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1
Content available remote Experimental validation of a novel thin-walled beam prototype
EN
In this paper, an experimental validation of a novel beam prototype is performed. Tensile tests, both until rupture and on the elastic domain were done in order to determine the material properties. They were used then in Finite Element Analysis model built in ANSYS Mechanical APDL. Three experimental tests were done to the prototype, and, in order to minimize errors, the average value of the three tests determined, and compared with results obtained from the numerical model. It was shown that it was possible to manufacture the beam by the presented manufacturing methodology. An acceptable correlation between the numerical an experimental results was found.
EN
In this work, novel types of internally reinforced hollow-box beams were structurally optimized using a Finite Element Updating code built in MATLAB. In total, 24 different beams were optimized under uncoupled bending and torsion loads. A new objective function was defined in order to consider the balance between mass and deflection on relevant nodal points. New formulae were developed in order to assess the efficiency of the code and of the structures. The efficiency of the code is determined by comparing the Finite Element results of the optimized solutions using ANSYS with the initial solutions. It was concluded that the optimization algorithm, built in Sequential Quadratic Programming (SQP) allowed to improve the effective mechanical behavior under bending in 8500%, showing a much better behavior than under torsion loadings. Therefore, the developed algorithm is effective in optimizing the novel FEM models under the studied conditions.
EN
In this work, novel types of internally reinforced hollow-box beams were structurally optimized using a Finite Element Updating code built in MATLAB. In total, 24 different beams were optimized under uncoupled bending and torsion loads. A new objective function was defined in order to consider the balance between mass and deflection on relevant nodal points. New formulae were developed in order to assess the efficiency of the code and of the structures. The efficiency of the code is determined by comparing the Finite Element results of the optimized solutions using ANSYS with the initial solutions. It was concluded that the optimization algorithm, built in Sequential Quadratic Programming (SQP) allowed to improve the effective mechanical behavior under bending in 8500%, showing a much better behavior than under torsion loadings. Therefore, the developed algorithm is effective in optimizing the novel FEM models under the studied conditions.
EN
Novel types of internally reinforced thin-walled beams are subjected to a feasibility analysis in terms of their effective mechanical behaviour. The novel beams are subjected to bending and torsion uncoupled loadings and are analysed in terms of their stiffness behaviour in static analysis. The models were built using the commercial Finite Element Method (FEM) software ANSYS Mechanical APDL. The feasibility of the models was determined by the comparison of the stiffness behaviour of the novel beams with simple hollow-box beams, having the same mass and dimensions, with the exception of the thickness. An efficiency parameter is used in order to determine the feasibility of the studied geometries. It is found that the novel geometries represent a great improvement under bending loading, better than under torsion loading. Nevertheless, for bending and torsion combined loadings, if bending loads are predominant, the beams can still be interesting for some applications, in particular those with mobile parts.
EN
Sandwich geometries, mainly panels and beams, are widely used in several transportation industries, namely aerospace, aeronautic and automotive. Sandwich geometries are known for their advantages in structural applications: high specific stiffness, low weight, and possibility of design optimization prior to manufacturing. This study aims to know the influence of the number of reinforcements (ribs), and of the thickness on the mechanical behaviour of sandwich beams subjected to bending and torsion uncoupled loadings. In this study, four geometries are compared: simple web-core beam, corrugated core, honeycomb core, and joined honeycomb core. The last three are asymmetric, due to the use of odd number of ribs. The influence of the geometry on the results is discussed by means of a parameter that establishes a relation between the stiffness behaviour and the mass of the object. It is shown that all relations are non-linear, despite the elastic nature of the analysis in both the FEM software and in the practical application.
EN
A polymeric split Hopkinson pressure bar technique (SHPB) is preferred for testing materials with low mechanical impedance. However, the use of polymeric bars requires additional analysis for data reduction, temperature complications and additional restrictions compared with traditional metallic pressure bars. A viscoelastic material, such as PMMA, exhibits both wave attenuation and wave dispersion. When a wave travels through a polymer bar, the wave amplitude decreases due to attenuation and the wave shape becomes distorted. Therefore, signals measured at given positions on a viscoelastic bar do not represent the pulse at another position along the pressure bar without complex corrections. This paper is concerned with the problem of correction of dispersion and attenuation of waves in the viscoelastic SHPB. It has been demonstrated that the Fast Fourier Transform (FFT) spectral analysis method used to reconstruct wave profiles on the measured signals which are being distorted by wave attenuation and dispersion effects is valid and allows for obtaining satisfactory results for tire rubber.
7
Content available On nonlocal modeling in continuum mechanics
EN
The objective of the paper is to provide an overview of nonlocal formulations for models of elastic solids. The author presents the physical foundations for nonlocal theońes of continuum mechanics, followed by vanous analytical and numeńcal techniques. The characteristics and range of practical applications for the presented approaches are discussed. The results of numerical simulations for the selected case studies are provided to demonstrate the properties of the described methods. The paper is illustrated with outcomes from peridynamic analyses. Fatigue and axial stretching were simulated to show the capabilities of the developed numeńcal tools.
PL
W artykule dokonano przeglądu nielokalnych sformułowań dla mechaniki bryły odkształcalnej. Autor przedstawia podstawy fizyczne nielokalnych teorii mechaniki kontinuum oraz dokonuje przeglądu technik analitycznych i numerycznych stosowanych w modelach matematycznych. W pracy przedyskutowano charakterystyki oraz zakres praktycznych zastosowań wspomnianych technik modelowania. Ocena własności nielokalnych modeli została przeprowadzana na podstawie wyników symulacji numerycznych dla wybranych typów analiz z zastosowaniem perydynamiki. Przedstawiono wyniki symulacji zmęczeniowych oraz jednoosiowego rozciągania, uzyskane przy użyciu opracowanych narzędzi analiz symulacyjnych.
PL
W pracy przedstawiono algorytm wprowadzania więzów pozwalających na uzyskanie ciągłego przejścia od modelu powłokowego pierwszego rzędu (Reissnera-Mindlina) do modelu trójwymiarowego poprzez strefę przejściową. W modelu powłokowym ma miejsce warunek braku odkształcenia w kierunku poprzecznym, natomiast w przypadku modelu trójwymiarowego warunek ten nie występuje. W obszarach przejściowych istnieje stan pośredni. Wynikające ze wspomnianego warunku więzy są w pracy wprowadzane na podstawie metody funkcji kary, a nie metody kolokacji, która nie jest w pełni efektywna. Skuteczność nowego algorytmu potwierdzono przykładami numerycznymi.
EN
In this research we present the algorithm of introduction of the constraints allowing the continuous transition from the first-order (Reissner-Mindlin) shell model, through the transition zone, up to the three-dimensional model. In the shell model the condition of lack of elongation in the transverse direction is assumed. This condition is not valid in the case of the three-dimensional model. In the transition zones the stress state is intermediate. The constraints resulting from this condition are introduced by means of the penalty method in this paper, in contrast to our previous attempts, where the collocation method was applied to the element nodes. Note that the previous approach appeared to be only partially efficacious. The effectiveness of the new algorithm is supported by numerical examples.
PL
Prezentowane badania dotyczą analizy struktur o złożonym opisie mechanicznym przy zastosowaniu adaptacyjnych elementów przejściowych. W niniejszej pracy skupiono się na analizie płyt zginanych oraz struktur zdominowanych membranowo. Uzyskane wyniki porównano pod kątem zastosowanego wariantu modelu przejściowego: klasycznego modelu przejściowego oraz modelu po wprowadzeniu modyfikacji algorytmu obliczeniowego. W obu przypadkach zestawiono obrazy naprężeń oraz krzywe zbieżności rozwiązań problemów struktur złożonych.
EN
Our research concerns the analysis of structures of complex mechanical description using adaptive transition elements. The present work focuses on the analysis of plates and membrane-dominated structures. The presented results are compared in relation to the applied transition models: the classical model and the model after introduction of modification of the calculation algorithm. In both cases the stress distributions and the convergence curves of the solutions to complex structure problems are compared.
EN
In this paper the possibilities and limits of solving equations of motion with non-material boundary conditions are investigated. Therefore the system of equations for the nonstationary motion of a three-dimensional body is derived. To overcome the time dependency of the boundary conditions an Arbitrary Lagrangean Eulerian (ALE) kinematics is used. In combination with the introduced operator notation a very clear formulation of the system of the equations of motion is derived. The model of a perfect flexible and inextensible string is used as an illustration. In this case analytical solutions are given in a closed form for an example with one non-material boundary condition. This allows studying the characteristics of such boundary conditions.
PL
Zaproponowano numeryczny model dynamiki membrany kołowej utwierdzonej na obwodzie w zakresie ugięć trwałych o wartości porównywalnej z jej grubością, aż do jej zniszczenia. Opisano sformułowania problemu, stosowane przy mniejszych ugięciach oraz przytoczono tzw. wstępny model numeryczny obejmujący analityczne sformułowanie membranowe z jednym stopniem swobody i ciągłym rozkładem masy oraz skalarny wariant różnicowej metody przeganiania. Przedyskutowano przykładowe wyniki obliczeń według tego modelu, wskazując na jego pewne niedogodności. W konsekwencji zaproponowano bardziej złożony model numeryczny obejmujący analityczne sformułowanie problemu w ujęciu z dwoma stopniami swobody i ciągłym rozkładem masy oraz wektorowym wariantem różnicowej metody przeganiania.
EN
A numerical model of the dynamics of a circular membrane, fixed at its periphery for deflections ranging from a value comparable with its thickness until its destruction is proposed. Problem formulations used in smaller deflections as well as the initial numerical model, comprising the analytical formulation with one degree of freedom and continuous weight displacement and a scalar variant of the numerical method of outstripping have been described. Sample calculation results, given by this model, were discussed, indicating some inconvenience of the model. Consequently, more complex numerical model, comprising analytical formulation with two degrees of freedom and continuous weight displacements and a vector variant of the numerical method of outstripping has been proposed.
12
Content available remote A coupled multi-physics model for induction heat treatment processes
EN
Several multi-physics problems are coupled in induction heat treatment processes. This makes them often difficult to control and understand. For instance, anticipations or minimizing distortions generated by such a process usually may require long and costly try-outs. A specific computational tool has been developed to help designing and optimizing this class of heat treatment operations. The tool is based on a multi-physics model which couples electromagnetic equations, heat transfer, mechanical response of the material, and metallurgical phase changes. This paper gives a short presentation of this tool. Emphasis is placed on analyzing which phenomena have to be taken into account. Simulations of the induction heating of a crankshaft are also presented.
PL
Obróbka cieplna z nagrzewaniem indukcyjnym obejmuje szereg zjawisk fizycznych. W konsekwencji ten proces jest trudny do sterowania i zrozumienia. Przykładowo, przewidywanie i minimalizacja zniekształcenia wyrobu wywołanego nagrzewaniem indukcyjnym wymaga wielu kosztownych prób. Opracowano dedykowane narzędzie numeryczne dla wspomagania projektowania tego typu operacji obróbki cieplnej. Narzędzie opiera się na wielo fizycznym modelu, który łączy równania elektromagnetyczne, transportu ciepła, mechanicznej odpowiedzi materiału i metalurgicznego opisu przemian fazowych. W artykule opisano podstawy modelu. Nacisk położono na ocenę, które mają najistotniejsze znaczenie i powinny być uwzględnione w analizie. Zaprezentowano wyniki symulacji nagrzewania indukcyjnego wału korbowego.
EN
Dispersion as the material property is discussed in the paper. The definition, origination and dispersion analysis are presented. The dispersive and non-dispersive constitutive models are studied. The mechanical problem of inelastic deformation of solids is considered. The evolution of viscoplastic flow describes material hardening and softening with formation of strain localization zone. Wave character and dispersion are recognized as fundamental elements in formulation and solution in dynamic, rate dependent processes with strain localization and shear band propagation. The physical and numerical aspects of dispersion clarify the development of deformation, stress or energy distribution and verify the solution procedure. The paper exposes the importance of dispersion phenomenon that should be carefully investigated in class of solid mechanics problems. The numerical results confirm the role of dispersion effects.
14
Content available remote High-accuracy discretization methods for solid mechanics
EN
Novel high-accuracy computational techniques for solid mechanics problems are presented. They include fourth-order and arbitrary-order finite difference methods based on Pade-type differencing formulas and a meshless method which uses radial basis functions in a "finite difference'' mode. Some results illustrating high performance of the suggested numerical methods are displayed.
PL
Obserwowane obecnie coraz szersze stosowanie metod eksperymentalnych w mechanice ciała stałego, jest spowodowane osiągnięciem granicy możliwości korzystania z modeli liniowych, jak również pojawiającą się koniecznością obserwacji nowych zjawisk i nowych procesów. Przyczynił się do tego również, szybki rozwój metod eksperymentalnych, dzięki zastosowaniu technik do niedawna stosowanych jedynie w laboratoriach fizyków. Ponadto pojawiły się nowe możliwości stworzone przez zastosowanie komputerów do zbierania i przetwarzania danych.
EN
Widespread application of experimental methods observed nowadays has more emerged as a result of the limits being reached by the linear approaches, together with the necessity for new states and processes to be observed. On the other hand, it should be noted that experimental methods have been developed rapidly for the last decade due to application of the techniques used until now m physical laboratories only, revealing new capabilities emerging from advanced computer methods of data acquisition and data processing.
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