Jianxue Feng¹, Xiuru Ma², Xiaowei Liu², Long Wang³, Zhongjie Wu^4,*, Guoxiong Mei⁵

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.40, No.1, pp. 1-8, 2024, DOI:10.23967/j.rimni.2024.01.007 - 12 February 2024

Abstract A closed form analytical solution is proposed to analyze the one-dimensional consolidation behavior of structured saturated clay soils under continuous drainage boundary. Firstly, the soil structural properties and arbitrary loading conditions are taken into account in the established mathematical model. Using the finite sine Fourier transform and characteristic function methods, analytical calculation is conducted, and the solution effectiveness is evaluated against the degradation of solutions and the results of finite difference analysis. Finally, the influences of interface parameter, properties of soil structure and structural yield stress on consolidation behaviors are discussed. Results show that the… More >

Yu-Ming Chu¹, Sobia Sultana², Shazia Karim³, Saima Rashid^4,*, Mohammed Shaaf Alharthi⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 761-791, 2024, DOI:10.32604/cmes.2023.028600 - 22 September 2023

Abstract The goal of this research is to develop a new, simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations (PDEs) with variable coefficient. ARA-transform is a robust and highly flexible generalization that unifies several existing transforms. The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion. The process of finding approximations for dynamical fractional-order PDEs is challenging, but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern… More >

Yan Zhang¹, Jichao Zhang¹, Xinxing Xu²

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.39, No.2, pp. 1-6, 2023, DOI:10.23967/j.rimni.2023.05.007 - 09 June 2023

Abstract In this paper, an analytical solution is developed to investigate soil consolidation around a pile under earthquake loading. The solution is validated using finite element method. The influence of various parameters on excess pore water pressure is analyzed. The results show that excess pore water pressure increases with depth and is positively correlated with n and N_eq / N₁ , while negatively correlated with η , χ , k_v , and t_d . The values of η , χ , k_v , N_eq / N₁ , and t_d affect excess pore water pressure during and after the earthquake, while… More >

Zuhur Alqahtani¹, Ahmed Eissa Hagag²

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.39, No.4, pp. 1-15, 2023, DOI:10.23967/j.rimni.2023.10.003 - 25 October 2023

Abstract This article introduces and illustrates a novel approximation to the compound KdV-Burgers equation. For such a challenge, the q-homotopy analysis transform technique (q-HATM) is a potent approach. The suggested procedure avoids the complexity seen in many other methods and provides an approximation that is extremely near to the exact solution. The uniqueness theorem and convergence analysis of the expected problem are explored with the aid of Banach's fixed-point theory. Through a difference in the fractional derivative, the normal frequency for the fractional solution to this issue changes. All of the discovered solutions are illustrated in More >

Areej Almuneef¹, Ahmed Eissa Hagag²

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.39, No.4, pp. 1-8, 2023, DOI:10.23967/j.rimni.2024.01.001 - 29 December 2023

Abstract The analysis of nonlinear events related to physical phenomena is a popular issue in the modern-day. The essential purpose of this work is to discover a novel approximate solution to the fractional nonlinear Benjamin Bona Mahony Peregrine Burgers equation (BBMPB) utilizing the natural decomposition method (NDM) of fractional order. The suggested approach provides analytical solutions that are extremely near to the exact solution whereas obviating the complexities associated with many other approaches. The expected issue’s uniqueness theorem and convergence analysis are explored using Banach’s fixed-point theory. The reliability and accuracy of the recommended method were More >

Linjuan Wang^1,*, Jianxiang Wang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09355

Abstract The prediction of overall dynamics of composite materials has been an intriguing research topic more than a century, and numerous approaches have been developed for this topic. One of the most successful representatives is the classical micromechanical models which assume that the behavior of a composite is the same as its constituents except for the difference in mechanical properties, e.g., effective moduli. With the development of advanced composite materials in recent years, especially metamaterials, it is found that the classical micromechanical models cannot describe complex dynamic responses of composites such as the dispersion and bandgaps… More >

Mohamed Shaimi^* , Rabha Khatyr, Jaafar Khalid Naciri

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-14, 2023, DOI:10.5098/hmt.20.23

Abstract This paper presents an exact analytical solution to the extended Graetz problem in microchannels and microtubes, including axial heat conduction, viscous dissipation, and rarefaction effects for an imposed constant wall temperature. The flow in the microchannel or microtube is assumed to be hydrodynamically fully developed. At the same time, the first-order slip-velocity and temperature jump models represent the wall boundary conditions. The energy equation is solved analytically, and the solution is obtained in terms of Kummer functions with expansion constants directly determined from explicit expressions. The local and fully developed Nusselt numbers are calculated in… More >

Li, Ping¹, Zhijian Chen², Yi Ding³

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.38, No.1, pp. 1-13, 2022, DOI:10.23967/j.rimni.2022.03.008 - 17 March 2022

Abstract In practice, the consolidation of soil around the pile has a great influence on the time-dependent bearing capacity of pile. However, most of the consolidation theory of soil around the pile neglects the disturbance effect of pile-driving on surrounding soil and regards the soil as homogeneous, which overestimates the consolidation efficiency of the soil, and obtains a higher pile bearing capacity. In view of this, a consolidation model of soil around a pipe pile considering soil disturbance effect is presented in this paper. Fourier transform and separation of variables are used to obtain the analytical… More >

Kue-Hong Chen^{1, *}, Cheng-Tsung Chen^{2, 3}

CMC-Computers, Materials & Continua, Vol.64, No.1, pp. 145-160, 2020, DOI:10.32604/cmc.2020.08864 - 20 May 2020

Abstract In this study, we applied a defined auxiliary problem in a novel error estimation technique to estimate the numerical error in the method of fundamental solutions (MFS) for solving the Helmholtz equation. The defined auxiliary problem is substituted for the real problem, and its analytical solution is generated using the complementary solution set of the governing equation. By solving the auxiliary problem and comparing the solution with the quasianalytical solution, an error curve of the MFS versus the source location parameters can be obtained. Thus, the optimal location parameter can be identified. The convergent numerical More >

Yongping Yu¹, Lihui Chen¹, Shaopeng Zheng¹, Baihui Zeng¹, Weipeng Sun^{2, ∗}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 185-200, 2020, DOI:10.32604/cmes.2020.07997 - 01 April 2020

Abstract This paper is focused on the post-buckling behavior of the fixed laminated composite beams with effects of axial compression force and the shear deformation. The analytical solutions are established for the original control equations (that is not simplified) by applying the Maclaurin series expansion, Chebyshev polynomials, the harmonic balance method and the Newton’s method. The validity of the present method is verified via comparing the analytical approximate solutions with the numerical ones which are obtained by the shooting method. The present third analytical approximate solutions can give excellent agreement with the numerical solutions for a More >