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1

Fully discrete approximations and an a priori error analysis of a two-temperature thermo-elastic model with microtemperatures

Baldonedo Jacobo, Fernández José R., Quintanilla Ramón

International Journal of Applied Mathematics and Computer Science

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2024

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Vol. 34, no. 1

93--103

EN

In this paper, we consider, from a numerical point of view, a two-temperature poro-thermoelastic problem. The model is written as a coupled linear system of hyperbolic and elliptic partial differential equations. An existence result is proved and energy decay properties are recalled. Then we introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained, from which the linear convergence of the approximation is deduced under an appropriate additional regularity. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation, the decay of the discrete energy and the behaviour of the solution depending on a constitutive parameter.

2

Frequency-based crack effect study on beams under free vibration using finite element analysis

Sahu Ompriya, Das Priyadarshi, Muni Manoj Kumar, Pradhan Nibedita, Basa Bidyadhar, Sahu Shishir Kumar

Engineering Transactions

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2024

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Vol. 72, iss. 1

95--114

EN

A numerical computation-based analysis of the free vibration analysis of uniform beams with rectangular cross-sections is presented in this work using finite element analysis. The approach involves dividing the beam into segments at the crack section, which is then modelled for simulation for eigenfrequencies on the ABAQUS platform. The numerical simulation results are in excellent agreement with the findings of previous research, confirming the efficacy and applicability of the developed beam model. A sequential comprehensive approach towards analysis of the effects of the position and depth of the cracks on the natural frequencies are addressed in numerical results. The research findings confirm that the simulation model is suitable for the vibration analysis of beams or beam-like elements with different cross-sections.

3

Modeling and numerical simulation of eddy current sensors for electromagnetic characterization of fluids

Miloudi Khaled, Moulai Hocine, Azizi Hakim

Przegląd Elektrotechniczny

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2023

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R. 99, nr 10

88--92

EN

This work aims to model a device enabling a useful and accurate electromagnetic characterization of fluids. The device developed is based on a non destructive testing (NDT) control technique evolving the eddy currents induced in the fluid to be characterized. The finite element method was used in the modeling to determine the conductivity of the fluid from the induced eddy current. In addition, an experimental device has been built. It consists of an absolute probe where the fluid control is made by determining its electrical conductivity by measuring the variations of the fluid impedance as a function of the applied voltage frequency. Good agreements are found between modeling results and experimental measurements. An inverse model that converges after only 7 iterations has been also proposed for the determination of the conductivity of fluids by the use of theoretical and experimental measurements.

PL

Niniejsza praca ma na celu zamodelowanie urządzenia umożliwiającego użyteczną i dokładną charakterystykę elektromagnetyczną płynów. Opracowane urządzenie opiera się na technice kontroli badań nieniszczących (NDT), która rozwija prądy wirowe indukowane w scharakteryzowanym płynie. W modelowaniu wykorzystano metodę elementów skończonych do wyznaczenia przewodności płynu z indukowanych prądów wirowych. Ponadto zbudowano eksperymentalne urządzenie. Składa się z sondy absolutnej, w której kontrola płynu odbywa się poprzez określenie jego przewodności elektrycznej poprzez pomiar zmian impedancji płynu w funkcji przyłożonej częstotliwości napięcia. Stwierdzono dobrą zgodność między wynikami modelowania a pomiarami eksperymentalnymi. Zaproponowano również model odwrotny, który zbiega się już po 7 iteracjach, do wyznaczania przewodnictwa płynów za pomocą pomiarów teoretycznych i eksperymentalnych.

4

Comparison of Monte Carlo and bootstrap analyses for residual life and confidence interval

Husnain M. M. N., Akramin M. R. M., Shaari M. S., Takahashi Akiyuki, Bashiri Abdullateef H., Alshoaibi Abdulnaser M.

Materials Science Poland

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2023

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Vol. 41, No. 1

15--26

EN

Failure starts with creation of a crack, then the propagation of the crack and eventually the fracture of the material. Furthermore, material selection, geometry, processing and residual stresses are critical factors that may contribute to uncertainty and prospective failure mechanisms in engineering. These issues may also arise in computational analysis, a problematic model, for instance, a three-dimensional surface fracture that may necessitate numerous degrees of freedom during analysis. However, considering the multiple incidents of material failure, detailed analysis and efforts to prevent premature material failure for safety and engineering integrity can be carried out. Thus, the objective of this study is to model crack growth in a surface-cracked structure. Aluminium alloy 7075-T6 was the material of interest in this study. The S-version finite element method (SFEM) was used to study fracture propagation. The numerical approach developed in this research was the probabilistic SFEM. Instead of mesh rebuilding, a typical finite element approach, the SFEM uses global–local element overlay method to create a fatigue crack growth model, which was then used for crack research. Empirical computation and previous experimental data were used to evaluate the stress intensity factor (SIF), surface crack growth and fatigue life. The SIF was determined using a virtual crack closure method (VCCM). In addition, the probabilistic approach is also a critical method to generate random parameters, such as Monte Carlo and bootstrap methods. The SIF, fatigue life and surface crack growth were validated and deemed to be within the acceptable range.

5

A parametric study of higher-mode natural frequencies of composite stiffened cylindrical shell with cut-out

Chaudhuri Puja Basu, Sahoo Sarmila, Mitra Anirban

Engineering Transactions

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2023

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Vol. 71, iss. 1

81--109

EN

A finite element-based dynamic study of cut-out borne composite cylindrical shells reinforced with stiffeners is conducted. Isoparametric shell element with eight nodes and beam element with three nodes are used to study the mode-frequency behavior of shells with varied edge conditions. Anti-symmetric angle-ply laminates of two, four and ten layers with varying lamination angles are considered. Ten-layer laminates are investigated further as they exhibit better performance in fundamental frequency than two and four-layer laminates. The reduced integration method is adopted to find the shell element’s stiffness and mass matrices and the subspace iteration method is used for the eigenvalue solution of free vibration formulation. Natural frequencies for the first five modes are considered. The effects of fiber orientation angle (θ), degree of orthotropy (E11/E22), and width/thickness ratio (b/h) on the natural frequency are determined through numerical studies. It is revealed that vibration behavior strongly depends on both the number and arrangement of boundary constraints.

6

Numerical failure analysis of laminated beams using a refined finite element model

Layachi Maroua, Khechai Abdelhak, Ghrieb Abderrahmane, Layachi Safa

Advances in Materials Science

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2023

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Vol. 23, nr 1(75)

32--57

EN

In the present investigation, laminated composite beams subjected to a bending static loading are studied in order to determine their failure mechanisms and the first ply failure (FPF) load. The FPF analysis is performed using a refined rectangular plate element. The present element is formulated based on the classical lamination theory (CLT) to calculate the in-plane stresses. To achieve this goal, several failure criterions, including Tsai-Wu, Tsai-Hill, Hashin, and Maximum Stress criteria, are used to predict failure mechanisms. These criterions are implemented within the finite element code to predict the different failure damages and responses of laminated beams from the initial loading to the final failure. The numerical results obtained using the present element compare favorably with those given by the analytic approaches. It is observed that the numerical results are very close to the analytical results, which demonstrates the accuracy of the present element. Finally, several parameters, such as fiber orientations, stacking sequences, and boundary conditions, are considered to determine and understand their effects on the strength of these laminated beams.

7

Numerical analysis of the effects of canal wall-up and canal wall-down mastoidectomy on the sound transmission characteristics of human ears

Liu Peihan, Liu Wen, Zhao Yu, Yan Shanshan, Jiang Wen, Liu Houguang, Wan Jin

Acta of Bioengineering and Biomechanics

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2023

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Vol. 25, no. 2

133--145

EN

The aim of this work was to study the effect of canal wall-up (CWU) and canal wall-down (CWD) and mastoid obliteration in conjunction with CWD (CWD-MO) mastoidectomy on the sound transmission characteristics of the human ear. Methods: Three mastoidectomy surgical methods, CWU, CWD and CWD-MO, were simulated on the freshly dissected cadaver heads. Then, the finite element (FE) models corresponding to these surgical methods were established by micro-computed tomography (Micro-CT) and reverse engineering technology, and the accuracy of the models was verified. Finally, the FE Models were used to analyze the effects of different surgical methods on the sound transmission characteristics of the human ear. Results: For CWU, since the integrity of the outer wall of the ear canal is ensured, the sound pressure (SP) gain of the ear canal and the stapes footplate displacement (FPD) gain after this operation are close to normal values. For CWD, due to severe damage to the outer wall of the ear canal, a negative gain of the ear canal SP occurs in the high-frequency range, and the resonance frequency is significantly reduced. For CWD-MO, the frequency range of SP negative gain in the ear canal is reduced due to the addition of fillers in the ear canal to reduce the degree of damage, and the resonance frequency is increased compared to CWD. Conclusions: The impact of three types of mastoidectomy, including CWU, CWD, and CWDMO, on the sound transmission characteristics of the human ear after surgery is relatively small.

8

Studies on the performance of impact resistant structure of hydraulic support in fully mechanized mining face under rock burst

Zhang Qiang, Zhang Runxin

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 4

649--658

EN

In order to solve the support problem of a fully mechanized coal face under rock burst and with the goal of safe and efficient coal mining, the present study hasenvisaged a hexagon periodic arrangement energy absorption structure. Based on the shell theory, the mechanical model of the impact resistant structure and hydraulic support was constructed using the finite element method. The mechanical properties of the hydraulic support under a full impact and a partial load impact of the roof were analysed, and the impact resistant structure was designed to prove the reliability of the structure. The results showed that the anti-impact structure reduced the stress and stress fluctuation of the column and effectively reduced the shape variable of the weak link of the hydraulic support. Furthermore, a delay in the time was observed, when the pressure of the hydraulic cylinder reached the yield strength, and there was a gain in the time for the opening of the large flow safety valve. Especially, under the action of partial load, the column did not bend, and the hydraulic cylinder was in the elastic range. Our results can provide new insights in the support of rock burst working face, which is of great significance concerning safety in the coal mining.

9

Numerical investigation of static behavior of bolted joints

Hammami Chaima

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 3

385--394

EN

This paper investigates the static behavior of bolted joints and the extent of its control in the design of assembled structures. An analysis method is thus first developed highlighting stresses distribution in the junction to dimension the functional performance area. A description of the joint characteristics is presented. Numerical simulations, comparing the complete and simplified finite element models relevance, are then carried out. The integration of results of this analysis in the design of multiple bolted joints structures in finally presented. Experiments on a testbed, where a viscoelastic material is introduced in joints interfaces to enhance global damping, validate the approach developed.

10

A conceptual sector-scale numerical modeling of a landslide in an open pit mine

Koca Tümay Kadakci

Archives of Mining Sciences

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2022

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Vol. 67, no. 2

275--287

EN

In this study, an old rotational landslide that has reactivated in the NW sector of an open-pit mine operated within the gneiss rock unit was evaluated for geological and hydrogeological properties. The pit slopes were susceptible to mass movement when there were variations in water inflows. Considering this fact, a conceptual numerical model concerning geostructural features, rainfall infiltration, and varying hydrological conditions was constructed. Initially, finite element (FE) groundwater seepage analyses were performed to evaluate the effect of water flow on stability in the dry and rainy seasons. The rainy season was simulated by vertical infiltration. Since the dewatering measures are of importance in open pit slope instability mitigation, pumping wells were designed to control water flow through the disturbed zone to improve the stability of the sector that can be triggered again with changing environmental conditions. The performance and organization of the pumping wells were also simulated in the FE model. This FE model was part of a dewatering plan. From this, the effect of the pumping rate from the wells on the stability of the sector was revealed. It was also found that there should be an increase in the pumping rate in the rainy season.

11

Application of Virtual Reality and High Performance Computing in Designing Rotary Forming Processes

Hojny Marcin, Marynowski Przemysław, Lipski Grzegorz, Gądek Tomasz, Nowacki Łukasz

Archives of Metallurgy and Materials

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2022

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Vol. 67, iss. 3

1099--1105

EN

This paper presents an innovative solution in the form of a virtual reality (VR) and high performance computing (HPC) system dedicated to aid designing rotary forming processes with laser beam reheating the material formed. The invented method allowing a virtual machine copy to be coupled with its actual counterpart and a computing engine utilizing GPU processors of graphic NVidia cards to accelerate computing are discussed. The completed experiments and simulations of the 316L stainless steel semi-product spinning process showed that the developed VR-HPC system solution allows the manufacturing process to be effectively engineered and controlled in industrial conditions.

12

Study the internal cracks effect on vibration of laminated composite square plates

Hassan M.S., Rashid Z.H., Sarhan R.A.

Archives of Materials Science and Engineering

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2022

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Vol. 116, nr 1

28--33

EN

Purpose: The study of cracks behaviour in a composite plate is of significant importance in the dynamics of the Mechanical parts in order to avoid design failures due to resonance or high amplitude vibrations. Design/methodology/approach: In this paper, a square glass-epoxy composite plate is adopted. The plate has four layers with symmetric and asymmetric lamination. Assuming the cracks are profound as defects. The results were obtained by using a numerical solution of mechanical APDL from ANSYS. Findings: It has been found for different boundary conditions that the rank of natural frequencies is decreased by increasing the crack ratio due to the reduction of the plate’s stiffness, whereas the crack direction has no mentioned effect for a small angle of rotation. Research limitations/implications: The accuracy of results is verified by comparing a single case of the current work with other previous investigations. value: Evaluate the influence of the crack length ratio, angle of the crack rotation, boundary conditions and lamination angles on the natural frequencies of the square composite plate with glass-epoxy materials.

13

Post buckling resistance reserve of corrugated girders with support stiffeners

Basiński Witold

Archives of Civil Engineering

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2022

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Vol. 68, nr 4

513--536

EN

The analysis of web-corrugated and trapezoidal profiled web girders focuses on the description of buckling resistance, possibly the ultimate resistance neglecting the post-buckling resistance reserve of girders. The problem is still the post-buckling resistance reserve and its possible application in practice. For this purpose this paper presents the analysis of tests on shear resistance of the corrugated web of SIN girders with the support stiffeners in the pre- and post-buckling zones. There are also presented values of the post-buckling resistance zone and the mutual relationships between pre- and post-buckling resistance zones. Values of these zones are related to optimization of the web-corrugated girders, which consists in enlarging the zone of pre-critical resistance and balancing between shear resistance and bending resistance. The experimental tests were performed on 20 girders with the following web depth: 500, 1000, 1250, and 1500 mm, composed of three pre-assembled units. The girders with a simply supported beam system and a simply supported beam with a single cantilever were made of pre-assembled units joined by means of high strength preloaded bolts. The numerical analysis by FEM was conducted for the models with web depth from hw = 500 to 1500 mm at the full range of web thickness 2,0; 2,5, and 3 mm. The tests showed that stiffness of the support stiffeners in the web-corrugated girders had an impact on the size of pre- and post-buckling resistance zones, which consequently reduced the zone of post-buckling resistance. Because the initiated loss of stability of the corrugated-web girders is an irreversible and rapid process, and the resulting displacements in the non-linear area are permanent, the application of the post-buckling resistance zone in practice can be troublesome. From the standpoint of the structural reliability, however, the post-buckling zone provides a yield delay, i.e. it may be regarded as a safety margin. Therefore, its most possible reduction is required.

PL

Analiza dźwigarów o faliście wyprofilowanym środniku jak i środniku trapezowym koncentruje się na opisie nośności krytycznej, ewentualnie nośności granicznej pomijając przedział nośności nadkrytycznej dźwigarów. Problemem otwartym pozostaje zatem przedział nośności nadkrytycznej i jego możliwość wykorzystania w praktyce. W tym celu w niniejszej pracy przedstawiono analizę badań nośności postaciowej falistego środnika dźwigarów SIN z żebrami podporowymi w zakresie do i pokrytycznym. Badania doświadczalne przeprowadzono na dwudziestu dźwigarach o wysokości środnika 500, 1000, 1250 i 1500 mm złożonych z trzech elementów wysyłkowych. Dźwigary o schemacie statycznym belki swobodnie podpartej oraz belki swobodnie podpartej z jednostronnym wspornikiem zbudowano z elementów wysyłkowych połączonych doczołowo na śruby sprężone. Z kolei analizę numeryczną FEM przeprowadzono na modelach o wysokościach środnika od hw = 500 do 1500 mm przy pełnym zakresie grubości środnika 2.0; 2.5 i 3 mm. W celu określenia początku niestateczności falistego środnika przeanalizowano przebiegi odkształceń na ukośnych tensometrach naklejonych na środniku. Tensometry naklejono w postaci rozety na kierunku spodziewanych największych odkształceń. Kąt pomiędzy tensometrami w rozetach wynosił 120°. Na podstawie charakteru wykresów odkształceń określono punkt początkowy utraty stateczności falistego środnika, wiążąc z nim obciążenie krytyczne PeB, które przyjęto w punkcie utraty liniowego charakteru zależności obciążenia od odkształcenia P(ε). Analizując proces utraty stateczności falistego środnika rozróżniono zniszczenie dźwigarów niskich o hw = 500 mm i wysokich od hw = 1000 mm przyporządkowując im punkty utraty stateczności rozgraniczające obszar dokrytyczny oraz nadkrytyczny. W przypadku dźwigarów niskich o wysokości środnika 500 mm z żebrami podporowymi opisano lokalny proces zniszczenia środnika. Z koeli w przypadku dźwigarów o wysokości środnika od hw = 1000 mm stwierdzono wzajemne powiązanie lokalnej oraz globalnej postaci zniszczenia prowadzące do ich interakcji. W wyniku przeprowadzonych badań wykazano, że w dźwigarach o falistym środniku występuje wpływ sztywności żeber podporowych na wielkość przedziałów do i nadkrytycznego, prowadząc do redukcji przedziału nadkrytycznego nośności dźwigarów. W dźwigarach o falistym środniku przedział nadkrytyczny jest przedziałem zarówno odkształceń jak i przemieszczeń nieliniowych środnika. Stwierdzono, że nie nadaje się jednak do wykorzystania w eksploatacji, gdyż zapoczątkowany proces utraty stateczności jest nieodwracalny oraz gwałtowny, a powstałe przemieszczenia w obszarze nieliniowym są trwałe. Stanowi natomiast z punktu widzenia bezpieczeństwa zabezpieczenie przed katastrofą w postaci przystanku plastycznego. Zapas nośności dźwigarów o falistym środniku wyniósł wg badań doświadczalnych od 19% do 21% w dźwigarach z podporowym żebrem podatnym oraz od 8% do 21% w dźwigarach z podporowym żebrem sztywnym. W przypadku analizy numerycznej był nieco mniejszy i oscylował w przedziale od 8% do 9% w dźwigarach z podporowym żebrem podatnym oraz od 3% do 9% w dźwigarach z żebrem podporowym usztywnionym. Oszacowanie nadwyżki nośności dźwigarów o falistym środniku dało odpowiedź o możliwościach zwiększania nośności dokrytycznej w drodze optymalizacji konstrukcji, np. poprzez zastosowanie usztywnionych żeber podporowych, czy też możliwych przekątnych żeber rozciąganych.

14

Application of the generalized nonlinear constitutive law in numerical analysis of hollow-core slabs

Staszak Natalia, Garbowski Tomasz, Ksit Barbara

Archives of Civil Engineering

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2022

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Vol. 68, nr 2

125--145

EN

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. They should be based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows for iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

PL

Nieliniowa analiza kanałowych płyt stropowych wymaga zastosowania zaawansowanych technik numerycznych, odpowiednich modeli konstytutywnych zarówno dla betonu jak i stali oraz konieczności posiadania odpowiednich umiejętności obliczeniowych. W przypadku nieliniowych analiz należy wziąć pod uwagę również sprężenie, pękanie, rysy, zmiękczenie materiału itp., co powoduje że zadanie obliczeniowe może znacznie przekroczyć możliwości zwykłego inżyniera. W celu wykonania obliczeń w tradycyjnym biurze projektowym potrzebne są uproszczone metody obliczeń. Najlepiej w oparciu o liniową metodę elementów skończonych (MES) z prostym podejściem uwzględniającym nieliniowości materiałowe. W artykule przedstawiono uproszczoną analizę kanałowych płyt w oparciu o uogólnione prawo konstytutywne. W proponowanej metodzie prosty rozkład tradycyjnej iteracyjnej liniowej analizy elementów skończonych oraz nieliniowej analizy algebraicznej przekroju poprzecznego płyty. Poprzez niezależną analizę przekroju płyty w różnych stanach odkształcenia, można uzyskać zdegradowaną sztywność płyty, co pozwala na iteracyjną aktualizację przemieszczeń oraz obrotów w węzłach modelu MES. To z kolei pozwala zaktualizować stan deformacji, a następnie skorygować translacje i obroty w węzach jeszcze raz. Proponowana tutaj metoda ma zastosowanie do analizy betonu zbrojonego cięgnami oraz sprężonych płyt kanałowych. Wyniki uzyskane z pełnego szczegółowego nieliniowego modelu 3D MES oraz z proponowanego podejścia są porównywane dla różnych przekrojów płyt. Uzyskane wyniki dają dobrą zbieżność.

15

Cyclic performance and shear resistance design of asymmetric diagonal stiffened beam-only-connected corrugated steel plate shear walls

Zheng Hong, Zhang Zhibin, Jiang Liqiang, Hu Yi, Wang Wei

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 4

art. no. e183, 2022

EN

The corrugated plate steel shear walls (CSPWs) are widely used as lateral force resistant members in high-rise buildings. However, buckling failure still easily occurred on corrugated steel plates subjected to earthquake loads, which is not good for the energy dissipation of structures. In this paper, the asymmetric diagonal stiffened beam-only-connected corrugated steel plate shear wall (ASW) is proposed. A test-validated FE modeling method is used to investigate the seismic performance of ASW, and the results are compared with the results of unstiffened corrugated steel plate shear wall (USW). Then parametric studies on the height-to-thickness ratio, wavelength, wave height of the corrugated plate and width-to-thickness ratio of the stiffeners are performed to investigate their effects on the seismic performance of ASW. Finally, a simplified theoretical model is developed to calculate the shear resistance of ASW, and the results are validated by tests and FE results. The results show that: (1) compared to the USW, the yield load and ultimate load of ASW increase 11.7% and 13.2%, respectively; (2) the theoretical calculation results are basically consistent with the FE and test results, and the errors between them are within ± 15%. These results can be used for seismic enhancement of CSPWs and seismic design of ASW.

16

A parametric analysis of free vibration and bending behavior of sandwich beam containing an open-cell metal foam core

Garg A., Chalak H. D., Belarbi M. O., Zenkour A. M.

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e56, 2022

EN

Free vibration and bending behavior of sandwich beams containing open-cell metal foam core are studied in the present work using zigzag theory. Hamilton’s principle and the principle of minimum potential energy are applied for determining the governing equations for free vibration and bending behavior, respectively. Three types of distribution of pores are used during the present study. The influence of the distribution of pores, end condition, thickness of the core, foam coefficients on beam behavior is studied in detail. The face sheets are assumed to be made up of the same material like foam. It was noticed that the nature of the distribution of pores and the end conditions widely determine the behavior of the beam.

17

Design and performance analysis of a mechanically coupled spring compliant to out-of-plane oscillation

Nguyen Duong Van, Nguyen Chien Quoc, Dang Hieu Van, Chu Hoang Manh

Archive of Mechanical Engineering

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2022

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LXIX, nr 4

629--643

EN

In this paper, a spring system symmetrically arranged around a circular plate compliant to out-of-plane oscillation is proposed. The spring system consists of single serpentine springs mutually coupled in a plane. Three theoretical mechanical models for evaluating the stiffness of the spring system are built, which are based on the flexural beam, Sigitta, and serpentine spring theories and equivalent mechanical spring structure models. The theoretically calculated results are in good agreement with numerical solutions using the finite element method, with errors less than 10% in the appropriate dimension ranges of the spring. Compared to similar spring structures without mechanical coupling, the proposed mechanically coupled spring shows advantage in suppressing the mode coupling.

18

Study on the mechanical properties of a type of spherical bearing

Yang Yingfang, Zhang Yan, Ju Jinsan

Journal of Theoretical and Applied Mechanics

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2021

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Vol. 59 nr 4

539--550

EN

The spherical bearing is widely used in highways, bridges and long-span structures. In order to study mechanical properties of a large-scale spherical bearing, a full-scale finite element model of the spherical bearing was established by using ABAQUS software, and the mechanical properties of the spherical bearing under four working conditions were simulated respectively when the upper bearing plate had different inclination angles. The ultimate bearing capacity of the spherical bearing under vertical tension was analyzed emphatically. The research results show that, in practical applications, the change in bearing capacity caused by the inclination angle of the upper bearing plate should be considered, and the wedge-shaped part should be strengthened.

19

L ∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition

Miloudi Madjda, Saadi Samira, Haiour Mohamed

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

452--461

EN

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.

20

Experimental and numerical evaluation of quasi-static indentation behaviour of laminates with polypropylene matrix

Mahdad M’hamed, Benidir Adel, Belaidi Idir

Composites Theory and Practice

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2021

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R. 21, nr 4

127--134

EN

This paper presents an analysis of the damage process of composite laminates subjected to low-velocity quasi-static indentation (QSI) load. The laminates were prepared using the compression moulding technique. The composites were made from orthotropic layers with E-glass or steel fibres and a polypropylene matrix. The quasi-static indentation tests were carried out at three levels of indentation energy under low-velocity. The experimental results reveal that using steel fibres increases the perforation threshold, which alludes to the importance of the fibre type in delineating damage regions. In contrast, the evolution of the damage and the perforation resistance of glass fibre reinforced laminates is somewhat different. A numerical model based on a finite element program was developed to understand the mechanisms of damage evolution in the laminates. It involves implementing the Matzenmiller-Lubliner-Taylor (MLT) damage model. A comparison between the experimental and numerical results was also made.