Bearing capacity of eccentrically loaded strip footing on spatially variable cohesive soil

The study considers the bearing capacity of eccentrically loaded strip footing on spatially variable, purely cohesive soil. The problem is solved using the random finite element method. The anisotropic random field of cohesion is generated using the Fourier series method, and individual problems within performed Monte Carlo simulations (MCSs) are solved using the Abaqus finite element code. The analysis includes eight different variants of the fluctuation scales and six values of load eccentricity. For each of these 48 cases, 1000 MCSs are performed and the probabilistic characteristics of the obtained values are calculated. The results of the analysis indicate that the mean value of the bearing capacity decreases linearly with eccentricity, which is consistent with Meyerhof's theory. However, the decrease in standard deviation and increase in the coefficient of variation of the bearing capacity observed are non-linear, which is particularly evident for small eccentricities. For one chosen variant of fluctuation scales, a reliability analysis investigating the influence of eccentricity on reliability index is performed. The results of the analysis conducted show that the value of the reliability index can be significantly influenced even by small eccentricities. This indicates the need to consider at least random eccentricities in future studies regarding probabilistic modelling of foundation bearing capacity.

Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions

In this study, the numerical solutions of the modified Fornberg–Whitham (mFW) equation, which describes immigration of the solitary wave and peakon waves with discontinuous first derivative at the peak, have been obtained by the collocation finite element method using quintic trigonometric B-spline bases. Although there are solutions of this equation by semi-analytical and analytical methods in the literature, there are very few studies on the solution of the equation by numerical methods. Any linearization technique has not been used while applying the method. The stability analysis of the applied method is examined by the von-Neumann Fourier series method. To show the performance of the method, we have considered three test problems with nonhomogeneous boundary conditions having analytical solutions. The error norms L 2 and L ∞ are calculated to demonstrate the accuracy and efficiency of the presented numerical scheme.

Influence Mechanism of Electromechanical Parameters on Transient Dynamics of FWD-EVs: Part I: Co-Modeling of IWM and Vehicle System

In-wheel motor (IWM), as an ideal power source of independent four-wheel drive electric vehicles, has been paid more and more attention due to its high-power density, low starting current, wide speed adjustment range, simple control system and robustness. However, the electromechanical issue is enlarged in both longitudinal and vertical because of in-wheel driven scheme. In this paper, the electromagnetic multi-field characteristic of IWM is investigated based on Fourier series method. The negative vibration coupling on vehicle dynamics is discussed by proposing a conjoint electromechanical FWD-EV model. Results shows that the motor incentive coupled with the vehicle system in multi-degree of freedom, caused the body and wheel resonance in the low speed, meanwhile deteriorated the anti-rollover capability of the IWM-EV in the high speed.

The Influence of Nonhomogeneous Interlayer Stiffness on Dynamic Response of Orbit-Girder System under Moving Load

Based on the finite Fourier series method and the principle of energy variation, a method for calculating the dynamic response of an orbit-girder system is proposed, which is suitable for general spring boundary and nonhomogeneous interlayer stiffness distribution. Two numerical examples are given to verify the effectiveness of the proposed method under different moving load speeds and different stiffness distribution patterns. Based on this method, the influence of boundary conditions, interlayer stiffness degradation mode and degradation amplitude as well as the motion load on the dynamic response of the orbit-girder system is analyzed. A formula for calculating the peak value of additional dynamic response caused by interlayer stiffness degradation is proposed based on the nonlinear fitting method, and the factors affecting the additional response are analyzed. Results show that the variation of boundary conditions does not affect the additional dynamic response of the orbit-girder system. The mode of interlayer stiffness degradation and the degree of nonhomogeneous distribution have a significant influence on the peak of additional dynamic response. The additional dynamic response peak value of the orbit-girder system increases significantly with an increasing degree of nonhomogeneous degradation of the interlayer stiffness. The orbit-girder system has multiple critical speeds under the action of moving load. The magnitude of moving load has an important effect on the additional response peaks of the orbit-girder system. The additional response peaks increase approximately linearly with the increase of the motion load.

Free vibration analysis of rectangular plates with arbitrary elastic boundary conditions

boundary conditions are In this paper, an improved Fourier series method is presented for the free vibration analysis of rectangular plates with arbitrary elastic conditions. The stiffness value of the restraining springs is determined as required to simulate the arbitrary elastic boundary conditions. The exact solution of plates with arbitrary elastic boundary conditions is solved by the introduced supplementary func-tions. The matrix eigenvalue equation of plates is derived by using boundary conditions and the governing equations. Compared with exist methods, the presented method can be easily applied to most of plate vibration problems with different boundary conditions. To validate the accuracy of the presented method, numerical simulations with different boundary conditions are presented.presented.

SPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM

In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.

Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method

An analytical model of laminated composite double-plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first-order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS’s vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates.

New Refinements for the Error Function with Applications in Diffusion Theory

In this paper we provide approximations for the error function using the Padé approximation method and the Fourier series method. These approximations have simple forms and acceptable bounds for the absolute error. Then we use them in diffusion theory.

Application of Local Fractional Homotopy Perturbation Method in Physical Problems

Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8.