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1

Nonlinear buckling mode transition analysis of axial-thermal-electrical‑loaded FG piezoelectric nanopanels incorporating nonlocal and couple stress tensors

Rao Rui, Ye Zijie, Yang Zhicheng, Sahmani Saeid, Safaei Babak

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 3

art. no. e125

EN

Piezoelectric nanostructures are one of the essential components in the design of electromechanical systems and devices at nanoscale. In the present exploration, a size-dependent panel model accommodating the both softening and stiffening features is introduced for nonlinear stability characteristics of functionally graded (FG) piezoelectric cylindrical nanopanels under combinations of axial mechanical load with external electric actuation and temperature change. In accordance with this objective, an efficient numerical strategy based upon the moving Kriging meshfree (MKM) technique is employed within the framework of the nonlocal couple stress (NCS) continuum elasticity. The established NCS-based numerical model has the capability to incorporate the buckling mode transition phenomenon as well as satisfying the function property of Kronecker delta via imposing essential boundary conditions with no use of predefined mesh and directly at the associated nodes. The NCS-based nonlinear equilibrium curves are traced including the modal transition corresponding to various parameter investigations of FG piezoelectric nanopanels. It is deduced that the nonlocal stress tensor leads to increase the difference between the minimum postbuckling loads associated with the first and second buckling modes, while the couple stress tensor causes to reduce it. It is also demonstrated that by changing the sign of electric actuation from negative to positive, the softening character of nonlocality as well as the strengthening character associated with the couple stress size dependency become a bit more significant. Furthermore, the roles of both unconventional stress tensors are more prominent in the value of the second bifurcation point in comparison with the first one.

2

Isogeometric nonlinear bending analysis of porous FG composite microplates with a central cutout modeled by the couple stress continuum quasi-3D plate theory

Rao Rui, Sahmani Saeid, Safaei Babak

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

214--230

EN

In the present investigation, by putting the isogeometric finite element methodology to use, the nonlinear flexural response of composite rectangular microplates having functionally graded (FG) porosity is predicted incorporating couple stress type of small scale effect. To accomplish this analysis, a non-uniform kind of rational B-spline functions are employed for an accurate geometrical description of cutouts with various shapes located at the center of microplates. The modified couple stress continuum elasticity is implemented within the framework of a new quasi-three-dimensional (quasi-3D) plate theory incorporating normal deflections with only four variables. By refining the power-law function, the porosity dependency in conjunction with the material gradient are taken into consideration in a simultaneous scheme. The couple stress-based nonlinear flexural curves are achieved numerically based upon a parametrical study. It is demonstrated that for a larger plate deflection, the role of couple stress type of small scale effect on the nonlinear bending curves of porous FG composite microplates is highlighted. It is seen that the gap between nonlinear flexural responses associated with different through-thickness porosity distribution schemes is somehow higher by taking the couple stress effect into account. Also, it is observed that the existence of a cutout at the center of composite microplates makes a change in the slope of their nonlinear flexural curve.

3

Chemical reaction effects on MHD flow past an impulsively started isothermal vertical plate with uniform mass diffusion

Chandrakala P., Narayana Bhaskar P.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

419--426

EN

A numerical technique is employed to derive a solution to the transient natural convection flow of an incompressible viscous fluid past an impulsively started infinite isothermal vertical plate with uniform mass diffusion in the presence of a magnetic field and homogeneous chemical reaction of first order. The governing equations are solved using implicit finite-difference method. The effects of velocity, temperature and concentration for different parameters such as the magnetic field parameter, chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the fluid velocity decreases with increasing the chemical reaction parameter and the magnetic field parameter.

4

Problem of the moving boundary in continuous casting solved by the analytic-numerical method

Grzymkowski R., Pleszczyński M., Hetmaniok E.

Archives of Foundry Engineering

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2013

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Vol. 13, iss. 1

33--38

EN

Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

5

Axisymmetric modeling of ultrashort-pulse laser interactions with thin metal film

Majchrzak E., Dziatkiewicz J.

Archives of Foundry Engineering

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2011

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Vol. 11, iss. 4

182-186

EN

The hyperbolic two-temperature model is used in order to describe the heat propagation in metal film subjected to an ultrashort-pulse laser heating. An axisymmetric heat source with Gaussian temporal and spatial distributions has been taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.

6

Identification of solidification process parameters

Mendakiewicz J.

Computer Assisted Mechanics and Engineering Sciences

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2010

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Vol. 17, no. 1

59-73

EN

In the paper, the identification problems connected with estimation of cast iron and mould thermophysical parameters are discussed. The additional information necessary to solve the problem results from the knowledge of cooling (heating) curves at the set of points from casting (mould) domain. The course of cooling (heating) curves results from the temperature measurements done in the real conditions of technological process, but at the present stage of research the numerical solution of direct problem plays the role of measured temperatures. In this place the problem of optimal sensors position in a system castingmould appears. Both the choice of measuring points and also the solution of inverse problem, using the gradient methods, require the application of sensitivity analysis methods. The theoretical considerations are illustrated by the examples of computations. The numerical algorithms presented base on the finite difference method (2D problems are considered).

7

Generalization of temporary temperature field correction method in numerical modelling of solidification

Mochnacki B., Szopa R.

Archives of Foundry Engineering

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2008

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Vol. 8, iss. 1 spec.

219--222

EN

The temporary temperature field correction method constitutes a very effective tool for numerical modelling of solidification. The most general version of this algorithm has been presented by Mochnacki [1] and Szopa [2], The basic idea of the method consists in the computations of temperature field for homogeneous domain (e.g. corresponding to molten metal or solid body) and obtained in this way a discrete temperature field for time t is in adequate way 'rebuilt' using the simple mathematical formulae. In this way the non-homogeneous geometry of solidifying casting is taken into account. This approach can be used in the case of macro modelling, in particular when the one domain approach [3, 4, 5, 6] is applied. The basic assumption of the algorithm presented in [ 1 ] and [2] was that the substitute thermal capacity (STC) [7, 8] of casting material can be approximated by a piece-wise constant function. In this paper the generalization of the method on a case of practically optional function describing a course of STC. In the final part of the paper one can find the example of numerical simulations using this approach.

PL

Metoda poprawiania chwilowego pola temperatury jest bardzo efektywnym narzędziem możliwym do wykorzystania przy modelowaniu procesu krzepnięcia. Przedstawioną w pracach Mochnackiego [1] i Szopy [2] wersję dotyczącą schodkowych zmian zastępczej pojemności cieplnej uogólniono na przypadek funkcji o dowolnym przebiegu.

8

Estimation of boundary heat flux between casting and mould using the global function specification method

Majchrzak E., Mochnacki B., Suchy J. S.

Archives of Foundry Engineering

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2008

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Vol. 8, iss. 1 spec.

193--198

EN

In the paper the global function specification method is used for identification of time dependent boundary heat flux between casting and mould. The additional information necessary to solve an inverse problem results from the knowledge of heating curves at the points selected from mould sub-domain. The mathematical model of thermal processes proceeding in the casting domain bases on the one domain approach. As the example, the ID system created by casting made from NiCr28W alloy and ceramic mould is considered. On the stage of numerical solution of direct problem and additional one the finite difference method has been applied.

PL

W pracy wykorzystano globalną metodę specyfikacji funkcji do identyfikacji zależnego od czasu strumienia ciepła wymienianego między odlewem a formą odlewniczą. Dodatkowa informacja niezbędna do rozwiązania sformułowanego zadania odwrotnego wynika ze znajomości krzywych nagrzewania w wybranych punktach z obszaru formy. Model matematyczny procesów cieplnych zachodzących w obszarze odlewu bazuje na podejściu odpowiadającym metodzie jednego obszaru. Przykładem ilustrującym rozważania teoretyczne jest rozwiązanie zadania dotyczącego procesów cieplnych w odlewie wykonanym ze stopu NiCr28W wytwarzanego w ceramicznej formie odlewniczej (zadanie ID). Na etapie realizacji numerycznej wykorzystano jawny schemat metody różnic skończonych dla nieliniowych.

9

Application of identification methods in solidification process modelling

Mendakiewicz J.

Archives of Foundry Engineering

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2008

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Vol. 8, iss. 1 spec.

203-210

EN

In the paper the identification problems connected with the estimation of cast iron and mould thermophysical parameters are discussed. The additional information necessary to solve the problem results from a knowledge of cooling (heating) curves at the set of points from casting (mould) domain. The course of cooling (heating) curves results from the temperature measurements done in the real conditions of technological process, but on the present stage of research the numerical solution of direct problem plays a role of measured temperatures. The identification algorithm basing on the gradient methods is used to estimate the parameters of casting-mould system (a case of simultaneous estimation of bigger number of parameters is also considered). On the stage of numerical realization the FDM is used (2D task). In the final part of the paper the examples of computations are shown.

PL

W pracy przedstawiono problemy identyfikacji związane z estymacją parametrów odlewu żeliwnego i masy formierskiej. Dodatkową informacją niezbędną do rozwiązywania tego typu zadań jest znajomość krzywych stygnięcia (nagrzewania) w zbiorze punktów odlewu/formy. Krzywe stygnięcia (nagrzewania) można otrzymać na podstawie pomiarów wykonanych w rzeczywistych warunkach przebiegu procesu. Na obecnym etapie badań krzywe te uzyskiwano poprzez rozwiązanie zadania bezpośredniego dla zadanych wartości parametrów procesu. Algorytmy identyfikacji bazujące na metodach gradientowych zastosowano do estymacji parametrów występujących w układzie odlew-forma. W końcowej części artykułu pokazano przykłady obliczeń.

10

Estimation of fatigue damage caused by actual roads and maneuvers on proving ground

Farrahi G. H., Khalaj A.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 14, nr 1-2

90--96

EN

Purpose: The objective of this paper is to estimate the cumulative fatigue damage in a vehicle component and to calculate the number of cycles driven on the proving ground to achieve the equivalent accumulated fatigue damage in design life. Design/methodology/approach: In order to achieve our objective, using ADAMS software, standard roads and proving ground events on which the vehicle model was to be driven were simulated. The load time history results were applied to an FEM model created in MSC/Nastran. Modal transient dynamic analysis was used to obtain the stress time history in the test component. Findings: The results showed that fast cornering has a greater damage effect than slow and moderate cornering. For primary evaluation of fatigue life (in our case) the cornering analysis is sufficient. The proving ground events had much more destruction effect than actual roads as the fatigue damage accumulated on our test component. Driving 1568 cycles (2462 km) on a proving ground was equal to driving 200000 km on actual roads. Research limitations/implications: The next stage in this research may be to study the effect of dimensions of proving ground events on accumulated fatigue damage. Practical implications: By using CAE and VPG the time and cost of developing the new models of vehicles decreases. Originality/value: The number of cycles which should be driven on the studied proving ground to achieve the accumulated fatigue damage in design life has been esimated.

11

Multiscaling analysis of a nonlinear boundary value problem in lubrication theory

Aliu E., Shepherd J. J., Connell H. J.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 3

455-470

EN

The method of multiple scales, a long standing alternative to the method of matched expansions, is applied to the nonlinear boundary value problem modelling the operation of a one-dimensional gas lubricated slider bearing, at large values of the bearing number. Approximate expansions for the pressure profile, load bearing capacity and the location of the centre of pressure are obtained, and compared with the results of applying matched expansions and numerical techniques.

12

Numeryczne prognozowanie przepływów powietrza w wentylowanych pomieszczeniach. Cz. 2. Możliwości i ograniczenia związane z wykorzystaniem techniki CFD do prognozowania przepływów wentylacyjnych

Lipska B.

Ciepłownictwo, Ogrzewnictwo, Wentylacja

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2000

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R. 31, nr 1

30-33

PL

Przedstawiono możliwości i ograniczenia związane z wykorzystaniem techniki CFD do prognozowania przepływów wentylacyjnych.

13

Numeryczne prognozowanie przepływów powietrza w wentylowanych pomieszczeniach. Cz. 1. Charakterystyka techniki numerycznej mechaniki płynów CFD (dokończenie z n-ru 10/99)

Lipska B.

Ciepłownictwo, Ogrzewnictwo, Wentylacja

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1999

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R. 30, nr 11

33-35

PL

Przedstawiono charakterystykę techniki numerycznej mechaniki płynów CFD w zastosowaniu do modelowania przepływów powietrza wentylacyjnego.

14

Numeryczne prognozowanie przepływów powietrza w wentylowanych pomieszczeniach. Cz. 1. Charakterystyka techniki numerycznej mechaniki płynów CFD w zastosowaniu do modelowania przepływów powietrza wentylacyjnego

Lipska B.

Ciepłownictwo, Ogrzewnictwo, Wentylacja

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1999

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R. 30, nr 10

30-34

PL

Przdstawiono charakterystykę techniki numerycznej mechaniki płynów CFD w zastosowaniu do modelowania przepływów powietrza wentylacyjnego.