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1

Assessment of slope stability using classification and regression algorithms subjected to internal and external factors

Singh Sudhir Kumar, Chakravarty Debashish

Archives of Mining Sciences

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2023

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Vol. 68, no. 1

87--102

EN

This study aims at developing a machine learning based classification and regression-based models for slope stability analysis. 1140 different cases have been analysed using the Morgenstern price method in GeoSlope for non-homogeneous cohesive slopes as input for classification and regression-based models. Slope failures presents a serious challenge across many countries of the world. Understanding the various factors responsible for slope failure is very crucial in mitigating this problem. Therefore, different parameters which may be responsible for failure of slope are considered in this study. 9 different parameters (cohesion, specific gravity, slope angle, thickness of layers, internal angle of friction, saturation condition, wind and rain, blasting conditions and cloud burst conditions) have been identified for the purpose of this study including internal, external and factors representing the geometry of the slope has been included. Four different classification algorithms namely Random Forest, logistic regression, Support Vector Machine (SVM), and K Nearest Neighbor (KNN) has been modelled and their performances have been evaluated on several performance metrics. A similar comparison based on performance indices has been made among three different regression models Decision tree, random forest, and XGBoost regression.

2

Thermal creep stress and strain analysis in a non-homogeneous spherical shell

Thakur P., Singh S. B., Pathania D. S., Verma G.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 4

1155--1165

EN

The purpose of this paper is to present study of thermal creep stress and strain rates in a non-homogeneous spherical shell by using Seth’s transition theory. Seth’s transition theory is applied to the problem of creep stresses and strain rates in the non-homogeneous spherical shell under steady-state temperature. Neither the yield criterion nor the associated flow rule is assumed here. With the introduction of thermal effect, values of circumferential stress decrease at the external surface as well as internal surface of the spherical shell. It means that the temperature dependent materials minimize the possibility of fracture at the internal surface of the spherical shell. The model proposed in this paper is used commonly as a design of chemical and oil plants, industrial gases and stream turbines, high speed structures involving aerodynamic heating.

3

Investigation of boundary condition effects on the stability of FGP beams in thermal environment

Nasirzadeh R., Behjat B., Kharazi M., Khabazaghdam A.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

1003--1014

EN

In this paper, stability and instability of Functionally Graded Piezoelectric (FGP) beams is investigated based on the Timoshenko beam theory. The material properties of the beam are considered to change gradually through thickness of the beam by a simple power law. By using the principle of minimum total potential energy, governing equations of the beam are derived. Stability behavior of the beam is predicted by solving the governing equations of the FGP beam. The results show that the homogeneity of boundary conditions plays a critical role in the stability of the FGP beam. While non-homogeneous boundary conditions lead to stable behavior of the FGP beam; homogeneous boundary conditions cause instability in the beam. By solving the eigenvalue equation of the FGP beam, the buckling load of the beam is obtained for the beams that have unstable behavior. Finally, the effects of various parameters on the buckling load of the unstable beam, such as power law index, temperature, applied voltage and aspect ratio are investigated, and the results are compared with the Euler-Bernoulli beam theory.

4

Metoda dyskretyzacji częściowej w analizie drgań własnych niejednorodnych płyt kołowych z wtrąceniami w postaci masy pierścieniowej

Żur K. K., Jaroszewicz J.

Biuletyn Wojskowej Akademii Technicznej

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2013

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Vol. 62, nr 3

145-156

PL

W pracy wykorzystano funkcję wpływu i metodę dyskretyzacji częściowej do analizy drgań własnych trojwarstwowej płyty kołowej typu ,,sandwich”, o stałej grubości i utwierdzonej na obwodzie. Wyznaczono sztywność zastępczą płyty oraz dokonano dyskretyzacji jej masy uwzględniając niejednorodność materiału. Konstruując macierz wpływu oraz wykorzystując wzory Bernsteina-Kieropiana, obliczono dokładne i przybliżone estymatory częstości drgań własnych płyty. W pracy zbadano wpływ pierścieniowej masy skupionej i symetrycznej niejednorodności materiału płyty na jej częstości drgań własnych.

EN

In the paper, influence function and method of partial discretization in free vibration analysis of non-homogeneous circular plate with constant thickness and clamped edges were presented. Discretization of mass of circular plate and calculation of replacing stiffness were achieved. Influence matrix and Bernstein-Kieropian’s estimators were calculated. The influence of additional annular mass and non-homogeneous material on a value of natural basic frequency of a sandwich circular plate was also presented.

5

Vibration of non-homogeneous visco-elastic circular plate of linearly varying thickness in steady state temperature field

Gupta A. K., Kumar L.

Journal of Theoretical and Applied Mechanics

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2010

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Vol. 48 nr 1

255-266

EN

An analysis is presented for free vibration of a non-homogeneous visco-elastic circular plate with linearly varying thickness in the radial direction subjected to a linear temperature distribution in that direction. The governing differential equation of motion for free vibration is obtained by the method of separation of variables. Rayleigh-Ritz's method has been applied. Deflection, time period and logarithmic decrement corresponding to the first two modes of vibrations of a clamped non-homogeneous visco-elastic circular plate for various values of non-homogeneity parameter, taper constant and thermal gradients are obtained and shown graphically for the Voigt-Kelvin model.

PL

W pracy przedstawiono analizę drgań swobodnych niejednorodnej lepko- sprężystej płyty kołowej o liniowo zmiennej grubości w kierunku promieniowym i poddanej polu temperatury o liniowym rozkładzie w tym kierunku. Konstytutywne równanie różniczkowe ruchu dla drgań swobodnych otrzymano poprzez separację zmiennych. Zastosowano metodę Rayleigha-Ritza. W wyniku analizy wyznaczono ugięcie płyty, okres drgań i logarytmiczny dekrement tłumienia dwóch pierwszych postaci drgań dla warunków brzegowych odpowiadających zamocowaniu niejednorodnej płyty na brzegu. Wyniki przedstawiono graficznie w funkcji parametru niejednorodności, stałej zawężania grubości oraz zmiennego gradientu temperatury przy wykorzystaniu modelu reologicznego Kelvina-Voigta opisującego właściwości materiału płyty.

6

Application of Adomian method on the solution of wave propagation in a linear random non-homogeneous viscoelastic semi-infinite rod

Ray S. S., Bera R. K.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 1

133-143

EN

The aim of the present problem is to investigate the efficiency of the method of Adomian for the solution of non-linear and complicated differential equation in a random medium. Here the problem is connected with the investigation of the mean and variance of the displacement distribution in a thin linear random non-homogeneous Biot type viscoelastic semi-infinite rod, due to general time-dependent displacement input at the rod. A truncated series solution of the wave problem following the method of Adomian after using the Laplace transform is obtained for small random variations in viscoelastic properties. Three specific cases concerning the probability measure as a function of the continuous type of random variable have been discussed.

7

Bounds for the effective shear modulus

Ecsedi I.

Engineering Transactions

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2005

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Vol. 53, iss. 4

415-423

EN

This paper deals with the uniform torsion of nonhomogeneus elastic beams. The concept of the effective shear modulus is deduced from torsional rigidity. Upper and lower bounds are derived for the effective shear modulus. It is proven that the effective shear modulus of a~compound beam is between the weighted arithmetic and harmonic means of shear moduli of the beam components.