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1

Application of the generalized nonlinear constitutive law in 2D shear flexible beam structures

Mrówczyński Damian, Gajewski Tomasz, Garbowski Tomasz

Archives of Civil Engineering

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2021

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Vol. 67, nr 3

157--176

EN

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

PL

W artykule przedstawiono zmodyfikowaną metodę elementów skończonych do nieliniowej analizy płaskich konstrukcji belkowych. Aby wziąć pod uwagę wpływ podatności na ścinanie, zastosowano belkowy element Timoshenki. Zaproponowany algorytm umożliwia stosowanie złożonych praw materiałowych bez konieczności implementacji zaawansowanych modeli konstytutywnych w procedurach elementów skończonych. Metoda jest łatwa do wdrożenia w powszechnie dostępnym oprogramowaniu CAE do liniowej analizy konstrukcji belkowych. Pozwala to na rozszerzenie funkcjonalności tych programów o nieliniowości materiałowe. Wykorzystując odkształcenia konstrukcji, obliczone z przemieszczeń węzłów oraz przedstawione tutaj uogólnione nieliniowe prawo konstytutywne, możliwe jest iteracyjne zmniejszanie sztywności konstrukcji na zginanie, ściskanie/rozciąganie i ścinanie. Stosując model belkowy z przekrojem wielowarstwowym oraz uogólnionymi odkształceniami i naprężeniami w celu uzyskania reprezentatywnego prawa konstytutywnego, łatwo jest modelować nie tylko złożone przekroje wielomateriałowe, ale także zaawansowane nieliniowe prawa konstytutywne (np. osłabienie materiału przy rozciąganiu). Zaproponowana metoda została zaimplementowana w środowisku MATLAB, a jej działanie pokazano na kilku przykładach numerycznych. Przeanalizowano przekroje dwuteownika stalowego oraz dwuteownika stalowego obetonowanego dla różnych wartości smukłości. Aby zweryfikować dokładność obliczeń, wyniki porównano z wartościami otrzymanymi z komercyjnego oprogramowania CAE. Porównanie pokazało dobrą korelację między modelem referencyjnym a proponowaną metodą.

2

A non-singular analytical technique for reinforced noncircular holes in orthotropic laminate

Mohan Pradeep, Kumar R. Ramesh

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

92--105

EN

The intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole Edg for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

3

Three-dimensional numerical model of solidification with motion of the liquid phase

Skrzypczak T., Węgrzyn-Skrzypczak E.

Archives of Foundry Engineering

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2011

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Vol. 11, iss. 2

127-132

EN

The paper presents numerical modeling of solidification process with convective motion of the liquid phase, generated both in the liquid and mushy zones. The transition region between the areas filled with liquid and solid is treated as a porous medium, which incorporates the suppression of fluid motion caused by the solid phase growth. Mathematical and numerical models of the phenomenon for threedimensional domain are presented. To solve the problem Finite Element Method is used. The results obtained from numerical simulation are presented and discussed.

PL

W pracy przedstawiono model matematyczny i numeryczny procesu krzepnięcia z uwzględnieniem ruchów konwekcyjnych fazy ciekłej, generowanych zarówno w strefie ciekłej jak i stało-ciekłej. Strefa przejściowa pomiędzy obszarem cieczy i ciała stałego traktowana jest jako ośrodek porowaty, w którym uwzględniono tłumienie ruchu cieczy wywołane narastaniem fazy stałej. Przedstawiono model matematyczny i numeryczny rozważanego procesu dla obszaru trójwymiarowego. Do rozwiązania zagadnienia wykorzystano metodę elementów skończonych. Przedstawiono i omówiono uzyskane wyniki.

4

Evaluation of bone stress distribution around thinly hydroxyapatite coated dental implant using finite element analysis

Ozeki K., Fukunaga K., Yaguchi T., Funakubo A., Asaoka T., Fukui Y., Aoki H.

Biocybernetics and Biomedical Engineering

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2007

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Vol. 27, no. 1-2

89-94

EN

Dental implants were coated with hydroxyapatite (HA) by the sputtering technique. The influences of the HA film thickness on the bone stress distribution was investigated using the three-dimensional finite element analysis. In this analysis, force of 100 N axial load was applied on the non-coated, thickly HA coated, and thinly HA coated titanium implants The maximum equivalent bone stresses were 21.5, 8.55 and 6.33 MPa for the non-coated, thickly HA coated, and thinly HA coated cylinder type implants, respectively. The bone stress of the screw type implants was 29.0, 9.20 and 9.03 MPa, respectively. The maximum bone stress of the thinly HA coated implant was lower than in the other implants. Eight types of the implant shape for the thinly HA coated implant were also designed, and the tiered neck type implant showed the lowest maximum bone stress in all the types.

5

The application of the finite element method in diagnostics of electrical drives

Fiser R., Ferkolj S.

Journal of Technical Physics

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2002

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Vol. 43, no 4

399-403

EN

The paper presents the application of the finite element method for predicting the performance of induction motor having asymmetry of stator and/or rotor winding due to the different combination and propagation of faults gained during heavy-duty operation. Quantities like magnetic vector potential, flux density, force components, rotor and stator currents, mutual and leakage inductance are determined very precisely. The detailed insight in magnetic field distribution of a squirrel cage induction motor, forms the basis for further evaluation of its operational behaviour. Increasing anomaly in magnetic field distribution due to the increasing stage of faults propagation results in a degradation of steady-state and dynamic performance of the induction motor and can be evaluated with computer simulation eliminating expensive and time-consuming laboratory tests.

6

Newly re-designed magnetic head for wire rope NDT

Miljavec D., Knez S.

Journal of Technical Physics

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2002

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Vol. 43, no 4

433-441

EN

The aim of the present paper is to analyse a newly re-designed magnetic head. Basic use of this head is in non-destructive testing (NDT) of wire ropes. The magnetic head system is composed of two main areas and three main parts. These areas are: magnetic flux leakage area in central region, and eddy current magnetic field area in outer side region of magnetic head. The analyses were carried out by analytic approach and by the finite element method. The value of induced voltage in flux leakage pick-up coils was calculated by axisymmetric 2D magnetostatic finite element analysis made by ferromagnetic rod to simulate the wire rope. Meanwhile, voltage induced by changes in eddy current magnetic field was calculated by a 2D transient linear motion finite element analysis. All numerically calculated results were compared with the measured ones on a geometrically similar ferromagnetic rod. Also, we have presented the measured results carried out by newly re-designed magnetic head on real steel wire rope with anomalies.

7

Motional finite element simulation of magnetic brakes and solid rotor induction machines

De Gersem H., Hameyer K.

Journal of Technical Physics

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2002

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Vol. 43, no 4

389-397

EN

The torques of a magnetic brake and a solid rotor induction machine, fed by sinusoidal voltage sources, are simulated by a motional finite element method. Oscillatory solutions occurring for motional models with elevated velocities, are prevented by adaptive mesh refinement relying upon intermediate solutions stabilised by upwinded finite element test functions. A relaxed successive approximation deals with the non-linear material properties. The connections of the conductors and windings within the finite element model to external loads, impedances and supplies are represented by an electric circuit and added to the system of equations. The technical examples indicate the advantages of the motional formulation.

8

Force calculation of the laboratory implementation of a radial active magnetic bearing

Polajzer B., Dolinar D., Stumberger G., Hameyer K.

Journal of Technical Physics

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2002

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Vol. 43, no 4

453-457

EN

Performances of the controlled active magnetic bearings can be sufficiently improved with the exact knowledge of the bearing force in the entire operating range. Therefore the magnetic force calculation of the laboratory implementation of a radial magnetic bearing, using 2D finite element method, is presented in the paper. Two methods for the force calculation are used, where both, i.e. the Maxwell stress tensor method and the virtual work method, give very close results. The verification of the bearing force calculation is performed by their comparison with measurements. The obtained results make it possible to perform a robust control design in the entire operating range.

9

Flux-weakening and output power capability estimation of interior permanent magnet synchronous motor in variable speed drive applications

Stumberger B., Hamler A., Jesenik M., Gorican V., Trlep M.

Journal of Technical Physics

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2002

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Vol. 43, no 4

489-494

EN

Flux-weakening and output power capability estimation of the four-pole interior permanent magnet synchronous motor (IPMSM) determined from the finite element method (FEM) analysis of magnetic conditions is presented. The influence of the iron loss on the output power capability (OPC) and the constant-power speed range (CPSR) of the tested IPMSM is included in the analysis by the posterior iron loss calculation. Results of the calculations are partially verified by the measurements.

10

Electromagnetic field analysis of 2D-3D structure of switched reluctance motors (disc-type)

Wiak S., Drzymała P., Welfle H.

Journal of Technical Physics

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2002

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Vol. 43, no 4

505-513

EN

In the paper comparative studies of 2D-3D disc-type Switched Reluctance Motor (SRM) structures are performed. The calculation of magnetic field distributions and the static torque characteristics have been computed by means of Finite Element Method (FEM) for 2D and 3D motor structures. It has been emphasized that the calculations of the model structure (thanks to axial symmetry) have been done for a half of the volume while the boundary conditions are predefined. 3D structure of the model motor is built up, then the mesh is generated for number of elements exceeding 100 000. The results of 3D calculations are presented in the form of the static torque characteristics and magnetic flux curves versus rotor angular positions and current densities in the stator winding as well. Disc-type SR motors thanks to their specific structures are commonly used in automotive system, servo-drives, etc. The motor structure consists of the stator core toroidally shaped in which slots are placed on both sides of the active surface; moreover stator windings are wounded as Gramma type (made of identical coils surrounding the stator core). SRM are proposed to be mounted at the wheel of gearless electric vehicles (small cars, wheelchair, scooters, etc.).

11

Comparative study of shunt reactor structures by field models

Wiak S., Drzymała P., Welfle H.

Journal of Technical Physics

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2002

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Vol. 43, no 4

513-520

EN

The paper presents the results of field analysis of the shunt reactor 3D structure based on a field method. The magnetic field computations have been carried out for the shell-type and two-limb structure of a one-phase shunt reactor, then to be assembled as a 3-phase unit. The field calculations are performed for 3-D model reactor structures with different number of core slices (different number of air gaps, but with constant intermediate - slice air gap length). The 3D structure of the model reactor is built up, then the mesh is generated for a number of elements exceeding 200 000. The optimal value of the ratio d/g (height of the intermediate-slice air gap/height of the limb slice) and the ratio d/g (height of the intermediate-slice air gap/diameter of the limb) are evaluated leading to minimum values of the weight and capitalized cost of the device.