Article
Mathematics
Anna Lucia Laguardia, Maria Grazia Russo
Summary: This paper presents a numerical method for solving two-dimensional Fredholm integral equations on general curvilinear domains of the plane. The method is based on a suitable Gauss-like cubature formula and its convergence, stability, and good conditioning are proven in appropriate subspaces of continuous functions. It is demonstrated that the proposed numerical strategy is fast for smooth known functions, inheriting the error behavior of the cubature formula. The efficiency of the method is illustrated through numerical examples and compared with other known methods in the literature.
Article
Engineering, Civil
S. R. Mahmoud, E. Ghandourah, Ali Algarni, Mohammed Balubaid, Abdelouahed Tounsi, Fouad Bourada
Summary: This work investigates the thermo-mechanical bending response of porous functionally graded sandwich plates for military and civil use. It proposes the integral four-unknown shear deformation theory to describe the kinematics of the structure. The differential equilibrium equations are determined using the principle of virtual work and solved with Navier's procedure. The study examines the influence of porosity parameters on the structural integrity and performs a detailed parametric investigation on the impact of volume fraction variation, geometrical ratios, and thermal load on the thermo-mechanical bending response of the porous functionally graded sandwich plates.
ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING
(2022)
Article
Mathematics, Applied
Fuat Usta
Summary: In this study, the Bernstein approximation method, along with the Riemann-Liouville fractional integral operator, was used to solve both the first and second kind of fractional Volterra integral equations. The proposed technique was shown to be applicable and efficient through convergence analysis and illustrative numerical experiments. All numerical calculations were carried out on a personal computer using MATLAB programs.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Thomas G. Anderson, Marc Bonnet, Shravan Veerapaneni
Summary: This study focuses on the mixing of passive tracers by an incompressible viscous fluid. A physically inspired surrogate norm, the negative index Sobolev norm, is used to quantify mixing in the complex fluid mixing domain. The computation of the norm requires the computation of an eigenbasis for L-2(Omega). Instead, a representative of the scalar concentration field in an appropriate Sobolev space is computed to obtain an equivalent definition of the norm. Fast and accurate potential theoretic methods are used to efficiently solve the elliptic problems related to the concentration field, and numerical results demonstrate the convergence of the approach.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Mechanical
Jurgen Becque
Summary: Starting from the Foppl-von Karman equations, this paper successfully derives a Winter-type equation to connect two concepts. By simplifying the equations, combining with a failure criterion, and using truncated Fourier series, excellent predictions of plate behavior postbuckling are achieved, resulting in a closed-form expression equivalent to the Winter equation.
JOURNAL OF ENGINEERING MECHANICS
(2021)
Article
Multidisciplinary Sciences
Ovgu Cidar Iyikal
Summary: This study focuses on the numerical solutions of linear two-dimensional Fredholm integral equations of the second kind using Bernstein operators. The method is illustrated using regularized-equal and Chebyshev collocation points. The obtained numerical results from illustrative examples demonstrate the accuracy and efficiency of the proposed algorithm for solving linear two-dimensional Fredholm integral equations of the second kind.
Article
Mathematics, Applied
Alireza Hosseinian, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a numerical method for solving nonlinear Volterra integral equations with delay arguments. The method uses the discrete collocation approach with thin plate splines as a type of radial basis functions. The method provides an effective and stable algorithm to estimate the solution, which can be easily implemented on a personal computer. The error analysis and convergence validation of the method are also provided.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Seyyed Amjad Samareh Hashemi, Habibollah Saeedi
Summary: A new combination method for numerically solving nonlinear Ito-Volterra stochastic integral equations is proposed in this paper, utilizing Adomian decomposition method, Triangular function approximation, quadrature methods, and Ito stochastic integration formula. The method is developed in two steps, with the main equation solved by ADM and the components calculated using TF-approximation, quadrature, and Ito stochastic integration formula. Theorems related to error and convergence analysis of the method are also presented, and several examples confirm its applicability, efficiency, and accuracy through comparisons.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Green & Sustainable Science & Technology
Mansi Singh, R. Gayen
Summary: In this study, the interaction of linear water waves with an array of three thin vertical plates, comprising of two plate wave energy converters and one flexible breakwater, submerged in water of finite depth in a two dimensional space, was investigated. The problem was solved by converting the associated boundary value problem into a system of coupled integral equations. The effects of the structural properties of the piezoelectric plates, such as submergence depths, plate lengths, distance from the breakwater, and different edge conditions, on wave attenuation and wave power absorption efficiency were analyzed. It was also examined how the presence of the non-uniform flexible plate with different flexibility and lengths could improve the performance of the system.
Article
Mathematics, Interdisciplinary Applications
A. T. El-Sayed, H. S. Bauomy
Summary: This study investigates the effects of nonlinear integral positive position feedback (NIPPF) and adaptive nonlinear integral positive position feedback (ANIPPF) controllers on a shearer's semi-direct drive cutting transmission system. The steady-state amplitude and stability of the nonlinear system under different parameter values are analyzed using analytic and numerical methods. The results show that the ANIPPF controller provides the best system control, effectively suppressing vibration amplitude and chaotic motion.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
N. V. Hoa
Summary: This paper focuses on establishing the existence and uniqueness results for two kinds of implicit uncertain fractional integral equations with the fuzzy concept. Various Ulam-Hyers stability and Ulam-Hyers-Rassias stability results of these equations are also presented, with examples included to illustrate the main findings.
IRANIAN JOURNAL OF FUZZY SYSTEMS
(2021)
Article
Mathematics, Applied
Mutaz Mohammad, Alexandre Trounev, Mohammed Alshbool
Summary: This work introduces a novel, efficient, and accurate numerical approximation method for solving the fractional diffusion-wave equation and nonlinear integro-differential equations using Euler wavelet approximation and matrix inversion. The proposed method achieves zero absolute error for several examples with known exact solutions and an absolute error of 0.x10(-31) for Fredholm and Volterra nonlinear integral equations. This new numerical scheme stands out in terms of its novelty, efficiency, and accuracy in numerical approximation.
Article
Computer Science, Information Systems
W. J. Liu, X. Q. Zhao
Summary: This paper presents highly accurate analytical approximate solutions for the dynamic oscillation of the parallel-plates model of an electrostatic micro-actuator. By applying a potential difference between the electrodes, the desired oscillatory effect is achieved, with a top movable electrode suspended over a bottom fixed electrode by a linear suspension. The periodic oscillation solutions are obtained using a generalized second-order Newton-harmonic balance method, and they show excellent agreement with the exact solution obtained through numerical integration. These analytical approximate solutions are useful for analysis and design of micro- and nano-devices utilizing electrostatic parallel plates.
Article
Automation & Control Systems
Jalaj Kumar, Suvendu Samanta
Summary: This article investigates the problem of high harmonics in inductive power transfer (IPT) circuits. By modifying and improving the topology structure, a new harmonic modeling method is proposed, which provides accurate results under extreme conditions.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuyuan Li, Wanqing Song, Yanan Jiang, Aleksey Kudreyko
Summary: This paper focuses on the nonlinear stochastic Volterra integral equations with doubly singular kernels and proposes a Galerkin approximate scheme for numerical solution. The strong convergence rate of the Galerkin method in the mean square sense is obtained, which improves the existing numerical schemes for the stochastic Volterra integral equations. Numerical examples are provided to support the theoretical results and highlight the advantages of the Galerkin method.
FRACTAL AND FRACTIONAL
(2022)
Article
Materials Science, Multidisciplinary
Olha Hrytsyna, Jan Sladek, Vladimir Sladek, Maryan Hrytsyna
Summary: A gradient-type theory with flexomagnetic/flexoelectric and micro-inertia effects is applied to study Love wave propagation in layered magneto-electro-elastic structures. The dispersion equations for two waveguide structures are numerically investigated, and it is found that the profile of dispersion curves depends on the material composition, guiding layer thickness, and relative values of the coefficients and length-scale parameter. The obtained results are beneficial for mathematical modeling of new small-sized acoustic devices.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Mechanics
W. Huang, J. J. Yang, J. Sladek, V. Sladek, P. H. Wen
Summary: In this study, axisymmetric cracked solid structures in functionally graded materials (FGMs) under static and dynamic loading are analyzed using the Finite Block Method (FBM). The equilibrium equations inside the rotating section of FGMs in the cylinder coordinate system are formulated in strong form based on axisymmetric elasticity theory. The FBM employs Lagrange polynomial interpolation with mapping techniques to construct shape functions for irregular finite or semi-infinite physical domains. A special approximation technique is proposed to handle singularities in the traction boundary conditions on the axis of symmetry. The stress intensity factor is calculated using the crack opening displacement. Time-dependent problems are solved using Laplace transform and Durbin's inverse approach. Numerical examples are provided to demonstrate the accuracy and convergence of the proposed method, and comparisons are made with analytical solutions, the finite element method, and other methods.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Engineering, Mechanical
J. C. Wen, J. Sladek, V. Sladek, M. H. Aliabadi, P. H. Wen
Summary: This paper presents a Method of Fundamental Solutions (MFS) combined with Erdogan's solutions for Functionally Graded Materials (FGM) to analyze 2D fracture problems under static and dynamic loads. Erdogan derived analytical solutions for a pair of static concentrated forces in an infinite isotropic plate with a straight cut. The contribution of non-homogeneity in equilibrium equations is treated as body forces and requires domain integrals based on Erdogan's fundamental solutions. In dynamic cases, Laplace transformation and Durbin inversion technique are used to determine time-dependent variables such as stress intensity factors. Numerical domain integrals are obtained using the sub-region technique. The accuracy of MFS is demonstrated through four numerical examples and comparisons with different numerical approaches are performed.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2023)
Article
Mechanics
V. Sladek, J. Sladek, L. Sator, Yueqiu Li
Summary: Based on the higher-grade continuum theory, this study investigates the propagation of longitudinal and transverse anti-plane elastic waves in nanoscale periodic laminates of piezoelectric dielectrics normal to the material. The inclusion of strain gradients, micro-inertia, and direct flexoelectricity phenomena is analyzed using a phenomenological description. The problem is analyzed using one-dimensional equations derived from the Hamilton variation principle. The results show that the transverse waves are unaffected by electric polarization, while the longitudinal waves are influenced. The study also explores the influence of micro-stiffness, micro-inertial length scale parameters, and flexoelectric coefficients on dispersion curves and frequency gaps through parametric analysis.
COMPOSITE STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
H. Wei, J. L. Zheng, J. Sladek, V. Sladek, P. H. Wen
Summary: This paper presents the development of Erdogans fundamental solution (MFS) method for solving a 2D in-plane crack problem under static and dynamic loads. Erdogan's analytical solutions for a cracked infinite domain with static concentrated force using complex variables are extended to 2D elasticity. Both Laplace transform technique and Durbin inversion technique are used to determine the time-dependent variables in the case of dynamic loads. The accuracy and convergence of the MFS are demonstrated through numerical examples, with comparisons to analytical solutions and finite element method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mechanics
Jan Sladek, Vladimir Sladek, Miroslav Repka, Siegfried Schmauder
Summary: The interface crack problem between two dissimilar materials under a thermal load is analyzed using the gradient elasticity theory, which takes into account the size effect in the very thin quasicrystal layer. This study considers the uncoupled thermo-elasticity, where the thermal fields are independent of the mechanical fields. Due to the inability of classical Fourier's law to accurately describe thermal transport in nano-sized structures, a novel gradient theory is developed for such structures, incorporating second derivatives of temperature in the constitutive equation for high-order heat flux. The governing equations and boundary conditions are derived from the principle of virtual work, and the mixed finite element method (MFEM) is employed for numerical analysis.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Mechanics
Tomas Profant, Jan Sladek, Vladimir Sladek, Michal Kotoul
Summary: The direct flexoelectric effect is a result of polarization in the material, which is influenced by strain gradients. Strain gradients are particularly prominent near material defects, especially crack tips, where the flexoelectric effect redistributes stress and affects crack propagation. This effect is size dependent and adds complexity to the equilibrium, constitutive, and boundary equations, as well as the asymptotic solution at the crack tip. The matched asymptotic expansion method is applied to derive expressions for amplitude factors in the flexoelectric asymptotic solution, which depend on stress intensity factors in mode I or mode II loadings. This method requires knowledge of the boundary layer, which is evaluated based on energetic criteria at the crack tip.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Materials Science, Multidisciplinary
O. Hrytsyna, J. Sladek, V. Sladek, Q. Deng, M. Hrytsyna
Summary: The modified strain gradient theory (MSGT) is developed to analyze the free vibration of elastic centrosymmetric tubes. The theory considers flexoelectric and micro-inertia effects and includes various parameters such as strain, stretch gradient, rotation gradient, dilatation gradient, polarization vector, and electric quadrupoles. The governing equations and boundary conditions are derived from the Hamilton variation principle, and the torsional vibration problem is solved analytically for non-piezoelectric nanotubes with fixed edges. The study investigates the influence of nanotube geometry, flexoelectric coefficient, micro-inertia, and micro-stiffness parameters on the natural frequency.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Materials Science, Multidisciplinary
T. Profant, J. Sladek, V. Sladek
Summary: The procedure for the assessment of amplitude factors in the asymptotic solution of interface crack between two flexoelectric materials is developed. Stress exponents and appropriate eigenvectors are evaluated from the eigenvalue problem assembled from boundary conditions at the tip of the crack. Amplitude factors of the asymptotic solution are computed from two-state integrals, representing independent equilibrium states. The results show that the two-state integrals can extract dominant terms of the asymptotic solution from the weak solution obtained by the finite element method. The amplitude factors play a crucial role in crack stability criteria problems.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Materials Science, Multidisciplinary
Isa Ahmadi, Jan Sladek, Vladimir Sladek
Summary: In this study, the free vibration of a two-directional functionally graded (2D-FG) thick curved nanobeam with a concentrated mass is investigated under various boundary conditions. The governing equations of the nanobeam are derived using Hamilton's principle and the first-order shear deformation theory (FSDT), where the small scale effect is captured by the nonlocal elasticity theory. A meshless formulation is developed to discretize the governing equations based on the local weak formulation and radial basis function. The presented meshless method is applied to study the free vibration of the one-directional and two-directional functional graded curved nanobeams, exploring the influence of parameters such as nonlocal parameter, FG power indexes, opening angle, edge conditions, and concentrated mass.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Mechanics
Xinpeng Tian, Mengkang Xu, Haiyang Zhou, Qian Deng, Jan Sladek, Vladimir Sladek
Summary: The flexoelectric effect around the tip of nano-cracks was simulated using a collocation mixed finite element method (MFEM). The results showed that the flexoelectric effect would be enhanced by increasing the tensile loading and crack length, and it played an important role in the fracture mechanics of materials.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Mechanics
Jan Sladek, Vladimir Sladek, Maryan Hrytsyna, Tomas Profant
Summary: This paper investigates the influence of flexoelectricity on the behavior of interface cracks between dissimilar dielectric materials under dynamic mechanical loads. The induced electric field affects the distribution and evolution of mechanical fields in dielectric materials. The strain gradient theory model is needed to consider the large strain gradients at the crack tip vicinity.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Dongliang Ji, Hui Cheng, Hongbao Zhao
Summary: The influence of crystal size on the macroscopic parameters of sandstone samples is studied using a rock model based on the Voronoi tessellated model. It is found that decreasing crystal size results in increased strength and elastic modulus. Strain energy density (SED) is shown to help explain the failure mechanisms of the sandstone samples. A constitutive model that considers the heterogeneity in elastic modulus and rock strength is developed and is in good agreement with experimental results. The study also identifies the triggering of surface damage on slopes by vibration excitation in engineering applications as well as proposes a constitutive model for quantitatively evaluating damage accumulation in mining tunnels.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Francesco Tornabene, Matteo Viscoti, Rossana Dimitri
Summary: This manuscript investigates the dynamic properties of doubly-curved shell structures laminated with innovative materials using the Generalized Differential Quadrature (GDQ) method. The displacement field variable follows the Equivalent Single Layer (ESL) approach, and the geometrical description of the structures is distorted by generalized isogeometric blending functions. Through non-uniform discrete computational grid, the fundamental equations derived from the Hamiltonian principle are solved in strong form. Parametric investigations show the influence of material property variation on the modal response of the structures.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Duy-Khuong Ly, Ho-Nam Vu, Chanachai Thongchom, Nguyen-Thoi Trung
Summary: This paper presents a novel numerical approach for nonlinear analysis and smart damping control in laminated functionally graded carbon nanotube reinforced magneto-electro-elastic (FG-CNTMEE) plate structures, taking into account multiple physical fields. The approach employs a multi-physical coupling isogeometric formulation to accurately capture the nonlinear strain-displacement relationship and the magneto-electro-elastic coupling properties. The smart constrained layer damping treatment is applied to achieve nonlinear damped responses. The formulation is transformed into the Laplace domain and converted back to the time domain through inverse techniques for smart control using viscoelastic materials.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Xiaoyang Xu, Jie Cheng, Sai Peng, Peng Yu
Summary: In this study, a smoothed particle hydrodynamics (SPH) method is developed to simulate viscoelastic fluid flows governed by the Phan-Thien-Tanner (PTT) constitutive equation. The method is validated by comparing its solutions with those obtained by the finite volume method (FVM). The method is also used to simulate the impact behavior and dynamics of a viscoelastic droplet, and the influences of various parameters are investigated. The results demonstrate the accuracy and capability of the SPH method in describing the rheological properties and surface variation characteristics of viscoelastic fluid flows.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Xueying Zhang, Yangjiong Wu
Summary: This paper proposes a high resolution strategy for the localized method of approximate particular solutions (LMAPS). The strategy aims to improve the accuracy and stability of numerical calculation by selecting upwind interpolation templates. Numerical results demonstrate that the proposed high-resolution LMAPS is effective and accurate, especially for solving the Navier-Stokes equations with high Reynolds number.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Yong-Tong Zheng, Yijun Liu, Xiao-Wei Gao, Yang Yang, Hai-Feng Peng
Summary: Structures with holes are common in engineering applications. Analyzing stress concentration effects caused by holes using FEM or BEM is challenging and time-consuming. This paper proposes improved methods for simulating holes and cylinders, reducing the number of nodes while maintaining stress accuracy. Numerical examples demonstrate the accuracy and efficiency of the proposed methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Chein-Shan Liu, Chung-Lun Kuo
Summary: The paper presents two new families of fundamental solutions for the 3D Laplace equation and proposes the methods of pseudo fundamental solutions and anisotropic fundamental solutions, which outperform the traditional 3D MFS.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Sima Shabani, Miroslaw Majkut, Slawomir Dykas, Krystian Smolka, Esmail Lakzian
Summary: This study validates and simulates steam condensing flows using different condensation models and equations of state, identifying the most suitable model. The results highlight the importance of choosing the appropriate numerical model for accurately predicting steam condensation flows.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
D. L. Guo, H. H. Zhang, X. L. Ji, S. Y. Han
Summary: In this study, the mechanical behaviors of 2-D orthotropic composites with arbitrary holes were investigated using the numerical manifold method (NMM). The proposed method was verified and found to have good convergence and accuracy. Additionally, the effects of material principal direction and hole configurations on the mechanical behaviors of the orthotropic composites were revealed.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Giacomo Rosilho de Souza, Rolf Krause, Simone Pezzuto
Summary: In this paper, we propose a boundary element method for accurately solving the cell-by-cell bidomain model of electrophysiology. The method removes the degeneracy in the system and reduces the number of degrees of freedom. Numerical experiments demonstrate the exponential convergence of our scheme in space and several biologically relevant experiments are provided.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Riku Toshimitsu, Hiroshi Isakari
Summary: This study extends a recent paper by Lai et al. (2018) by introducing a novel boundary integral formulation for scalar wave scattering analysis in two-dimensional layered and half-spaces. The modified integral formulation eliminates fictitious eigenvalues and reasonable parameter settings ensure efficient and accurate numerical solutions. The proposed method is demonstrated to be effective through numerical examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Ebutalib Celik, Merve Gurbuz-Caldag
Summary: In this paper, a new meshless method based on domain decomposition for an L-shaped domain is proposed, which uses RBF-FD formulation at interface points and classical FD in sub-regions to improve the solution accuracy. The proposed numerical method is applied to simulate benchmark results for a divided-lid driven cavity and solve Navier-Stokes equations with Lorentz force term in a single-lid L-shaped cavity exposed to inclined magnetic field, and the flow structure is analyzed in terms of streamline topology under different magnetic field rotations and strengths.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Hanqing Liu, Fajie Wang, Lin Qiu, Cheng Chi
Summary: This paper presents a novel method that combines the singular boundary method with the Loop subdivision surfaces for acoustic simulation of complex structures, overcoming technical challenges in handling boundary nodes.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
