Article
Mathematics, Applied
Yanhui Zhou, Yanlong Zhang, Jiming Wu
Summary: In this paper, a polygonal finite volume element method (PFVEM) is proposed and analyzed for solving the anisotropic diffusion equation on convex polygonal meshes, based on the Wachspress generalized barycentric coordinates. The PFVEM reduces to the classical P-1-FVEM on triangular meshes but is not identical to the classical Q(1)-FVEM on quadrilateral meshes. The paper provides a new proof for Proposition 8 in [19], a crucial result for the derivation of interpolation error estimates. Furthermore, the H-2 error estimate of the Wachspress interpolation is proven for the error analysis of the PFVEM, and the optimal H-1 error estimate for the finite volume element solution is obtained under the coercivity assumption. Several numerical examples are presented to demonstrate the efficiency and robustness of the proposed method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Physics, Mathematical
Yanlong Zhang
Summary: In this article, we propose and analyze a quadratic serendipity finite volume element method for arbitrary convex polygonal meshes based on the idea of serendipity element. We introduce the explicit construction of quadratic serendipity element shape function and select the quadratic serendipity element function space as the trial function space. Furthermore, we construct a family of unified dual partitions for arbitrary convex polygonal meshes, which is crucial to the finite volume element scheme, and present a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom. The optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained under certain geometric assumption conditions and verified by numerical experiments.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
S. Vengatesan, Sundararajan Natarajan, P. V. Jeyakarthikeyan
Summary: In this work, a new n +1 integration scheme over arbitrary polygonal elements based on centroid approximation and Richardson extrapolation scheme is proposed. The polygonal element is divided into quadrilateral subcells for numerical integration. The bilinear form is computed at the centroid of the polygonal element and at the center of the quadrilateral cells, resulting in less computational time and fewer integration points compared to existing approaches.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Junchao Wu, Dongdong Wang
Summary: This study focuses on the accuracy analysis of Galerkin meshfree methods, revealing the significant influence of numerical integration on error estimates. It is found that the integration difficulty of meshfree methods leads to the loss of the Galerkin orthogonality condition, affecting the establishment of error bounds.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Water Resources
Sajedeh Farmani, Mahnaz Ghaeini-Hessaroeyeh, Saleh Hamzehei-Javaran
Summary: In this study, the finite element method is employed to investigate water penetration in soil. By using new spherical Hankel shape functions, the method's accuracy and robustness are improved. The comparisons indicate that this method is more precise in handling seepage problems.
APPLIED WATER SCIENCE
(2023)
Article
Engineering, Multidisciplinary
George Bourantas, Benjamin F. Zwick, Grand R. Joldes, Adam Wittek, Karol Miller
Summary: This paper presents a meshless method belonging to the family of element-free Galerkin (EFG) methods, which allows accurate enforcement of essential boundary conditions using a total Lagrangian formulation with explicit time integration for simplicity and robust computations. The effectiveness and accuracy of the proposed method is demonstrated through 3D numerical examples.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics, Applied
William McLean
Summary: The Mittag-Leffler function is computed using a quadrature approximation of a contour integral representation, with a focus on evaluating on the real line. The main difference in this approach lies in the handling of poles in the integrand, compared to similar methods in existing literature. The study also delves into rational approximation of the Mittag-Leffler function on the negative real axis.
Article
Computer Science, Software Engineering
Yusuf H. Sahin, Alican Mertan, Gozde Unal
Summary: This paper proposes a representation method based on the local orientation distribution of point clouds to capture contextual shape information. The spherical neighborhood of a point is divided into predefined cone volumes, and statistics inside each volume are used as point features. By constructing the ODFNet model, state-of-the-art accuracy for object classification and segmentation tasks is achieved on different datasets.
COMPUTERS & GRAPHICS-UK
(2022)
Article
Engineering, Multidisciplinary
Changkye Lee, Sundararajan Natarajan, Seong-Hoon Kee, Jurng-Jae Yee
Summary: This work aims to investigate topology optimization with arbitrary polygonal domain discretization using a modified cell-based smoothed finite element method (S-FEM). By using linear polynomial basis function as the weight function, the accuracy is improved and an optimal convergence rate is achieved. In this proposed scheme, an optimal topology procedure is conducted over the smoothing domains, where structural materials are distributed and filtered.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2022)
Article
Mathematics, Applied
Zhaoliang Meng, Jintao Cui, Zhongxuan Luo
Summary: A new nonparametric nonconforming quadrilateral finite element is introduced to approximate the general second-order elliptic problem in two dimensions, along with optimal numerical integration formulas. These formulas, derived on a reference quadrilateral and involving only two quadrature nodes, are not required to be exact for all shape functions and can be used with other low-order elements in numerical tests.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Geochemistry & Geophysics
Shaobo Xia, Sheng Xu, Ruisheng Wang, Jonathan Li, Guanghui Wang
Summary: This study presents a method to extract individual buildings from ALS point clouds using widely accessible polygonal footprints. The method can achieve high instance-level building mapping accuracy around 90% and future work will focus on improving classification errors in preprocessing, shape inconsistencies between point clouds and polygons, as well as building footprint delineation and updating in postprocessing.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2022)
Article
Computer Science, Software Engineering
Philippe Maincon
Summary: EspyInsideFunction is a package for the Julia programming language that allows accessing the values of local variables within a function from outside. This is particularly useful for obtaining intermediate results in a solution process.
Article
Computer Science, Theory & Methods
Dinh Dung
Summary: This paper investigates the approximation of weighted integrals over Rd for integrands from weighted Sobolev spaces of mixed smoothness. Upper and lower bounds of the convergence rate of optimal quadratures with respect to n integration nodes for functions from these spaces are proved. In the one-dimensional case (d = 1), the right convergence rate of optimal quadratures is obtained. For d >= 2, the upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic crosses in the function domain Rd.
JOURNAL OF COMPLEXITY
(2023)
Article
Engineering, Multidisciplinary
Amir Latifaghili, Milad Bybordiani, Recep Emre Erkmen, Daniel Dias-da-Costa
Summary: The generalized finite element method has shown efficiency in handling crack propagation and internal boundaries. A novel approach based on enrichment Laplace shape functions effectively eliminates sources of oscillations, with excellent agreement with experimental/numerical data in structural examples with highly stiff cracks.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Mathematics, Applied
Song Lu, Xianmin Xu
Summary: This paper numerically studies several finite element methods for the Laplace-Beltrami eigenvalue problem on surfaces, including the original variant, a stabilized isoparametric element, and a new method with exact geometric descriptions. The impact of geometric consistency on the eigenvalue problem is carefully studied, and numerical experiments suggest that all methods have optimal convergence rates while geometric consistency significantly improves numerical accuracy.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Li Chen, Peter Z. Berke, Thierry J. Massart, Lars A. A. Beex, Marco Magliulo, Stephane P. A. Bordas
Summary: The quasicontinuum (QC) method is a concurrent multiscale approach that combines fully resolved lattice models in small regions of interest and coarse-grained models elsewhere. A new refinement indicator based on the energies of cells at coarse-grained domain surfaces is introduced in this study. This indicator is incorporated in an adaptive scheme of a generalized QC method, showing its impact on adaptive simulations in various lattice deformation scenarios.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Van-Nam Hoang, Trung Pham, Sawekchai Tangaramvong, Stephane P. A. Bordas, H. Nguyen-Xuan
Summary: This paper presents a novel robust concurrent topology optimization method for the design of uniform/non-uniform porous infills under the accidental change of loads. The method directly models multiscale structures and seeks robust designs by simultaneously optimizing macro- and microscopic structures through the minimization of the weighted sum of the expected compliance and standard deviation.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Shaima M. Dsouza, Tittu M. Varghese, Ean Tat Ooi, Sundararajan Natarajan, Stephane P. A. Bordas
Summary: This paper introduces a non-intrusive scaled boundary finite element method for handling multiple input uncertainties, including material and geometric uncertainties such as the shape and size of inclusions. A polynomial chaos expansion is utilized to represent the input and output uncertainties, and the efficiency and accuracy of the proposed framework are demonstrated through comparison with the conventional Monte Carlo method. A sensitivity analysis based on Sobol' indices is employed to identify the critical input parameter that has a higher influence on the output response.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Computer Science, Interdisciplinary Applications
A. Elouneg, D. Sutula, J. Chambert, A. Lejeune, S. P. A. Bordas, E. Jacquet
Summary: This study presents an open-source framework based on finite element model updating for identifying mechanical parameters of heterogeneous hyperelastic materials from full-field data. By simulating uniaxial tensile experiments on isotropic soft tissues, a model was established and parameter estimation was conducted, accurately identifying at least 4 parameters.
COMPUTERS & STRUCTURES
(2021)
Article
Acoustics
A. Calderon Hurtado, P. Peralta, R. O. Ruiz, M. Makki Alamdari, E. Atroshchenko
Summary: The study extended the PEH model to plates of variable thickness, investigated the impact of different shapes on power output, and optimized the thickness parameters to achieve optimal voltage and power outcomes.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Engineering, Mechanical
Patricio Peralta, O. Rafael Ruiz, Hussein Rappel, P. A. Stephane Bordas
Summary: This new framework utilizes dynamic estimators to infer the electromechanical properties in Piezoelectric Energy Harvesters (PEHs), overcoming the mismatch issue in updating properties associated with a set of PEHs. By modifying the likelihood function, the framework is able to account for a predictive model with three outputs obtained from the FRF.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Acoustics
E. Atroshchenko, C. Anitescu, T. Khajah, A. Calderon Hurtado
Summary: In this study, a numerical framework based on isogeometric collocation is developed to solve boundary value problems (BVPs) with absorbing boundary conditions (ABCs). The approach offers advantages such as lower computational cost, reduced pollution error, and the ability to evaluate higher order derivatives. The accuracy of the ABCs is analyzed through comparison with analytical solutions, and a detailed parametric study is conducted.
Article
Thermodynamics
Chintan Jansari, Stephane P. A. Bordas, Elena Atroshchenko
Summary: There is a growing interest in controlled heat flux manipulation to improve thermal apparatus efficiency. This study focuses on thermal metamaterial-based heat manipulators and optimizes their shape using Particle Swarm Optimization (PSO) method. The results show that the optimal shape of heat manipulators can be achieved by designing the thermal conductivity of the materials and adjusting the geometry parameters.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Computer Science, Interdisciplinary Applications
Changkye Lee, Indra Vir Singh, Sundararajan Natarajan
Summary: In this paper, the cell-based smoothed finite-element method (CS-FEM) is proposed for solving boundary value problems of gradient elasticity in two and three dimensions. The method eliminates the need for explicit form of the shape functions and iso-parametric mapping. The results show that the proposed framework is accurate and robust.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mechanics
Yicong Li, Tiantang Yu, Sundararajan Natarajan, Tinh Quoc Bui
Summary: This work aims to study dynamic crack propagation in brittle materials under time-dependent loading conditions using the adaptive isogeometric phase-field approach. The proposed approach combines the advantages of the phase-field method and isogeometric analysis, and is enhanced by utilizing locally refined non-uniform rational B-spline basis. The results demonstrate that the proposed approach can achieve accurate results with reduced degrees-of-freedom.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Acoustics
A. Calderon Hurtado, K. Kaur, M. Makki Alamdari, E. Atroshchenko, K. C. Chang, C. W. Kim
Summary: This paper proposes an unsupervised approach for bridge health monitoring using only the measured responses from a vehicle passing over a bridge. A data-driven framework based on adversarial autoencoder (AAE) is adopted, which incorporates generative capabilities of AAE and pre-processing techniques for better representation of data. The proposed framework is able to detect and estimate the severity of damage in the bridge, overcoming limitations of other unsupervised learning approaches.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Engineering, Multidisciplinary
Tiancheng Zhang, Hirshikesh, Tiantang Yu, Chen Xing, Sundararajan Natarajan
Summary: This work presents an adaptive phase-field method incorporated into a finite element framework combined with variable-node elements to investigate cohesive dynamic fracture. The proposed framework utilizes a hybrid form of the history field to drive the crack evolution and employs a staggered iteration scheme to compute the displacement and phase-field variables. The error indicator, utilizing the phase-field and history strain variables, is used to control the adaptive refinement process. The variable-node element technique facilitates adaptive mesh refinement and acts as a transition element between coarse and refined elements. The proposed method shows significant improvement in computational efficiency without sacrificing numerical accuracy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Mechanical
M. D. Iqbal, C. Birk, E. T. Ooi, S. Natarajan, H. Gravenkamp
Summary: This paper extends the scaled boundary finite element method (SBFEM) to model fracture in functionally graded materials (FGMs) and examines the effects of fully coupled transient thermoelasticity. It utilizes the previously developed SBFEM supplementary shape functions to model thermal stresses and approximates the spatial variation of thermal and mechanical properties of FGMs by polynomial functions. The dynamic stress intensity factors (SIFs) are evaluated semi-analytically from their definitions without the need for additional post-processing. This approach is validated through numerical examples and comparison with reference solutions.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Javier Videla, Ahmed Mostafa Shaaban, Elena Atroshchenko
Summary: In this paper, an adaptive shape optimization algorithm based on the concept of Geometry Independent Field approximation and the Sequential Quadratic Programming method for time harmonic acoustics is proposed. The method uses Non-Uniform Rational Basis Splines for geometry parametrization and hierarchical T-meshes for solution approximation, allowing for local and adaptive refinement of the solution to match boundary changes. The results demonstrate the high accuracy and efficiency of the technique.
COMPUTERS & STRUCTURES
(2024)
Article
Materials Science, Multidisciplinary
Rupesh Kumar Mahendran, Hirshikesh, Sundararajan Natarajan
Summary: This paper studies the effect of stress-diffusion interactions on the localization of plastic strain in an elastoplastic material using a fully coupled chemo-mechanical system. The transient coupled system is solved using a finite element formulation in the open-source finite element solver FEniCS. The role of geometric discontinuities and stress concentrations as well as plastic yielding on the diffusion-deformation process are investigated.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Jose Pedro G. Carvalho, Denis E. C. Vargas, Breno P. Jacob, Beatriz S. L. P. Lima, Patricia H. Hallak, Afonso C. C. Lemonge
Summary: This paper formulates a multi-objective structural optimization problem and utilizes multiple evolutionary algorithms to solve it. By optimizing the grouping of structural members, the best truss structure can be found. After analyzing various benchmark problems, the study reveals the existence of competitive structural member configurations beyond symmetry-based groupings.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Se-Hyeon Kang, Hyun-Seok Kim, Seonho Cho
Summary: This paper investigates shape identification using peridynamic theory and gradient-based optimization. The particle-based and non-local characteristics of peridynamics allow for direct interface modeling, avoiding remeshing difficulties. The boundary of scatterers is parameterized using B-spline surfaces, and design sensitivity is obtained using an efficient adjoint variable method. The accuracy and efficiency of the proposed method are verified through numerical examples.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Laura Rio-Martin, A. Prieto
Summary: Any numerical procedure in mechanics requires selecting an appropriate constitutive model for the material. The common assumptions for linear wave propagation in viscoelastic materials include the standard linear solid, Maxwell, Kelvin-Voigt, and fractional derivative models. Typically, the intrinsic parameters of the mathematical model are estimated based on available experimental data to fit the mechanical response of the chosen constitutive law. However, this approach may suffer from the uncertainty of inadequate model selection. In this work, the mathematical modeling and selection of frequency-dependent constitutive laws for linear viscoelastic materials are solely performed based on experimental measurements without imposing any functional frequency dependence. This data-driven methodology involves solving an inverse problem for each frequency.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Pramod Kumar Gupta, Chandrabhan Singh
Summary: In this paper, a novel algorithm is developed to generate the geometrical model of coarse aggregate, and it is further applied in the generation of a finite element model for concrete. Through numerical simulation and comparison with existing literature, the effectiveness of the meso-model is verified.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiao Wang, Qingrui Yue, Xiaogang Liu
Summary: This study proposes a graph neural networks-based method to recover the missing connection information in crack meshes, and comparative analysis shows that the trained GraphSAGE outperforms other GNNs on triangular meshing task, revealing the potential of GNNs in restoring missing information.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Dhiraj S. Bombarde, Manish Agrawal, Sachin S. Gautam, Arup Nandy
Summary: The study introduces a novel twenty-seven node quadratic EAS element, addressing the underutilization of quadratic elements in existing 3D EAS elements. Additionally, a six-node wedge and an eighteen-node wedge EAS element are presented in the manuscript.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Hau T. Mai, Seunghye Lee, Joowon Kang, Jaehong Lee
Summary: In this work, an effective Damage-Informed Neural Network (DINN) is developed for pinpointing the position and extent of structural damage. By using a deep neural network and Bayesian optimization algorithm, the proposed method outperforms other algorithms in terms of accuracy and efficiency.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Qingsong Xiong, Qingzhao Kong, Haibei Xiong, Lijia Liao, Cheng Yuan
Summary: This study proposes a novel physics-informed deep 1D convolutional neural network (SSM-CNN) for enhanced seismic response modeling. By construing the differential nexus of state variables derived from the state-space representation of initial structural response, an innovative parameter-free physics-constrained mechanism is designed and embedded for performance enhancement. Experimental validations confirmed the effectiveness and superiority of physics-informed SSM-CNN in seismic response prediction.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
D. Herrero-Perez, S. G. Pico-Vicente
Summary: This work presents an efficient, flexible, and scalable strategy for implementing density-based topology optimization formulation in fail-safe structural design. The use of non-overlapping domain decomposition, adaptive mesh refinement, and computing buffers allows for successful evaluation of fault cases.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiangyang Cui, Gongcheng Peng, Qi Ran, Huan Zhang, She Li
Summary: A novel degenerated shell element called MITC4+R is developed, which eliminates various locking problems common to shell elements and significantly improves the computational efficiency. It is based on assumed natural strain method and introduces a physical stabilization term.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Shouyan Jiang, Wangtao Deng, Ean Tat Ooi, Liguo Sun, Chengbin Du
Summary: This study presents an innovative data-driven algorithm that combines the scaled boundary finite element method and a deep learning framework for identifying crack-like defects in large-scale structures. The proposed algorithm accurately determines the number, location, and depth of cracks and is robust to noise. It provides valuable insight into the detection and diagnosis of structural defects.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Shiqiang Qin, Jiacheng Feng, Jian Tang, Xuejin Huo, Yunlai Zhou, Fei Yang, Magd Abdel Wahab
Summary: This study assesses the condition of a CFST arch bridge using in-situ vibration measurements, finite element model updating, and an improved artificial fish swarm algorithm. The results indicate that the bridge has good dynamic performance, but track conditions need improvement before operation.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Md. Imrul Reza Shishir, Alireza Tabarraei
Summary: In this paper, a density-based topology optimization method using neural networks is proposed for designing multi-material domains under combined thermo-mechanical loading. The method achieves automatic sensitivity analysis and removes the need for other optimization algorithms. Experimental results show that the method can handle high-resolution re-sampling, resulting in more refined and smooth optimal topologies.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Bartosz Sobczyk, Lukasz Pyrzowski, Mikolaj Miskiewicz
Summary: This paper describes the problems encountered during the analysis of the structural response of historic masonry railroad arch bridges. It focuses on the stiffness of the masonry arches, their strengths, and the estimation of railroad load intensity. The paper presents computational models created to efficiently describe the responses of the bridges under typical loading conditions and discusses the outcomes of nonlinear static analyses. The possible causes of the deterioration of the bridges' condition were identified through these analyses.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
T. Koudelka, T. Krejci, J. Kruis
Summary: This paper presents a numerical model for the coupled hydro-mechanical behaviour of partially saturated soils, and demonstrates its effective application through a numerical example.
COMPUTERS & STRUCTURES
(2024)