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1

Static analysis of thin-walled beams using two-phase local-nonlocal integral model

Günay M. G.

Archives of Mechanics

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2023

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Vol. 75, nr 6

673--695

EN

A mathematical model is developed for static analysis of small-scale thinwalled beams having arbitrary cross sections. Constitutive relations of the thin-walled beams are defined upon the two-phase local-nonlocal mixture model with integral formulation. The developed model includes flexural-torsional coupling and warping effects. Governing equations of the thin-walled beams having nonlocal property are derived by using the principle of minimum potential energy. The displacement based finite element method is used to solve both local and nonlocal part of the model. The effect of the nonlocal parameters on the static behavior of micro-scale thin-walled beams having closed and open cross-sections is examined and discussed for various nonlocal parameters and boundary conditions.

2

Dent-to-stiffener evaluation concept for thin-walled steel cylinders

Akarsu Oğuzhan, Bayrak Bariş, Kiliç Mahmut, Maali Mahyar, Aydin Abdulkadir Cüneyt

Architecture Civil Engineering Environment

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2023

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Vol. 16, no. 3

43--54

EN

Defects/imperfections can occur during manufacturing, assembly, welding, and other processes, which can reduce the critical buckling load. However, the axial buckling load is beyond the scope of this work, and there are many studies on the stiffening effect of longitudinal dents. This concept combined the idea of the dent-to-stiffener evaluation concept for thin-walled steel cylinders. This study aims to transform the dents into artificial dents for a stiffening effect on the buckling phenomena. For this purpose, 37 thin-walled steel cylinder models, including the perfect model, were designed for varying dent shapes, dent widths, dent depths, dent lengths, and dent angles. The study also contributed to the effect of dent parameters on the critical buckling load of thin-walled steel cylinders. In particular, increasing the initial buckling will motivate the industry to convert dents into stiffeners with small artificial touches to enhance the longevity of the structure. The results showed that the introduction of certain artificial dents can significantly increase the critical buckling load of cylinders, thus improving their resistance against buckling, which has significant implications for various industries that use thin-walled steel cylinders in their structures. The proposed simulations for transforming dents into artificial stiffeners can be a valuable tool for enhancing the longevity and safety of thin-walled steel cylinders and other structures.

3

Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Szybiński Józef, Ruta Piotr

Studia Geotechnica et Mechanica

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2019

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Vol. 41, nr 1

1--12

EN

This article deals with the vibrations of a nonprismatic thin-walled beam with an open cross section and any geometrical parameters. The thin-walled beam model presented in this article was described using the membrane shell theory, whilst the equations were derived based on the Vlasov theory assumptions. The model is a generalisation of the model presented by Wilde (1968) in ‘The torsion of thin-walled bars with variable cross-section’, Archives of Mechanics, 4, 20, pp. 431–443. The Hamilton principle was used to derive equations describing the vibrations of the beam. The equations were derived relative to an arbitrary rectilinear reference axis, taking into account the curving of the beam axis and the axis formed by the shear centres of the beam cross sections. In most works known to the present authors, the equations describing the nonprismatic thin-walled beam vibration problem do not take into account the effects stemming from the curving (the inclination of the walls of the thin-walledcross section towards to the beam axis) of the analysed systems. The recurrence algorithm described in Lewanowicz’s work (1976) ‘Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series’, Applicationes Mathematicae, XV(3), pp. 345–396, was used to solve the derived equations with variable coefficients. The obtained solutions of the equations have the form of series relative to Legendre polynomials. A numerical example dealing with the free vibrations of the beam was solved to verify the model and the effectiveness of the presented solution method. The results were compared with the results yielded by finite elements method (FEM).

4

The numerical investigation of thin-walled beams with modified C-sections

Grenda M.

Archives of Mechanical Technology and Materials

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2018

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Vol. 38

57--66

EN

Demand for thin-walled structures has been increasing for many years. Cold-formed, thin-walled channel beams are the subject of presented research. The local elastic buckling and limit load of these beams subjected to pure bending are investigated. This study includes numerical investigation called the Finite Strip Method (FSM). The presented results give a deep insight into behaviour of such beams and may be used to validate analytical models. The number of works devoted to the theory of thin-walled structures has been steadily growing in recent years. It means that is an increasing interest in practical methods of manufacturing cold-formed thin-walled beams with complicated cross-sections, including also beams with web stiffeners. The ratio of transverse dimensions of beam to its wall-thickness is high, therefore, thin-walled beams are prone to local buckling that may interact with other buckling modes. The stability constraints should be always considered when using cold-formed thin-walled beams.

5

Draft JIG structure design for measuring deformation of thin-walled robotic or conveyor components

Michalik Peter, Zajac Jozef, Straka Ľuboslav, Nowakowski Lukasz, Ambrozy Martin

Advances in Science and Technology. Research Journal

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2018

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Vol. 12, no 3

55--60

EN

The paper presents the general function, the division and the description of the main jig parts. It gives account of the basics and principles of a measuring jig structure using CAD applications. The main part delves into design of individual measurement jig options for measuring deformations of thin-walled robotic and conveyor components. Tension and stress analyses for each option have been performed. Subsequent to stress analysis, a suitable option was selected, with a description of its main parts, the production process and the necessary production equipment. Finally, the jig produced for the purpose of measuring deformation of thin-walled robotic and conveyor components is presented.

6

Assessment of the manufacturing possibility of thin-walled robotic portals for conveyance workplaces

Michalik Peter, Dobranský Jozef, Hrabovský Leopold, Petruš Michal

Advances in Science and Technology. Research Journal

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2018

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Vol. 12, no 1

338--345

EN

The paper discusses evaluation of machining solutions for oversized thin-walled robotic portal component for conveyance workplaces. The following portal CNC machining centers have been selected. Firstly, a FSGC 300 “portal type” portal was proposed, with a 50000 mm “X” axis and Heidenhain control system, the second portal was a DMU 340 portal with the maximum axis “X” of 6000 mm and Siemens Sinumerik control system and the last portal was the VF-10 / 40 one, with the maximum axis “X” of 3048 mm and Fanuc control system. Further, the method of fixing a thin-walled robotic portal is designed and individual options are evaluated for their economy. The CAM software application used for programming the production was SolidWorks.

7

Stability and load carrying capacity of multi-cell thin-walled columns of rectangular cross-sections

Królak M., Kowal-Michalska K., Mania R. J., Świniarski J.

Journal of Theoretical and Applied Mechanics

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2009

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Vol. 47 nr 2

435-456

EN

The paper concerns theoretical, numerical and experimental analysis of the stability and ultimate load of multi-cell thin-walled columns of rectangular and square cross-sections subjected to axial compression (uniform shortening of the column). The theoretical analysis deals with the local and global stability of multi-cell orthotropic columns of a rectangular profile with rectangular cells. It has been shown that for a multi-cell column made of the same material and having the same cross-section area, the value of local buckling stress of the column walls grows rapidly with an increase of the cell number. The experiment conducted for isotropic columns has also proved a significant growth of the ultimate load with the increase of the cell number. The paper gives some conclusions which can be useful in design of thin-walled box columns.

PL

Praca poświęcona jest teoretycznej, numerycznej i doświadczalnej analizie stateczności i nośności granicznej wielokomorowych cienkościennych słupów o prostokątnych i kwadratowych przekrojach poprzecznych poddanych osiowemu ściskaniu (odpowia- dającemu równomiernemu skróceniu słupa). Rozważania teoretyczne dotyczą lokalnej i globalnej utraty stateczności wielokomorowych ortotropowych słupów o obrysie prostokątnym, z prostokątnymi komorami. Wykazano, że dla wielokomorowego słupa wykonanego z tego samego materiału i o takim samym polu przekroju poprzecznego wartości lokalnego naprężenia krytycznego ścian słupa wzrastają gwałtownie wraz ze wzrostem liczby komór. Doświadczenia przeprowadzone dla izotropowych słupów potwierdziły wzrost zarówno naprężeń krytycznych, jak i nośności badanych modeli wraz ze wzrostem komór. W pracy podano pewne wnioski, które mogą być przydatne przy projektowaniu cienkościennych słupów o przekrojach skrzynkowych.

8

Optymalizacja konstrukcji wieloprzęsłowych o przekrojach lokalnie zdwojonych

Biegus A., Czepiżak D.

Prace Naukowe Instytutu Budownictwa Politechniki Wrocławskiej. Studia i Materiały

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2006

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Vol. 86, nr 17

29-39

PL

Przedstawiono wyniki analiz optymalizacyjnych płatwi, rygli ściennych i blach fałdowych, których przekroje są lokalnie zdwojone. Konstrukcjom tym można przyporządkować schematy belek o lokalnie zmiennych sztywnościach na zginanie przęseł skrajnych lub/i stref podpór. Celem pracy jest wyznaczenie optymalnych długości lokalnych wzmocnień a, ustrojów dwu, trzy, cztero i pięcio-przęsłowych. W analizach przyjęto zmienne długości a, i sztywności EJ, wzmocnień wszystkich stref podpór i przęseł skrajnych ustrojów. Na potrzeby wykonanej analizy parametrycznej ustroje rozwiązano metodą całkowania równania różniczkowego linii ugięcia IV rzędu. W analizie efektywności ustrojów rozpatrzono wariantowe rozwiązania konstrukcyjne, a także ich materiałochłonność i pracochłonność.

EN

Theoretical results of optimization of purlins, wall girts and corrugated sheets with locally doubled cross-sections have been presented herein (fig. 1). The schemes of beams (fig. 2-5) with changes in stiff-ness in the region of external spans or/and internal supports, having the length ah have been assigned to the tested structures. The determination of the optimal lengths a-, of local strengthening of tested structures appears as the work's purpose. Additionally, the comparative test results associated with the effectiveness of the both, material exploitation and technological parameters of alternative solutions of locally strength-ened thin-walled structures have been presented.