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1

Analiza następstw potencjalnej awarii wanty mostu podwieszonego w Bydgoszczy

Żółtowski Krzysztof, Kalitowski Przemysław

Materiały Budowlane

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2022

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nr 4

92--96

PL

Most Uniwersytecki został zamknięty po siedmiu latach od oddania do użytkowania. Powodem były widoczne gołym okiem objawy znacznego przeciążenia w obrębie zakotwień. Krytyczne elementy konstrukcji mostu zostały wzmocnione i przywrócono go do ruchu. W artykule przedstawiono nieliniowe analizy statyczne i dynamiczne wykonane na modelu MES, prezentujące cztery scenariusze przebiegu zachowania konstrukcji po utracie nośności mocowania wanty. Wykazały one, że przy przyjętych założeniach urwanie jednej z want prowadziłoby do nieuchronnej katastrofy.

EN

The University Bridge was closed seven years after it was put into use. The reason wasthe notice dsymptoms of significant overload in the area of the anchorages. Critical elements of the bridge structure were strengthened and it was brought back into service. The paper presents nonlinear static and dynamic analyzes performed on the FEM model, presenting four scenarios of the behavior of the structure after breaking the cable anchorage. The results showed that, under the adopted assumptions, breaking one of the cables would lead to an inevitable disaster.

2

Limit cycle oscillation prediction based on Finite Element-Modal approach

Ahmad K., Wu Z., Rahman H.

Archive of Mechanical Engineering

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2018

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Vol. LXV, nr 4

497--514

EN

The central theme of this work was to analyze high aspect ratio structure having structural nonlinearity in low subsonic flow and to model nonlinear stiffness by finite element-modal approach. Total stiffness of high aspect ratio wing can be decomposed to linear and nonlinear stiffnesses. Linear stiffness is modeled by its eigenvalues and eigenvectors, while nonlinear stiffness is calculated by the method of combined Finite Element-Modal approach. The nonlinear modal stiffness is calculated by defining nonlinear static load cases first. The nonlinear stiffness in the present work is modeled in two ways, i.e., based on bending modes only and based on bending and torsion modes both. Doublet lattice method (DLM) is used for dynamic analysis which accounts for the dependency of aerodynamic forces and moments on the frequency content of dynamic motion. Minimum state rational fraction approximation (RFA) of the aerodynamic influence coefficient (AIC) matrix is used to formulate full aeroelastic state-space time domain equation. Time domain dynamics analyses show that structure behavior becomes exponentially growing at speed above the flutter speed when linear stiffness is considered, however, Limit Cycle Oscillations (LCO) is observed when linear stiffness along with nonlinear stiffness, modeled by FE-Modal approach is considered. The amplitude of LCO increases with the increase in the speed. This method is based on cantilevered configuration. Nonlinear static tests are generated while wing root chord is fixed in all degrees of freedom and it needs modification if one requires considering full aircraft. It uses dedicated commercial finite element package in conjunction with commercial aeroelastic package making the method very attractive for quick nonlinear aeroelastic analysis. It is the extension of M.Y. Harmin and J.E. Cooper method in which they used the same equations of motion and modeled geometrical nonlinearity in bending modes only. In the current work, geometrical nonlinearities in bending and in torsion modes have been considered.

3

A Fundamental Study on the Free Vibration of Geometrical Nonlinear Cantlever Beam using an Exact Solution and Experimental Investigation

Jamal-Omidi M., Shayanmehr M., Sazesh S.

Archive of Mechanical Engineering

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2018

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Vol. LXV, nr 1

65--82

EN

Two fundamental challenges in investigation of nonlinear behavior of cantilever beam are the reliability of developed theory in facing with the reality and selecting the proper assumptions for solving the theory-provided equation. In this study, one of the most applicable theory and assumption for analyzing the nonlinear behavior of the cantilever beam is examined analytically and experimentally. The theory is concerned with the slender inextensible cantilever beam with large deformation nonlinearity, and the assumption is using the first-mode discretization in dealing with the partial differential equation provided by the theory. In the analytical study, firstly the equation of motion is derived based on the theory of large deformable inextensible beam. Then, the partial differential equation of motion is discretized using the Galerkin method via the assumption of the first mode. An exact solution to the obtained nonlinear ordinary differential equation is developed, because the available semi analytical and approximated methods, due to their limitations, are not always sufficiently reliable. Finally, an experiment set-up is developed to measure the nonlinear frequency of oscillations of an aluminum beam within a domain of initial displacement. The results show that the proposed analytical method has excellent convergence with experimental data.

4

From full-scale testing of steel lattice towers to stochastic reliability analysis

Szafran J., Kamiński M.

Archives of Mechanics

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2017

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Vol. 69, nr 4-5

371--388

EN

Analysis of the steel lattice telecommunication structure exposed to the wind pressure, whose average value is treated as the Gaussian random variable. The Least Squares Method is provided here for symbolic recovery of the polynomial responses of this structure in addition to the given uncertainty source and it serves to the twentieth order perturbation-based approximations for the first four probabilistic moments and coefficients. Static numerical analysis has been carried out by the use of the incremental BFGS (Broyden–Fletcher–Goldfarb–Shanno) procedure necessary for the so-called P-delta effect in steel structures, while the basic statistics of the ultimate limit state have been included into the formulas for the reliability indices of both first and second order. This study shows that the safety margin of such structures is definitely wider than it follows the basic Eurocodes statements, which means that designed durability period for these telecommunication structures is definitely longer.

5

A simplified model of concrete for analysis of reinforced concrete elements

Szcześniak A., Stolarski A.

Biuletyn Wojskowej Akademii Technicznej

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2016

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Vol. 65, nr 4

55--68

EN

The elastic-plastic material model for concrete developed by considering the stress softening and degradation of the deformation modulus for the concrete was presented in the paper. A reduced plane stress state for the compression/tension range with shear was assumed. During the loading process, the model describes four phases of concrete behaviour during compression: achieving the elastic compressive concrete strength, perfectly plastic flow, material softening, and failure/crushing. The model describes three tension phases: achieving elastic tensile concrete strength, material softening, and failure/cracking. The failure phases were interpreted as achieving a stressless state in the material softening process. The proposed model is simplified and very effective to describe the most important properties of nonlinear behaviour of material. The model of concrete can be used for analysis of failure mechanism of reinforced concrete structural elements.

PL

W pracy przedstawiono model betonu jako materiału sprężysto-plastycznego z uwzględnieniem osłabienia i degradacji modułu odkształcenia. Przyjęto założenie zredukowanego, płaskiego stanu naprężenia dla ściskania/rozciągania i ścinania. Model betonu pozwala na opis sprężystego osiągnięcia początkowej wytrzymałości, idealnego płynięcia plastycznego i osłabienia materiałowego przy ściskaniu oraz sprężystego osiągnięcia wytrzymałości i osłabienia materiałowego przy rozciąganiu. Procesy zniszczenia, tj. zarysowania i zmiażdżenia, modelowane są jako stany beznaprężeniowe osiągane w procesie osłabienia materiałowego, odpowiednio przy rozciąganiu i ściskaniu. Proponowany model odkształcenia betonu umożliwia efektywny opis najistotniejszych właściwości nieliniowego zachowania materiału i może być stosowany do analizy mechanizmu zniszczenia prętowych, żelbetowych elementów konstrukcyjnych.

6

Walking the Line. Traveling Forces vs Moving Masses

Bogacz R., Frischmuth K., Konowrocki R.

Symulacja w Badaniach i Rozwoju

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2015

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Vol. 6, nr 3

165--173

EN

In railway mechanics, and more general, in civil engineering and vehicle dynamics, the problem of simultaneous modeling of a track and a vehicle has been the subject of many papers. Often one of the coupled subsystems is highly simplified in order to be able to obtain results on the other. For example, when the propagation of waves in the track is the main concern, vehicles such as a train or a taxiing airplane, are treated as an external force, travelling at a certain speed along a given path. In that case, the force is assumed as independent of the motion in the track, which results from the load. On the other hand, dynamical simulations of vehicles typically run on a defined ground, which is given and invariant, whatever the motion of the vehicle. In order to make a track model more realistic, the vehicle model may be improved, without going as far as to couple a full-fledged vehicle model with a realistic model of a track consisting of rails on sleepers, supported via some subgrade on the ground. A first simple step is to attach an additional mass in the contact point, i.e. the position, where the external force is applied.

PL

W inżynierii kolejowej lub ogólniej - w budownictwie i dynamice pojazdów zagadnienie równoczesnego modelowania toru i pojazdu było przedmiotem wielu badań. Często jeden ze sprzężonych układów był nadmiernie upraszczany, aby uzyskać rozwiązanie problemu. Zagadnienie struny najczęściej rozpatruje się w zakresie małych przesunięć i kątów, poszukiwana jest wówczas funkcja skalarna jednej zmiennej. Gdy konfiguracja aktualna odbiega znacznie od konfiguracji materialnej, wyniki uzyskane mogą być fizycznie nieakceptowalne. W pracy do rozwiązywania tego typu zadań zaleca się podejście parametryczne. Zalety takiego podejścia demonstrowane są na podanych przykładach z zakresu modelowania współpracy pojazdu z trakcją oraz popularnych sportów rekreacyjnych.

7

Metoda relaksacji dynamicznej w analizie zginanych elementów żelbetowych

Szcześniak A., Stolarski A.

Biuletyn Wojskowej Akademii Technicznej

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2015

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Vol. 64, nr 4

223-239

PL

W pracy przedstawiono metodę analizy nieliniowego zachowania elementów żelbetowych poddanych działaniu krótkotrwałego obciążenia statycznego. Przeprowadzono rozważania w zakresie modelowania procesów odkształcania elementu żelbetowego. Metodę analizy wytężenia układu konstrukcyjnego opracowano z wykorzystaniem metody różnic skończonych. Do rozwiązania układów nieliniowych równań równowagi zastosowano metodę relaksacji dynamicznej, która po wprowadzeniu tłumienia krytycznego pozwala na opis statycznego zachowania elementu konstrukcyjnego. W celu zwiększenia skuteczności metody w zakresie analizy pokrytycznej, w procedurze obliczeniowej uwzględniono parametr długości łuku na ścieżce równowagi.

EN

The paper presents a method for the analysis of nonlinear behaviour of reinforced concrete bent elements subjected to short-term static load. The considerations in the range of modelling of deformation processes of reinforced concrete element were carried out. The method of structure effort analysis was developed using the finite difference method. The Dynamic Relaxation Method, which — after introduction of critical damping — allows for description of the static behaviour of a structural element, was used to solve the system of nonlinear equilibrium equations. In order to increase the method effectiveness in the range of the post-critical analysis, the Arc Length Parameter on the equilibrium path was introduced into the computational procedure.

8

Analiza wytężenia słupów żelbetowych metodą relaksacji dynamicznej

Szcześniak A., Stolarski A.

Biuletyn Wojskowej Akademii Technicznej

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2014

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Vol. 63, nr 2

155-170

PL

W pracy przedstawiono metodę analizy statycznego odkształcenia słupów żelbetowych z uwzględnieniem nieliniowości geometrycznej i nieliniowości fizycznych materiałów konstrukcyjnych. Dla stali zbrojeniowej zastosowano model materiału sprężysto-plastyczny ze wzmocnieniem. Dla betonu przyjęto model sprężysto-plastyczny z uwzględnieniem osłabienia materiałowego. Metodę analizy wytężenia układu konstrukcyjnego opracowano z wykorzystaniem metody różnic skończonych. Opracowano efektywną metodę relaksacji dynamicznej rozwiązania układu równań równowagi elementów żelbetowych. Na podstawie metody rozwiązania zbudowano własne procedury numeryczne i program obliczeniowy. W celu sprawdzenia poprawności wprowadzonych procedur obliczeniowych wykonano analizę numeryczną słupów żelbetowych przegubowo podpartych i obciążonych siłą podłużną działającą na zadanym mimośrodzie. Otrzymane wyniki analizy porównano z wynikami doświadczalnymi zaczerpniętymi z literatury oraz wynikami obliczeń analitycznych.

EN

The method of the analysis of static deformation of reinforced concrete columns with regard to geometrical nonlinearity of the columns and physical nonlinearity of structural materials was presented in the paper. For reinforcing steel, the elastic-plastic model of material with material hardening was applied. The elastic-plastic model of material with material softening was used for concrete. The method of effort analysis of the structural system was developed using the finite difference method. The effective dynamic relaxation method for solution of the systems of the equilibrium equations of reinforced concrete columns was developed. It was the basis for preparation of the own numerical procedures and numerical program. The reinforced concrete simple supported columns, under eccentric compression, were numerically analysed. The numerical results were compared with experimental results, taken from literature, and with theoretical solutions.

9

Large deflections of nonlinearly elastic functionally graded composite beams

Sitar M., Kosel F., Brojan M.

Archives of Civil and Mechanical Engineering

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2014

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Vol. 14, no. 4

700--709

EN

The paper discusses governing differential equation for determining large deflections of slender, non-homogeneous beam subjected to a combined loading and composed of a finite number of laminae, which are made of nonlinearly elastic, modified Ludwick's type of material with different stress–strain relations in tension and compression domain. The material properties are varying arbitrarily through the beam's thickness. When the thickness of laminae is sufficiently small and the variation of mechanical properties is close to continuous, the beam can be considered as made of functionally graded material (FGM). The derived equations are solved numerically and tested on several examples. From a comparison of the results obtained and those found in the literature a good agreement was observed.

10

An initially deformed flat frame finite element

Zamorowski J.

Archives of Civil Engineering

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2013

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Vol. 59, nr 3

381--400

EN

The paper presents the author’s non-linear FEM solution of an initially stressless deformed flat frame element, in which the nodes are situated along the axis of the bar initially straight. It has been assumed that each node may sustain arbitrary displacements and rotation. The solution takes into account the effect of shear, the geometrical non-linearity with large displacements (Green-Lagrange’s strain tensor) and moderate rotations (i.e. such ones which allow a linear-elastic behaviour of the material) and alternative small rotations when the second Piola-Kirchhoff stress tensor is applied. This solution is based on [1], concerning beams without any initial bow imperfections. The convergence of the obtained results at different numbers of nodes and Gauss points in the element was tested basing on the example of circular arcs with a central angle of 120º-180º. The analysis concerned elements with two, three, five, seven, nine and eleven nodes, for the same number of points of numerical integration and also with one more or less. Moreover, the effect of distributing the load on the convergence of the results was analyzed.

11

Metoda analizy niesprężystych elementów żelbetowych ściskanych mimośrodowo

Stolarczuk A., Stolarski A.

Biuletyn Wojskowej Akademii Technicznej

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2009

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Vol. 58, nr 4

317-334

PL

W pracy przedstawiono metodę analizy statycznego odkształcania ściskanych elementów żelbetowych z uwzględnieniem nieliniowości geometrycznej elementów i nieliniowości fizycznych materiałów konstrukcyjnych: betonu i stali. Dla stali zbrojeniowej zastosowano model materiału sprężysto - idealnie plastycznego. Dla betonu przyjęto model materiału sprężysto - plastycznego z uwzględnieniem osłabienia materiałowego. Metodę analizy wytężenia układu konstrukcyjnego opracowano z wykorzystaniem metody różnic skończonych. Opracowano efektywne algorytmy rozwiązania układów równań konstytutywnych i przyrostowych równań równowagi prętowych elementów żelbetowych umożliwiających analizę wyboczenia.

EN

Theoretical formulation and algorithmization of the method of the analysis of behaviour of compressed reinforced concrete members subjected to the short - duration static loading were introduced in the paper. The method of analysis of the structure effort is the basis of development of the own numeric procedures and computational programmes using the finite difference method. The received order of the physical nonlinearity of constitutive equations for the concrete makes possible tracing the material soft ening phenomena as well as cracking and crushing in the areas of critical effort of the reinforced concrete bar member. The received order of the geometrical nonlinearity of strain - displacement relationships makes possible the analysis of buckling phenomena of the reinforced concrete bar member.

12

Postbuckling characteristics of the short superelastic shape memory alloy columns- experiment and quantitative analysis

Rahman M. A., Tani J.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 4

941-955

EN

A few unique buckling and postbuckling characteristics of short superelastic shape memory alloy (SMA) columns are observed experimentally and explained in terms of numerical simulation. Interestingly, it is found from the load-deformation curves that during compression the SMA column with slenderness ratio of 38 exhibits two distinct buckling loads, the other one being higher, completely contrary to the general notion that load falls off monotonously for all columns in the postbuckling region. Similarly, for of 28, the SMA column can sustain a significantly high load after a distinct change in the mode of deformation. Based on the large deformation theory as well as the nonlinear stress-strain relations, the load-deformation curves of the short SMA columns have been predicted by using the FEM code ANSYS. Precise and quantitative analyses of these results verify the fact that the SMA column's behavior can be attributed to the special nature of the stress-strain curves.

13

Stability of inelastic bilayered conical shells

Paczos P., Zielnica J.

Journal of Theoretical and Applied Mechanics

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2003

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Vol. 41 nr 3

575-591

EN

The paper deals with the derivation of the basic stability equations of bilayered elastic-plastic conical shells and a approximate solution to these equations, both theroretocally and by numerical procedures. The subject of the analysis is a bilayered open conical shell under a combined load comprising longitudinal forces and external pressure. Kirchhoff-Love's hypotheses hold for the layers, and use is made of constitutive relations in the form of generalized Hooke's law for the elastic stability analysis, and the Prandtl-Reuss incremental plasticity theory for the stability analysis in the elastic-plastic range. The stability equations are derived using the virtual work principle, and Ritz's method is applied to solve the equations. An iterative computer algorithm has been developed which made it possible to analyse the shells in the elastic, elastic-plastic or totally plastic prebuckling state of stress. The numerical results are presented in diagrams.

PL

Tematem pracy jest wyprowadzenie podstawowych równań stateczności dwuwarstwowych otwartych sprężysto-plastycznych powłok stożkowych i przybliżone rozwiązanie tych równań w sposób analityczny i numeryczny. Przedmiotem analizy jest swobodnie podparta dwuwarstwowa powłoka w kształcie wycinka stożka poddana działaniu obciążenia złożonego w postaci sił podłużnych i ciśnienia poprzecznego. Równania stateczności wyprowadzono na podstawie zasady minimum energii potencjalnej powłoki, a do rozwiązania zastosowano metodę Ritza. Wyniki numeryczne otrzymano za pomocą specjalnie zbudowanej iteracyjnej procedury numerycznej z wykorzystaniem komputera.