Article
Mathematics, Interdisciplinary Applications
Jianghuai Li
Summary: This paper proposes a new shell element formulation using the scaled boundary finite element method, which can effectively avoid Poisson thickness locking phenomenon and demonstrate good applicability and efficiency in numerical calculations.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Civil
Jianghuai Li
Summary: This study proposes new finite element methods for functionally graded piezoelectric shells that can accurately, efficiently, and comprehensively describe such structures. The shell element is treated as a three-dimensional continuum and its middle surface is represented with a quadrilateral spectral element. The shell geometry is described by scaling the middle surface along the thickness, while the displacements and electric potential are approximated using consistent quadratic Lagrange interpolation. The developed approach is verified by solving piezoelectric or functionally graded plate problems with reference solutions. The influence of power-law index and span-to-thickness ratio on the static and free vibration behaviors of the functionally graded structures is investigated and the optimal value of lambda for general functionally graded shells is determined.
THIN-WALLED STRUCTURES
(2023)
Article
Computer Science, Interdisciplinary Applications
Jianghuai Li, Zihua Zhang, Lei Liu
Summary: This paper introduces new variable-order shell elements that only require the discretization of the shell mid-surface, utilize the assumed natural strain method to eliminate locking effects, and demonstrate superior performance in terms of applicability, accuracy, and efficiency.
COMPUTERS & STRUCTURES
(2022)
Article
Mathematics, Applied
Chong-Jun Li, Ying Zhang, Yan-Mei Jia, Juan Chen
Summary: The paper introduces a powerful method for solving elastostatics problems based on polygonal elements, the scaled boundary finite element method (SBFEM). It presents the construction of a quadratic polygonal scaled boundary element and a polygonal scaled boundary thin plate element which can possess the second order completeness. The proposed method avoids computing the shape functions of SBFEM and shows good accuracy in numerical examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mechanics
Jianghuai Li, Zihua Zhang, Zhenwen Zhang
Summary: This paper presents new shell elements for the analysis of functionally graded plates and shells with varying material properties through the thickness. The shell element is treated as a three-dimensional linear elastic body and its middle surface is represented with a quadrilateral spectral element. The shell geometry is described by scaling the middle surface and the displacements are approximated using quadratic Lagrange shape functions. The developed shell elements eliminate various locking phenomena and require only the shell mid surface to be discretized. The formulation is validated through benchmark examples and gravity load problems.
COMPOSITE STRUCTURES
(2022)
Article
Engineering, Multidisciplinary
Carolin Birk, Maximilian Reichel, Joerg Schroeder
Summary: In this work, a hybrid SBFEM-FEM approach is proposed for efficient calculation of magnetic stray fields in unbounded domains. The method divides the entire domain into finite and infinite sub-regions, models the interior domain using finite elements, reduces the exterior domain onto the boundary of the interior domain using SBFEM, and provides a semi-analytical solution for the magnetostatic problem in an unbounded domain.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Andrea Vezzosi, Andrea Bertoni, Guido Goldoni
Summary: We investigate the electronic band structure of modulation-doped GaAs/AlGaAs core-shell nanowires using an 8-band Burt-Foreman k??p Hamiltonian approach. We consider Coulomb interactions and map the equations onto optimized real-space grids using the finite element method. We obtain self-consistent charge-density, single-particle subbands, density of states, and absorption spectra at different doping regimes, and observe unique features in the anisotropy of linearly polarized optical absorption.
Article
Mechanics
Guoqiang Wei, Pascal Lardeur, Frederic Druesne
Summary: A new solid-shell approach for thin to very thick structures is proposed, applying plate or shell displacement fields directly on a solid finite element model. Three theories were considered and resulted in FOSS, MFOSS, and HOSS models. Kinematic relations are imposed at nodes to meet displacement fields. Comparison with the solid approach showed that the HOSS model gives excellent results for both thin and thick cases.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Nai-Cheng Wu, Ying-Qing Huang, Hai -Bo Chen
Summary: In this paper, a new incompatible unsymmetric 8-node hexahedral solid-shell element is proposed with different sets of trial and test functions. The new element inherits advantages from the original solid element and also eliminates typical locking phenomena for shell elements. Numerical investigations show that the new element is insensitive to mesh distortion and has rapid convergence. It can provide locking-free predictions with high precision for thin shell structures. Furthermore, the accuracy of the element is demonstrated in geometrically nonlinear analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Daniel Hoover, Ashok V. Kumar
Summary: An immersed boundary shell element formulation based on Kirchhoff-Love shell theory is presented in this study, using a background mesh consisting of uniform 3D B-spline elements within which the geometry and the boundaries are embedded. The formulation includes a 3D shell element under small deformation assumptions with three translational degrees of freedom per node and quadratic B-Spline shape functions, essential boundary conditions are applied using the step boundary method, and benchmark problems are used to validate the presented 3D Bspline thin shell element.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2021)
Article
Engineering, Geological
Jia-Long Li, Ding-Hao Yu, Gang Li
Summary: The inelastic seismic response analysis of large infrastructure requires consideration of soil-structure dynamic interaction and refined simulation, with a focus on developing efficient solving algorithms and appropriate element formulations for achieving precise and flexible mesh generation. Various emerging algorithms, such as the scaled boundary finite element method (SBFEM), are being developed to accelerate the computation of inelastic response analyses. Implementing semi-analytical methods with Gaussian numerical integration and inelasticity-separated approaches can improve nonlinear solving efficiency without compromising precision, as demonstrated in numerical examples.
SOIL DYNAMICS AND EARTHQUAKE ENGINEERING
(2022)
Article
Mechanics
Hirshikesh, A. L. N. Pramod, Ean Tat Ooi, Chongmin Song, Sundararajan Natarajan
Summary: This work presents a framework for adaptive contact analysis in deformable solids, utilizing the SBFEM error indicator and quadtree decomposition, implemented and demonstrated using Abaqus for solving engineering significant contact problems.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Engineering, Multidisciplinary
Karolinne O. Coelho, Philippe R. B. Devloo, Sonia M. Gomes
Summary: The Scaled Boundary Finite Element Method (SBFEM) is a technique for constructing approximation spaces using a semi-analytical approach, with a focus on deriving a priori error estimates for solutions of harmonic test problems. By characterizing SBFEM spaces in the context of Duffy's approximations and investigating similarities with virtual harmonic approximations, optimal convergence rates for smooth solutions have been confirmed through numerical experiments with polytopal meshes. The SBFEM method also shows optimal accuracy rates for approximating a point singular solution and finite element approximations elsewhere.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(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
Mathematics, Applied
Fleurianne Bertrand, Daniele Boffi, Gonzalo G. de Diego
Summary: SBFEM is a boundary element method for approximating solutions to PDEs without needing a fundamental solution. A theoretical framework for convergence analysis of SBFEM is proposed, using a space of semi-discrete functions and an interpolation operator. Error estimates for this operator are proved, demonstrating optimal convergence in SBFEM, supported by two numerical examples.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2021)
Review
Computer Science, Interdisciplinary Applications
Hauke Gravenkamp, Albert A. Saputra, Sascha Duczek
Summary: The scaled boundary finite element method (SBFEM) is a semi-analytical approach that combines finite element approximation with analytical solutions to solve partial differential equations. Various shape functions have been used to interpolate solutions on the boundary. This study aims to review the advantages and disadvantages of different interpolants in the context of SBFEM and provide recommendations for their application.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2021)
Correction
Engineering, Multidisciplinary
Milan Wallner, Carolin Birk, Hauke Gravenkamp
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Junqi Zhang, Ankit Ankit, Hauke Gravenkamp, Sascha Eisentraeger, Chongmin Song
Summary: This paper introduces a parallel explicit solver utilizing the advantages of balanced octree meshes and employing the scaled boundary finite element method (SBFEM). By pre-computing the stiffness and mass matrices of unique cell patterns, the hanging nodes problem in standard finite element analysis is avoided. The proposed scheme is implemented in a distributed computing environment and its performance is evaluated through various numerical benchmark examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Mechanical
Simon Pfeil, Hauke Gravenkamp, Fabian Duvigneau, Elmar Woschke
Summary: This study introduces a semi-analytical solution of the Reynolds equation based on the Scaled Boundary Finite Element Method to reduce the numerical effort in rotor system dynamics simulation. By discretizing the two-dimensional pressure field in one direction and using an analytical formulation in the other direction, a new approach is employed to solve the system of non-homogeneous ordinary differential equations.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Acoustics
Dominik Itner, Hauke Gravenkamp, Dmitrij Dreiling, Nadine Feldmann, Bernd Henning
Summary: This paper presents an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders, demonstrating efficiency and accuracy. The model allows for applying various loads on the cylinder surface and increases efficiency by limiting the number of Fourier coefficients and dynamically adjusting discretization.
Article
Engineering, Multidisciplinary
S. Eisentrager, J. Eisentrager, H. Gravenkamp, C. G. Provatidis
Summary: This article comprehensively discusses the construction and performance assessment of versatile transition elements for applications in dynamics, focusing on the use of special shape function construction to achieve diagonalization of the mass matrix.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
M. D. Iqbal, C. Birk, E. T. Ooi, H. Gravenkamp
Summary: This study presents the development of the scaled boundary finite element method for modeling discrete crack propagation induced by thermal loads. The SBFEM excels in accurately modeling stress singularities at sharp crack tips. The formulation for steady-state thermal stress analysis is presented, with consideration for initial strains due to temperature in subsequent stress analysis. Several numerical examples are provided to validate the technique and illustrate its features.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Joerg Schroeder, Maximilian Reichel, Carolin Birk
Summary: In this paper, an efficient and simple finite-element procedure is proposed for solving open boundary problems in magnetostatics. The method avoids the restrictions of conventional methods in handling the exterior space.
COMPUTATIONAL MECHANICS
(2022)
Article
Mechanics
M. D. Iqbal, C. Birk, E. T. Ooi, A. L. N. Pramod, S. Natarajan, H. Gravenkamp, C. Song
Summary: The scaled boundary finite element method is extended to model fracture in functionally graded materials under coupled thermo-mechanical loads. The proposed technique is validated through numerical examples for isotropic and orthotropic FGMs.
ENGINEERING FRACTURE MECHANICS
(2022)
Article
Materials Science, Multidisciplinary
Sundararajan Natarajan, Ean Tat Ooi, Carolin Birk, Chongmin Song
Summary: This paper proposes a quadtree-based adaptive phase-field method for solving dynamic brittle fracture problems in isotropic material. Through numerical studies, the efficiency of this method in capturing crack morphology is demonstrated.
INTERNATIONAL JOURNAL OF FRACTURE
(2022)
Article
Engineering, Multidisciplinary
Carolin Birk, Maximilian Reichel, Joerg Schroeder
Summary: In this work, a hybrid SBFEM-FEM approach is proposed for efficient calculation of magnetic stray fields in unbounded domains. The method divides the entire domain into finite and infinite sub-regions, models the interior domain using finite elements, reduces the exterior domain onto the boundary of the interior domain using SBFEM, and provides a semi-analytical solution for the magnetostatic problem in an unbounded domain.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
R. Assaf, C. Birk, S. Natarajan, H. Gravenkamp
Summary: An adaptive phase-field approach is proposed for three-dimensional fracture modeling in brittle materials. The scaled boundary finite element method (SBFEM) is used to solve the equations, and the accuracy of the solution is ensured using an error indicator and a phase-field evolution criterion. The computational cost is reduced by exploiting the geometric similarity of cells in balanced octree meshes.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Simon Pfeil, Hauke Gravenkamp, Fabian Duvigneau, Elmar Woschke
Summary: A semi-analytical solution of the Reynolds equation is developed based on the scaled boundary finite element method (SBFEM), combining it with a nonlinear cavitation model. The resulting bearing forces are in good agreement with a standard numerical reference solution.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
