Article
Engineering, Multidisciplinary
Giovanna C. Andrade, Sandra A. Santos
Summary: This paper presents a level-set-based strategy for minimizing structural compliance, using radial basis functions with compact support and Hilbertian velocity extensions. An augmented Lagrangian scheme is adopted to handle volume constraint, and the finite element method is used to solve the linear elasticity model and the variational problem associated with the velocity field computation.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Thermodynamics
Tiantian Zhang, Xiaoqing Yang
Summary: This paper develops a parametric level set-based topology optimization method for the design of micro-channel heat sinks, and its effectiveness is confirmed through numerical experiments and experimental tests.
APPLIED THERMAL ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Jiajing Li, Liang Gao, Mengli Ye, Hao Li, Lizhou Li
Summary: This study proposes a novel method for the topology optimization of irregular flow domains using a parametric level set method (PLSM). The CS-RBFs-based PLSM is improved to be suitable for nonuniform meshes, expanding its application in engineering. A gradient-based algorithm with Stokes equations as state constraints is used to solve the optimization problem, aiming to minimize power dissipation under the volume constraint of flow channels. The PLSM avoids solving the Hamilton-Jacobi partial differential equation directly, and a self-adaptation support radius approach allows the PLSM to be applied to engineering problems with irregular geometries.
JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Zhuo Huang, Ye Tian, Kang Yang, Tielin Shi, Qi Xia
Summary: A shape and generalized topology optimization method based on the level set-based density method is proposed for designing curved grid stiffeners. The method combines level set functions and basis functions to describe the overall layout and curvilinear path of the stiffeners, and uses interval projection to describe the width. The combination operation similar to Boolean operation union is achieved using the p-norm method. The proposed method is validated through numerical examples, demonstrating its effectiveness in changing the shape and topology of stiffeners during optimization.
JOURNAL OF MECHANICAL DESIGN
(2023)
Article
Mathematics, Applied
Zhiying Ma, Xinxiang Li, C. S. Chen
Summary: A new Kansa method with fictitious center approach is proposed in this paper, where the radial basis function (RBF) approximation is augmented by polynomial basis functions. The proposed approach significantly improves the accuracy and stability of the previously proposed ghost point method using radial basis functions, eliminating the difficulty of selecting a good RBF shape parameter. Two numerical examples are presented to demonstrate the effectiveness and improvement of the proposed method over previous methods.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Mingtao Cui, Chenchun Luo, Guang Li, Min Pan
Summary: The parameterized level set method using radial basis functions has improved efficiency and stability in structural topology optimization. By introducing a shape sensitivity constraint factor based on CS-RBF, the method can control step length and increase optimization speed during iterations. Various numerical examples demonstrate the feasibility and effectiveness of this approach for single-material and multi-material topology optimization.
ENGINEERING WITH COMPUTERS
(2021)
Article
Engineering, Mechanical
Baseer Ullah, Wajid Khan, Siraj-ul-Islam, Zahur Ullah
Summary: This paper presents a novel approach that combines a meshless element-free Galerkin method with a radial basis functions-based level set algorithm for topology optimization. The proposed method allows for solving the optimization problems using a single discretization scheme and effectively handles topological modifications of the structural geometry.
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Gregoire Allaire, Martin Bihr, Beniamin Bogosel, Matias Godoy
Summary: This paper focuses on the accessibility constraint, a geometric constraint for shape and topology optimization of structures in additive manufacturing. The constraint is motivated by the difficulty in removing sacrificial supports hidden within complex geometries of structures. The paper presents a mathematical approach to evaluate this accessibility constraint using distance functions and eikonal equations, allowing for shape derivatives computation. Numerical demonstrations show that the approach enables simultaneous optimization of mechanical performance and accessibility of building supports, ensuring manufacturability.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Marine
Baiwei Feng, Chengsheng Zhan, Zuyuan Liu, Xide Cheng, Haichao Chang
Summary: The Wendland psi 3,1 (W) function was selected for hull surface modification based on radial basis functions (RBF) interpolation. A case study validated the advantages of this method, resulting in optimized hull form with reduced wave-making resistance and total resistance. The findings support the feasibility and value of RBF interpolation-based surface modification in engineering practice.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Ying Zhou, Liang Gao, Hao Li
Summary: This paper presents a topology optimization design method for 3D chiral-type auxetic metamaterials that can be readily manufactured with explicit and smooth boundaries.
ENGINEERING WITH COMPUTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Shangjun Shi, Pingzhang Zhou, Zhenhua Lu
Summary: This article presents a novel topological design approach inspired by the density method and parametric level set method to control structural complexity and improve computational efficiency. By combining radial basis function and the SIMP formula, the distribution of fictitious density field in the design domain is described to control structural complexity. The proposed method can naturally avoid checkerboard design and reduce the number of design variables by redefining support points.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Khaled Mohamed, Hassan Elgamal, Sallam A. Kouritem
Summary: This research focuses on optimizing the geometry and natural frequency of piezoelectric energy harvesters to improve efficiency. The combination of genetic algorithm and COMSOL optimization module has significantly increased power output. Experimental validation of COMSOL results and investigation into the impact of cantilever length, tip mass, and piezoelectric material volume on output voltage were conducted.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Engineering, Multidisciplinary
Perle Geoffroy-Donders, Gregoire Allaire, Georgios Michailidis, Olivier Pantz
Summary: This article addresses the coupled optimization of the external boundary and infill material in a structure. The proposed method optimizes the infill material using homogenization and the macroscopic shape using the Hadamard method. Unique features include the infill material following the boundary displacement during optimization and the dehomogenization step for creating a smoothly varying lattice infill. Numerical examples demonstrate the effectiveness of the approach, particularly for design-dependent loads.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Construction & Building Technology
Wonsik Junga, Thanh T. Banhb, Nam G. Luuc, Dongkyu Lee
Summary: This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating radial basis functions (RBFs) into an implicit level set (ILS) method. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. To solve the optimization problem, a LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation into a system of coupled non-linear ordinary differential equations. The paper presents detailed mathematical expressions for topology optimization of bi-directional functionally graded beams with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG).
STEEL AND COMPOSITE STRUCTURES
(2023)
Article
Mathematics
Mohammad Heidari, Maryam Mohammadi, Stefano De Marchi
Summary: This paper discusses the problem of choosing the scale or shape parameter of radial basis functions (RBFs) in kernel-based methods. It introduces a direct relation between the shape parameter and the curvature of RBFs at each point. Based on this relation, RBFs are characterized as scalable or unscalable, and their curvature is used to classify commonly used RBFs. The paper then proposes a curvature-based scaled RBFs method, where the shape parameters depend on the function values and approximate curvature values of the function to be approximated. Numerical experiments show that this method performs better than the standard fixed-scale basis and other shape parameter selection methods.
MATHEMATICAL MODELLING AND ANALYSIS
(2023)
Article
Physics, Multidisciplinary
Mehnaz Shakeel, Shahida Parveen, Siraj-ul Islam, Iltaf Hussain
Summary: This study examines the interaction of counter-propagating ion acoustic shock waves in three-component unmagnetized plasmas with inertial warm ions, superthermal electrons and positrons. Mathematical equations and phase shifts for the shock wave are derived and analyzed, with a focus on the effects of electron temperature, positron temperature ratio, spectral index, and positron concentration on the phase shift. The behavior of ion acoustic shock wave in e-p-i plasma with fractional parameter is also investigated using numerical methods.
Article
Engineering, Multidisciplinary
Suliman Khan, Sakhi Zaman, Siraj-ul Islam
Summary: Two splitting algorithms are proposed for approximation of Cauchy type singular integrals, using multi-resolution quadrature and analytical evaluation for different scenarios. The methods are validated numerically to ensure accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics, Applied
Sakhi Zaman, Siraj-ul-Islam, Muhammad Munib Khan, Imtiaz Ahmad
Summary: Accurate algorithms are proposed for approximating integrals involving highly oscillatory Bessel functions, transforming them into oscillatory integrals with Fourier kernels using complex line integration technique. The method involves evaluating inner non-oscillatory improper integrals and outer highly oscillatory integrals using a modified meshfree collocation method. The algorithms' error estimates are theoretically derived and numerically verified.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Mechanical
Baseer Ullah, Wajid Khan, Siraj-ul-Islam, Zahur Ullah
Summary: This paper presents a novel approach that combines a meshless element-free Galerkin method with a radial basis functions-based level set algorithm for topology optimization. The proposed method allows for solving the optimization problems using a single discretization scheme and effectively handles topological modifications of the structural geometry.
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING
(2022)
Article
Multidisciplinary Sciences
Imran Aziz, Muhammad Nisar, Siraj-ul-Islam
Summary: This study explores numerical solutions to elliptic, parabolic, and hyperbolic equations with nonlocal boundary conditions using the Haar wavelet collocation method. The method is applicable to both linear and nonlinear problems, and numerical results confirm its simplicity and effectiveness.
PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Zahur Ullah, Baseer Ullah, Wajid Khan, Siraj-ul-Islam
Summary: This paper presents a proportional topology optimisation (PTO) method with a maximum entropy-based meshless method for two-dimensional linear elastic structures. The method is efficient in computing maxent basis functions and possesses a weak Kronecker delta property for easy imposition of boundary conditions. The PTO method is simple, accurate, and efficient compared to standard topology optimisation methods. The paper also provides a detailed implementation of computational algorithms for both minimum compliance and stress constraint problems. Numerical examples show the accuracy, efficiency, and robustness of the developed algorithms, which can handle large topological changes and exhibit excellent optimisation convergence characteristics.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Applied
Zaheer-ud- Din, Siraj-ul- Islam, Sakhi Zaman
Summary: A meshless procedure based on a multi-quadric radial basis function is proposed for the numerical solution of oscillatory Volterra integral equations. By transforming the integral operator into a differential operator using Liven's formulation, the numerical solution of the differential equation is obtained through a meshless procedure on global and local support domains. Theoretical error bounds are derived in the inverse power of the frequency parameter. The proposed technique is also applied to the perturbed form of the Volterra integral equation of the second kind, and the accuracy and efficiency of the procedure are validated through numerical benchmark problems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Muhammad Ahsan, Thanh Tran, Siraj-ul-Islam, Iltaf Hussain
Summary: This article proposes a hybrid numerical method based on Haar wavelets and finite differences for shock ridden evolutionary nonlinear time-dependent partial differential equations (PDEs). A linear procedure using Taylor expansions is adopted to linearize the nonlinearity. Convergence analysis is performed in space and time, and the computational stability of the proposed method is also discussed. Benchmark cases related to 1-D and 2-D Burgers' type equations are considered to verify the theory, and the proposed method is numerically compared with existing methods in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Rahat Zarin, Siraj-ul-Islam, Nadeem Haider, Naeem-ul-Islam
Summary: In this paper, a reaction-diffusion epidemic mathematical model is proposed to analyze the transmission mechanism of COVID-19. The model includes six classes dependent on time and space: Susceptible, Exposed, Asymptomatically infected, Symptomatic infected, Quarantine, and Recovered or Removed (SEQIaIsR). The threshold number R0 is calculated using the next-generation matrix approach. The model is simulated using the operator splitting approach based on finite difference and meshless methods, and stability analysis of the equilibrium points is conducted.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mechanics
Lei Wan, Zahur Ullah, Dongmin Yang, Brian G. Falzon
Summary: This study proposes a probability embedded approach for predicting the failure of IM7/8552 unidirectional carbon fibre reinforced polymer (CFRP) composite materials under biaxial stress states. The approach combines micromechanical modelling, artificial neural networks (ANNs), and uncertainty quantification. The ANN models show excellent performance in regression and classification problems, achieving low mean square error (MSE) and mean absolute error (MAE) for regression, and high prediction probability for classification. The failure strength predicted by the ANNs is in good agreement with the theoretically predicted failure envelopes.
COMPOSITE STRUCTURES
(2023)
Article
Materials Science, Composites
Lei Wan, Zahur Ullah, Dongmin Yang, Brian G. G. Falzon
Summary: The inter-fibre failure analysis of carbon fibre-reinforced polymer composites under biaxial loading was investigated in this study. Two commonly used failure criteria, Tsai-Wu and Hashin, were comprehensively evaluated using finite element-based micromechanical analysis. The study utilized high-fidelity three-dimensional representative volume elements subjected to biaxial loadings, assuming transversely isotropic and linearly elastic carbon fibers. The mechanical response of the matrix and fiber-matrix interface was simulated using the Drucker-Prager plastic damage constitutive model and cohesive zone model, respectively. The study found that the micromechanics-based numerical model was effective in assessing the two failure criteria.
JOURNAL OF COMPOSITE MATERIALS
(2023)
Article
Mathematics, Applied
Shumaila Yasmeen, Siraj-Ul-Islam, Rohul Amin
Summary: Higher order Haar wavelet method (HOHWM) is used for second kind integral equations, including Fredholm and Volterra types. The method also works for nonlinear problems. HOHWM shows second and fourth-order convergence, which is an improvement compared to the first-order convergence of Haar wavelet method (HWM).
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mechanics
S. L. J. Millen, M. Dahale, T. Fisher, A. Samy, K. Thompson, K. Ramaswamy, C. Ralph, E. Archer, A. McIlhagger, Z. Ullah, B. G. Falzon
Summary: A novel finite element modelling approach is proposed to simulate the LVI and CAI response of 3D woven carbon/epoxy composites. The binder reinforcement is modelled with an elliptical cross-section accounting for compaction, which leads to accurate predictions of damage area and CAI strength. Experimental results show good agreement with the predictions.
COMPOSITE STRUCTURES
(2023)
Article
Energy & Fuels
Amir Sohail, Naeem Ul Islam, Azhar Ul Haq, Siraj Ul Islam, Imran Shafi, Jaebyung Park
Summary: Renewable energy, particularly solar energy, is considered as an economical and energy efficient alternative to fossil fuel. However, effective system health monitoring is crucial for optimal performance. Traditional monitoring methods have limitations, and thus this study proposes two main approaches.
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)