The value of the critical load is 110 N, while the Euler load Ρ e = 1112 N, then γ = 3.1796. Another approach was used for a line diagram of the truncated cone of the sewing needle, where the critical load Ρ cr = 57 N, the Euler load Ρ e = 118 N, and γ = 3.13. For the line diagram of a sewing needle with a constant cross-section ϕ = 1.965 mm, l = 7.3185 (Ε – 13) m4, (formula) & η = 2.467. Then Ρ cr = 103 N, Ρ e = 413 N & (formula). For a sewing needle a constant cross-section and the penetration load is uniformly distributed, the geometric characterictic is found to be ῆ = 7.839, γ = 1.22, Ρ cr = Ρ cr(ql)cr = 328 N & q = 5472 N/m (≈6 N/mm). The present work aims to open as yet untouched areas for more and intensive academic and experimental studies, in the field of how penetration forces affect critical loads. The work is the first step in the evaluation of the mechanics of the industrial sewing needle.

PL

W pracy badano igłę do szycia stosowaną w przemysłowej maszynie do szycia. Do badań użyto dwustopniowej igły do szycia o wymiarach: dł. = 60 mm, ϕ = 2.5 mm i średnicy 1.45 mm. Igłę potraktowano jako kolumnę z nieruchomym i wolnym końcem, z dwiema sekcjami: Ι0 (Ι1) = 1.9615 (E – 12) m4 oraz (I2) = 2.0516 (E – 13) m4. Górna długość częściowa wynosiła: a = 31.2 mm, podczas gdy dolna długość częściowa to: b = 28.2 mm. Celem pracy było otwarcie jeszcze nietkniętych obszarów dla bardziej intensywnych badań akademickich i eksperymentalnych w zakresie wpływu sił penetracji na obciążenia krytyczne.

8

Reliability and failure studies of firefighters' helmets in simulated operational conditions

Walczak Agata, Pieniak Daniel, Kamocka-Bronisz Renata

Journal of KONBiN

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2020

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Vol. 50, iss. 4

31--40

EN

The aim of the study was to determinate the fracture mechanism of firefighters' helmets caused by the impact load in simulated operational conditions. Moreover the aim of the study was to assess the reliability of the personal protective equipment. Tests were conducted with the use of the drop tower system. On each type of helmet 5 impact tests were performed. The active force corresponding to impact energy of 60 J and the passive force (force in the place of the neck spine) was registered. Based on the results, it can be statement that helmets' structure influences their reliability and values of the active and passive forces. Additionally, the majority of tested helmets exceeded the acceptable threshold values of passive force.

PL

Celem badań było określenie mechanizmu niszczenia hełmów strażackich spowodowanego obciążeniem udarowym w symulowanych warunkach narażeni operacyjnych, a także ocena niezawodności sprzętu ochrony indywidualnej. Testy przeprowadzono z wykorzystaniem młota udarowego opadowego. Na każdym typie hełmu przeprowadzono po 5 testów udarowych. Rejestrowano siłę czynną odpowiadająca energii uderzenia 60 J oraz siłę bierną (siłę w miejscu kręgosłupa szyjnego). Na podstawie wyników można stwierdzić, że konstrukcja hełmów i ich stan wpływają na ich niezawodność i wartości sił czynnych i biernych. W przypadku większości badanych hełmów przekroczono dopuszczalne wartości progowe sił biernych.

9

Analytical and numerical studies of an unsymmetrical sandwich beam – bending, buckling and free vibration

Magnucki Krzysztof, Magnucka-Blandzi Ewa, Lewiński Jerzy, Milecki Szymon

Engineering Transactions

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2019

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Vol. 67, iss. 4

491--512

EN

The subject of the paper is an unsymmetrical sandwich beam. The thicknesses and mechanical properties of the beam faces are different. Mathematical model of the beam is formulated based on the classical broken-line hypothesis. The equations of motions of the beam is derived on the ground of the Hamilton’s principle. Bending, buckling and free-vibration are studied in detail for exemplary unsymmetrical structure of the beam. The values of deflection, critical force and natural frequency are determined for the selected beam cases. Moreover, the same examples are computed with the use of two FEM systems, i.e. SolidWorks and ABAQUS, in order to compare the analytical and numerical calculation. The results are presented in tables and figures.

10

Ocena stateczności konstrukcji ram stalowych według Eurokodu 3

Pogonowska-Płatek Sylwia, Dornowski Wojciech

Biuletyn Wojskowej Akademii Technicznej

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2019

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Vol. 68, nr 2

145--163

PL

Praca zawiera jakościowe i ilościowe porównanie proponowanych w EC3 metod oceny stateczności konstrukcji ram. Podstawę stanowi stalowa rama portalowa poddana zróżnicowanemu obciążeniu. Uwzględniono imperfekcję globalną (przechyłową) oraz imperfekcje lokalne w słupach ramy. Przeprowadzono ocenę wrażliwości konstrukcji na efekty II rzędu. Obciążenie krytyczne ramy wyznaczono dla symetrycznej i antysymetrycznej postaci wyboczenia. Efekty II rzędu uwzględniono, wykorzystując metodę elementów skończonych.

EN

In the paper, the qualitative and quantitative comparison of EC3 methods to verify the global stability of the structure is presented. The steel portal frame subjected to varied loads is considered. The initial global sway imperfection and the initial local bow imperfections of member frame are taken into account. The sensitivity of a structure to the 2nd order effects is assessed indirectly using the elastic critical load. The elastic critical load of a frame is calculated according to the buckling mode. The 2nd order effects are taken into account using the finite element method.

11

Application of an interface damage model to steel reinforced concrete: a study of the size effect

Vodička R., Krajníková K., Baranová L.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2018

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z. 65, nr 4

103--112

EN

Influence of the size of steel reinforcement of a concrete structure on crack initiation at the interface between the steel fibre and the concrete body of the structure is under consideration. Numerical analysis is provided using a quasistatic delamination model for interface rupture based on an energetic approach using a cohesive zone model for providing the interface stress-strain relation. The obtained results confirm expected dependence of the critical load which causes triggering of the interface crack on a structure dimension parameter.

12

Wpływ właściwości mechanicznych okładzin i rdzenia na stateczność belek trójwarstwowych poddanych zginaniu trójpunktowemu

Wstawska I.

Technical Issues

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2017

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nr 2

42--47

EN

The objective of this work is the numerical analysis of the stability of three-layered beams with a metal foam core. The beams were subjected to three-point bending. The analysis of the local buckling and the influence of material properties of the faces and the core on critical loads and buckling shape was performed. The calculations were made in elastic range on a family of beams with different mechanical properties of the faces and the core. Calculations of critical loads and buckling shape were performed. The analysis of the finite element model (FEM) of three-layered beam has been performed with the use of ANSYS software. The upper and the lower face have been retreated from the core by half of the thickness. Tie constrains have been applied between the core and the faces. Due to symmetry of the model only a quarter of the beam has been modelled with proper boundary conditions on the symmetry planes.

13

Elastic buckling of a rhombic frame under in-plane load

Magnucki K., Kędzia P., Grygorowicz M., Lewiński J.

Modelowanie Inżynierskie

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2017

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T. 33, nr 64

53--60

EN

The paper is devoted to elastic buckling of symmetrical rhombic frame with cross-member under tensile in-plane load. Mathematical models of the frame for pre-buckling, in-plane buckling and lateral buckling states are formulated. The frame consists of four arms and one cross beam. Each arm is of the same rectangular cross section. Cross section of thin-walled rectangular pipe is for cross member. Load acts in joint of pair of arms. Analytical critical loads are calculated for these models. Numerical models in ANSYS and SolidWorks FEM systems are formulated. Numerical critical loads are calculated in FEM systems. The comparison of analytical and numerical results is presented in Tables and in Figures.

PL

Praca poświęcona jest wyboczeniu symetrycznej ramy rombowej z belką poprzeczną. Rama poddana jest obciążeniu rozciągającemu w jej płaszczyźnie. W pracy zostały sformułowane matematyczne modele wyboczenia ramy w dwóch prostopadłych płaszczyznach. Rama zbudowana jest z czterech ramion oraz poprzecznej belki. Każde z ramion ma przekrój prostokątny, podczas gdy belka poprzeczna ma kształt rury profilowanej prostokątnej. Obciążenie przyłożone jest w miejscu połączenia każdej pary ramion. W pracy wyznaczono analitycznie obciążenie krytyczne dla zdefiniowanych modeli. Zdefiniowano również numeryczny model ramy w systemach ANSYS i SOLIDWORKS Simulation w celu porównania wyników otrzymanych metodą elementów skończonych z rozwiązaniami analitycznymi. Wyniki zostały przedstawione w tabelach i na rysunkach.

14

Bending and buckling of a metal seven-layer beam with a lengthwise corrugated main core – comparative analysis with the sandwich beam

Magnucka-Blandzi E., Rodak M.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 1

41--53

EN

The subject of analytical investigations is a metal seven-layer beam, a plate band with a lengthwise trapezoidal corrugated main core and two crosswise trapezoidal corrugated cores of faces. The hypothesis of deformation of normal to the middle surface of the beam after bending is formulated. Equations of equilibrium are derived based on the theorem of mini- mum total potential energy. The equations are analytically solved. Three point bending and buckling for axially compression of the simply supported beam are theoretically studied. The deflection and the critical axial force are determined for different values of the trapezoidal corrugation pitch of the main core. Moreover, an adequate model of the sandwich beam with steel foam core is formulated. The deflection and the critical axial force are determined for this sandwich beam. The results studied of the seven layer beam and the adequate sandwich beam are compared and presented in tables and figures.

15

Statistical analysis of mechanical damage in nanopillar arrays with mixed-mode load transfer

Derda T.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 3

5--16

EN

In the framework of the Fibre Bundle Model we explore the effect of mixed-mode load transfer in two-dimensional arrays of nanopillars. The mixed-mode load redistribution scheme serves as an interpolation between limiting cases, namely global and local transfer. Two types of loading processes are employed i.e. quasi-static and sudden loading. By varying the weight parameter, we identify two behaviours: the GLS and LLS regime. As a regime indicator we use distribution of critical loads and function fitting probability of system breakdown.

16

Ocena wyboczenia pasów dolnych z płaszczyzny kratownic usztywnionych obudową dachową

Biegus A.

Inżynieria i Budownictwo

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2017

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R. 73, nr 6

293--298

PL

Przedstawiono modele i zasady oceny wyboczenia pasów dolnych z płaszczyzny kratownic, które umożliwiają zrezygnowanie ze stężeń prętowych. Uwzględniono w nich sztywność giętną płatwi lub blachy trapezowej (obudowy dachu), ich połączenia z pasem górnym oraz prętów wykratowania kratownicy, które ograniczają przemieszczenia boczne pasa dolnego kratownicy. Podano sposób oceny sztywności giętnych obudowy dachu i jej połączenia z pasem górnym kratownicy oraz ich prętów wykratowania o geometrii V, N i W. Przedstawiona ocena stateczności z płaszczyzny kratownicy dotyczy pasów dolnych jednogałęziowych i dwugałęziowych. Analizowane zagadnienie zilustrowano przykładem obliczeniowym.

EN

The paper introduces models and rules of valuation of the out-of-plane buckling of bottom chords in truss systems that enable resignations from the classic strut bracings. The procedure accounts for: the flexural stiffness of purlins or trapezoidal sheets (roof covering), the stiffness of connection to the upper truss chord, and the flexural stiffness of the truss web members of V, N, W geometry, as factors limiting the lateral displacements of the bottom truss chord. The presented method of evaluation of the out-of-plane buckling is related to the both single solid and doubled built-up bottom chords. The analyzed case has been illustrated by calculation example.

17

Analiza drgań poprzecznych smukłej kolumny o zmiennym przekroju poprzecznym przy obciążeniu uogólnionym z siłą skierowaną do bieguna dodatniego

Szmidla J., Jurczyńska A.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2017

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z. 64, nr 2/I

191--202

PL

W pracy zawarto wyniki rozważań teoretycznych oraz analizę numeryczną zagadnienia drgań swobodnych smukłego układu o zmiennym przekroju poprzecznym poddanego działaniu wybranego przypadku obciążenia swoistego. Analizowane obciążenie uogólnione z siłą skierowaną do bieguna dodatniego realizowane jest poprzez strukturę zbudowaną z głowic z zarysie kołowym: wywołującą i przejmującą obciążenie. W celu zamodelowania niepryzmatyczności kolumny, układ podzielono na n pryzmatycznych segmentów o równej długości i grubości oraz zmiennej szerokości opisanej za pomocą funkcji liniowej oraz wielomianu drugiego stopnia, przy zachowaniu warunku stałej objętości sumarycznej. W oparciu o model fizyczny układu zdefiniowano zależności określające energię mechaniczną struktury. Problem sformułowano na podstawie zasady Hamiltona (metoda drgań, kinetyczne kryterium utraty stateczności). Biorąc pod uwagę geometryczne warunki brzegowe oraz geometryczne warunki ciągłości wyznaczono różniczkowe równania ruchu poszczególnych segmentów kolumny oraz brakujące do opisu układu naturalne warunki brzegowe i naturalne warunki ciągłości. W oparciu o tak zdefiniowany model matematyczny opracowano autorskie algorytmy obliczeniowe umożliwiające badania numeryczne drgań poprzecznych układu. W ramach przeprowadzonych obliczeń określono zakres zmian częstości drgań własnych w funkcji obciążenia zewnętrznego. Dyskusji poddano wpływ zmiennych parametrów geometrycznych kolumny na wartość częstości drgań oraz typ układu, uwzględniając parametry określające kształt kolumny oraz geometrię struktury realizującej obciążenie.

EN

The results of the theoretical considerations and numerical analysis of the issue of the free vibration of the slender system of the variable cross-section under selected case of the specific load were included in this work. Analyzed generalized load with a force directed towards the positive pole is realized by the structure built of heads of the circular outlines: loading and receiving heads. In order to model the variable cross-section of the column, the system was divided into n prismatic segments of the equal length and thickness and the variable width described by the linear function and the polynomial of degree 2, fulfilling the condition of the constant total volume. On the basis of the physical model of the system, the mechanical energy of the structure was defined. The issue of the free vibration was formulated taking into account the Hamilton’s principle (energetic method, kinetic criterion of the stability loss). Taking into consideration the geometric boundary conditions and the geometric continuity conditions, the differential equations of motion of particular segments of the column as well as the natural boundary condition and the natural continuity conditions were determined. On the basis of so-defined mathematical model, the computation algorithms enabling numerical examination of the transverse vibration of the column were developed. Within the scope of the carried-out calculations, the range of the changes in the frequency of the free vibration as a function of the external load was determined. An influence of the variable geometric parameters of the column on the value of the natural frequency and the type of the system was discussed, including the parameters describing the shape of the column as well as the geometry of the loading structure.

18

Combined load buckling for cylindrical shells based on a symplectic elasticity approach

Sun J., Xu X., Lim C. W.

Journal of Theoretical and Applied Mechanics

|

2016

|

Vol. 54 nr 3

705--716

EN

Buckling behavior of cylindrical shells subjected to combined pressure, torsion and axial compression is presented by employing a symplectic method. Both symmetric and non- -symmetric boundary conditions are considered. Hamiltonian canonical equations are established by introducing four pairs of dual variables. Then, solution of fundamental equations is converted into a symplectic eigenvalue problem. It is concluded that the influence of pressure on buckling solutions is more significant than that due to compressive load, in particular for a longer external pressured cylindrical shell. Besides, buckling loads and circumferential wavenumbers can be reduced greatly by relaxed in-plane axial constraints.

19

Free vibrations of column locally resting on the Winkler elastic foundation under the specific load

Szmidla J., Cieślińska-Gąsior I.

Journal of Applied Mathematics and Computational Mechanics

|

2016

|

Vol. 15, nr 1

181-190

EN

The results of theoretical and numerical research into free vibrations of column subjected to the follower force directed towards the positive pole locally resting on Winkler elastic foundation were presented in this work. Differential equations of motion and boundary conditions of considered system were determined taking into account total mechanical energy and Hamilton’s principle. On the basis of solution of boundary problem, the courses of free vibrations frequency curves as a function of external load were obtained taking into consideration parameters of length and location of Winkler elastic base and also parameters describing loading head geometry.

20

Elastic buckling of a triangular frame subject to in-plane tension

Magnucki K., Milecki S.

Journal of Theoretical and Applied Mechanics

|

2015

|

Vol. 53 nr 3

581--591

EN

The paper is devoted to elastic buckling of a symmetrical triangular frame under tensile in-plane load. Three mathematical models of the triangular frame are formulated. The first model deals with the pre-buckling state, the second one with the in-plane buckling state, and the third one with the lateral buckling state of the frame. The FEM-numerical model of the frame is formulated and the critical loads are calculated. The comparison of the results obtained in the analytical and numerical-FEM analysis is presented in tables and graphs in figures.