Finite element method for landslide analysis No.9

Stress analysis and damage evolution in individual plies of notched composite laminates subjected to in-plane loads

Slope stability is a topic of great importance in civil engineering, as slope failures can cause considerable damage to infrastructure and downstream properties. In this study, we applied the Fellenius slice method, using both the analytical method, as well as the numerical method, which was performed using the SLOPE/W module of the Geostudio software. The results obtained by both methods showed that the increase in soil cohesion improves the stability of the slope. The safety coefficients obtained by the analytical method vary between 0.534 and 1.086, while those obtained by the numerical method vary between 0.539 and 1.096, for cohesion values ranging from 4 kPa to 20 kPa. The safety coefficients obtained by the analytical and numerical methods follow straight lines of equation y=0.0344x+0.4092 and y=0.0345x+0.4169, respectively. The results of the analytical method show that a safety factor of 1.5 is achieved at a value of 32 kPa for the cohesion, while the numerical method shows a safety factor of 1.5 achieved at a value of 32 kPa for the cohesion. The difference between the two cohesions is explained by the smaller number of slices used in the analytical method. Nevertheless, the equation from the analytical method can be used as a general guide to evaluate the evolution of the safety coefficient of a slope with surcharge under long-term behavior with incremental cohesion, but this does not exclude verification by dedicated software based on the finite element method.

Calculation of radial and axial forces and leakage reactance of transformer coils is performed in many papers using different analytical and numerical methods. But most of the analytical methods are extended only for transformers with uniform equal-height windings and then are not very accurate for transformer with no uniform winding arrangement. In this paper, some simple techniques for calculating leakage reactance and forces acting on the transformer coils are presented. This study is accomplished by using 2-1) planar models utilizing the finite element and Roth methods. Just by modeling the transformer and using FEM, the magnetic vector potential is calculated over each node of model and then using several post-processing procedures, the transformer leakage reactance is calculated. Also, this reactance is obtained by analytical method (Roth method) and then results are verified by experiments. The short circuit current and hence the radial and axial forces on the transformer coils during short circuit condition are calculated. Considering some especial cases, the impact of the windings arrangement on the axial force is analyzed and net axial force acting against the yoke are calculated

In this paper the static analysis of the truss is investigated. The analytical and computational method of the roof structures are presented. At the beginning, the analytical method is used for determination of values of external supports, axial forces and principal stresses in truss. Then the computational method is used for the solution of the same problems. The roof structure is modeled by the finite element method, where the bar members are represented by the truss elements. The finite element model loaded by external forces, without and with self-weight of structure is computed. At the end, the analytical and computational buckling analysis for the trusses with maximal compressive axial force is performed. The comparison of results of analytical and computational method shows that all methods are accurate enough, but of course computational method is faster and more adaptive for any subsequent changes.

The main objective of this work is to check the compatibility of Finite element method (FEM) to determine the modal parameters of the rotor system and to compare the results with analytical method. Current work is an attempt to implement different finite element (FE) models for the estimation of modal parameters. Two different order elements from Beam, Axisymmetric and Solid FE models are considered. The analysis is carried out on the rotor system and the accuracy of the results and the computation time of the FE models are estimated. The FE results are compared with the analytical method. It is observed that FE model can be used to simulate even at higher order frequencies, which is a limitation of analytical model. The analysis shows that the FE results closely match with analytical method and also the study summarizes that proper choosing of FE helps in developing rotor models in both a desirable accuracy and efficiency. Finally, a Campbell diagram is generated using the analytical method and FEM. The critical speeds are also calculated from the Campbell diagram. The closeness of the results between the two methods is checked.

Two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. In this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. An analytical model is developed based on Marciniak-Kuczynski method associated Hill’s non-quadratic yield criterion. Forming limit diagrams are also obtained numerically based on finite element method using Bifurcation theory and ductile fracture criteria. Furthermore, experiments are carried out on Al3105-St14 two-layer sheet. Theoretical results from various methods are compared with results obtained from experiments to evaluate the competency of discussed analytical and numerical methods to predict the formability of two-layer sheets. The results show that analytical and numerical approaches discussed in this paper have good capabilities to predict the formability of two-layer sheets. However, the analytical method based on M-K model and numerical approach based on bifurcation theory are more suitable to determine the forming limit diagram of Al3105-St14 two-layer sheets.

Frame fatigue life assessment of a mining dump truck based on finite element method and multibody dynamic analysis

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson’s ratio is taken as a constant. Coulomb’s dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion–collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

The Authors of this research developed an analytical calculation method to estimate the strength of nose cone structures made of orthotropic materials, which were crucial components in aircraft and spacecraft. Strength analysis of nose cones had been comprehensively addressed for isotropic materials; however, the lack of efficient approaches for orthotropic materials presented a challenge. In this research, a new analytical method was proposed, combining membrane stress theory for isotropic materials with classical laminate theory for orthotropic materials. This approach enabled the determination of stresses on the nose cone shell structure in both meridional and circumferential directions in an efficient and straightforward manner. The analysis results indicated that the developed analytical method exhibited stress distribution trends similar to those obtained using the Finite Element Method. Stresses in the +45° and –45° direction, as well as in-plane shear stress and Tsai-Wu failure indices, showed trend similarity between the two methods. Despite specific numerical differences in the calculation results, these consistent trends suggested that the analytical method could serve as a tool for the preliminary design of a nose cone structure with a similar configuration analyzed in this study.

A discontinuous deformation and displacement (DDD) analysis method is proposed for modelling the rock failure process. This method combines the rock failure process analysis (RFPA) method (based on finite element method) and discontinuous deformation analysis (DDA) method. RFPA is used to simulate crack initiation, propagation and coalescence processes of rock during the small deformation state. The DDA method is used to simulate the movement of blocks created by the multiple cracks modelled by the RFPA. The newly developed DDD method is particularly suitable for modelling both crack propagation and block movement during the rock failure process because of the natural and convenient coupling of continuous and discontinuous deformation analyses. The proposed method has been used to simulate crack initiation, propagation and coalescence within a slope as well as the block movement during the landslide process. Numerical modelling results indicate that the proposed DDD method can automatically simulate crack propagation and block movement during the rock failure process without degrading accuracy.

Although simple finite elements as truss members and beam members in frames have been used in structural analysis for many years, the general finite element methods of analysis have been developped only recently in parallel with the development of digital computers. It is the use of general matrix methods in high speed digital computers that makes the general finite element methods feasible. At the present time the finite element methods are being used extensively in the analysis and design of flight vehicle structures as well as in other types of structures. Many large general purpose computer programs as well as many specialized programs have been developed for the analysis of structures. These computer programs use various finite elements and usually calculate and assemble the element matrices by one of the three methods of analysis described in previous chapters. Most of the general programs use the displacement method of analysis; a few general programs and many specialized programs use the force method of analysis; a few programs use the mixed method, while some programs use more than one method.

Comparison of meshing characteristics of helical gears with spalling fault using analytical and finite-element methods

Cross-weld creep specimens have been widely studied in order to aid in the understanding of the creep behaviour of real, welded structures. The studies published to date have been of an analytical, numerical, or experimental nature. This review describes the analytical methods used to predict the creep behaviour of cross-weld specimens with simple geometries. For both simple and more complex geometries, use of the finite element (FE) method to obtain stationary state stresses and strains has been made, and the solutions contrasted with those of the simpler analytical methods. Use of the creep continuum damage constitutive equations in FE analyses to predict the failure times of, and rupture positions in, cross-weld specimens has been described. The effect of various features, defined by the analysis methods, is highlighted. Problems with the experimental validation of these effects are considered and selected experimental data from creep tests on cross-weld creep specimens for various materials and geometries are presented. These are interpreted using the results from the analytical and numerical methods described. The potentials and limitations of the methods presented are discussed.

In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.