Article
Engineering, Geological
Ting Zhang, Xiaoping Zhou, Qihu Qian
Summary: This study proposes a peridynamic Drucker-Prager plastic model with a fractional order derivative to investigate the plastic behavior of rocks surrounding tunnels. The model employs the Caputo fractional derivative for its mathematical simplicity and uses multiple parameters to specify the direction of plastic deformation, including the fractional order and interval of the fractional derivative. The proposed model is a more generalized version compared to the traditional peridynamic Drucker-Prager plastic model, as it includes the typical nonassociated flow rule.
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS
(2022)
Article
Automation & Control Systems
Peter Gangl, Kevin Sturm
Summary: In this paper, we investigate the optimal distribution of two materials on C-2 submanifolds M of dimension d - 1 in R-d using the topological derivative. We analyze the perturbation of the differential operator and material coefficients and derive the corresponding topological derivative. Finally, we demonstrate how the topological derivative, together with a level set method on the surface, can be used to numerically solve the topology optimization problem.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Samuel Amstutz
Summary: This paper provides a self-contained introduction to the mathematical aspects of the topological derivative, with full justifications given on simple model problems using a modern approach. Closed expressions of topological derivatives are obtained and commented, covering several cases in a unified and didactic presentation. Some elements of proof are novel.
ENGINEERING COMPUTATIONS
(2022)
Article
Engineering, Multidisciplinary
Ting Zhang, Xiao-Ping Zhou
Summary: In this study, an ordinary state-based peridynamic (OSB-PD) plastic model is developed for simulating the large deformation of geomaterials. The OSB-PD model incorporates the PD dilatation, which is equivalent to the volumetric strain, and the PD material parameters are determined using an energy density matching approach. The PD force is calculated as the Frechet derivative of the PD energy density and is collinear with the deformed bond. The proposed model is verified through simulations of benchmark problems, including plate deformation and L-shaped panel test.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mechanics
Jiahao Kong, Haoyue Han, Tao Wang, Guangyan Huang, Zhuo Zhuang
Summary: This paper introduces a phase-field model for polymer foam materials by combining the phase-field method with the crushable foam model. The model is calibrated using experimental data and successfully simulates the fracture processes of polyurethane under different loading conditions. The study is important for the engineering applications of polymer foam materials.
ENGINEERING FRACTURE MECHANICS
(2024)
Article
Construction & Building Technology
Ali Permanoon, Amir Houshang Akhaveissy
Summary: The research introduces a novel technique to reduce the computational cost and memory usage of numerical modeling of structures with semi-brittle mechanical properties on a meso scale. By modeling certain parts of the numerical model on meso scale and the rest on macro scale, computational complexity and memory use are decreased without sacrificing accuracy. The paper develops non-linear topology optimization using the Drucker-Prager yield criterion and integrates it into ANSYS finite element software, and provides examples to analyze the application of this method.
CONSTRUCTION AND BUILDING MATERIALS
(2022)
Article
Computer Science, Interdisciplinary Applications
Lei Wang, Xingyu Zhao, Zhangming Wu, Wenpin Chen
Summary: This study presents an uncertainty-oriented cross-scale topology optimization model with global stress reliability constraint, local displacement constraint, and micro-manufacturing control based on evidence theory. The model designs the material distribution of both the macrostructure and the cell microstructure for a two-dimensional porous material structure. The uncertainty parameters are processed using evidence theory to evaluate the reliability of the structural strength performance.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Marcelo H. Kobayashi, Robert A. Canfield, Raymond M. Kolonay
Summary: This paper introduces a two-point topological derivative for elasticity and a cellular developmental method for layout optimization of structures. The method can easily account for member sizes and angle constraints among members of the frame and solve optimization problems in structural mechanics. Benchmark problems are solved to demonstrate the capability of the cellular developmental method.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Geological
Hongbo Du, Feng Dai, Mingdong Wei, Ang Li, Zelin Yan
Summary: The study finds that static confining pressure and dynamic loading rate enhance the load-carrying capacity of rocks, but the shear component limits the dynamic peak stress. With an increase in static confining pressure, the failure surface expands outward, while the compressive deformation modulus of rocks decreases with increasing shear component. The fragmentation behavior of rocks is restricted by static confining pressure and the shear component of dynamic loading, leading to a change in failure pattern as specimen inclination angle and static confining pressure increase.
ROCK MECHANICS AND ROCK ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Inocencio Castanar, Joan Baiges, Ramon Codina, Henning Venghaus
Summary: In this work, a topological optimization algorithm based on the topological derivative concept is proposed for both nearly and fully incompressible materials. By introducing a new decomposition of the Polarization tensor and applying mixed formulations and Variational Multiscale method, the accuracy of stress computation for incompressible material behavior is improved.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Mechanical
W. Q. Shen
Summary: This study establishes a macroscopic yield criterion for geomaterials considering the effects of different scales of porosity and mineral grains. The criterion is validated through comparisons with numerical results and experimental data.
INTERNATIONAL JOURNAL OF PLASTICITY
(2022)
Article
Computer Science, Interdisciplinary Applications
Ting Zhang, Xiao-Ping Zhou, Qi-Hu Qian
Summary: This paper proposes an ordinary state-based peridynamic model with shear deformation based on the Drucker-Prager model and the associated flow rule to study the plastic and damage behaviors of geomaterials. By considering the second invariant of the stress deviator and the first invariant function of the stress tensor as the function of peridynamic energy density, the nonlocal form of the Drucker-Prager yield function can be used in peridynamics.
ENGINEERING WITH COMPUTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jorge Morvan Marotte Luz Filho, Raquel Mattoso, Lucas Fernandez
Summary: This article presents an educational code using the concept of topological derivative, level-set domain representation method and adaptive mesh refinement processes for compliance minimization in structural optimization. The code is implemented in linearized elasticity framework for both plane strain and plane stress. The topological derivative is used as a steepest descent direction within the numerical procedure, similar to gradient-based methods. Adaptive mesh refinement processes are employed for enhancing resolution. The article provides explanations on computing topological derivatives and a step-by-step description of the code, along with numerical results showing the effectiveness and robustness of the proposed approach.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
A. A. Novotny, C. G. Lopes, R. B. Santos
Summary: This paper proposes a regularization formulation to address the difficulties of topology optimization of structures subject to self-weight loading, introduces a 0-1 topology design algorithm using the topological derivative method, and validates the effectiveness of the approach through numerical experiments.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Mechanical
Ting Zhang, Jian-Zhi Zhang
Summary: This paper proposes a method that combines the OSB-PD plastic model with the D-P criterion to numerically reproduce localized deformation and locate the critical failure surface of slopes. The strength reduction method is used to estimate the critical failure surface and factor of safety.
ENGINEERING FAILURE ANALYSIS
(2022)
Article
Mathematics, Applied
L. Fernandez, A. A. Novotny, R. Prakash, J. Sokolowski
Summary: The topological derivative method is used to solve a pollution sources reconstruction problem by minimizing a shape functional measuring the misfit between known data and the solution of the state equation. Two different cases are considered: reconstruction of unknown sources when the velocity of the leakages is given, and finding out the mean velocity and locations of leakages when the size of pollution sources is known. The proposed algorithm is shown to be capable of reconstructing multiple pollution sources in both cases through numerical examples.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Raquel Mattoso, Antonio A. Novotny
Summary: This work focuses on pointwise antennas design in hyperthermia treatment to selectively heat a specified target using optimal current densities. The methodology involves solving the steady-state heat equation and Helmholtz problem, minimizing an objective functional, and using sensitivities to devise antenna design algorithms. Numerical experiments demonstrate the capability of the proposed methodology to selectively heat the target up to the desired temperature.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Computer Science, Interdisciplinary Applications
Dirlei Ruscheinsky, Fernando Carvalho, Carla Anflor, Andre Antonio Novotny
Summary: This study conducted sensitivity analysis using the topological derivative method and devised a topology design algorithm based on a level-set representation method, resulting in simple analytical expressions. These findings provide useful insights for practical applications such as heat exchange topology design and membrane eigenvalue maximization.
ENGINEERING COMPUTATIONS
(2021)
Article
Engineering, Multidisciplinary
P. Menoret, M. Hrizi, A. A. Novotny
Summary: This work focuses on an inverse source problem related to the Poisson equation, aiming to reconstruct the unknown support location and size of a mass distribution using the Kohn-Vogelius formulation and topological derivative method. The resulting reconstruction procedure is non-iterative and robust with respect to noisy data. Numerical results from different examples of the Kohn-Vogelius type functional demonstrate the method's effectiveness and compare the robustness of each functional in solving the inverse source problem.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
F. S. Carvalho, D. Ruscheinsky, S. M. Giusti, C. T. M. Anflor, A. A. Novotny
Summary: This work introduces the topological derivatives of L(2) and energy norms associated with the solution to Kirchhoff and Reissner-Mindlin plate bending models. Closed forms of the sensitivities are presented based on existing theoretical results. An analytical formula is used with a level-set domain representation method to devise a simple topology design algorithm for plates under elastic support and free vibration condition. Several finite element-based numerical experiments demonstrate its applications for compliance minimization and eigenvalue maximization of Kirchhoff and Reissner-Mindlin plate structures under bending effects.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Interdisciplinary Applications
A. A. Novotny, C. G. Lopes, R. B. Santos
Summary: This paper proposes a regularization formulation to address the difficulties of topology optimization of structures subject to self-weight loading, introduces a 0-1 topology design algorithm using the topological derivative method, and validates the effectiveness of the approach through numerical experiments.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Industrial
Andre Jacomel Torii, Antonio Andre Novotny
Summary: This work presents priori error estimates for local reliability-based sensitivity analysis using the Score Function Method and Weak Approach with Monte Carlo Simulation. The results are crucial for practical parameter selection in local sensitivity analysis, and can also be utilized for future development of a posteriori error estimates and adaptive schemes. The theoretical results, initially obtained for the one dimensional case, are also applicable in multidimensional contexts, as evidenced by numerical experiments.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2021)
Editorial Material
Computer Science, Interdisciplinary Applications
Antonio Andre Novotny, Sebastian Miguel Giusti, Samuel Amstutz
ENGINEERING COMPUTATIONS
(2022)
Article
Mathematics, Applied
R. Prakash, M. Hrizi, A. A. Novotny
Summary: This paper presents a noniterative method for solving an inverse source problem governed by the two-dimensional time-fractional diffusion equation, using the topological derivative method to minimize a shape functional for reconstructing the geometrical support of the unknown source. The study results indicate that the proposed approach can efficiently and quickly reconstruct multiple anomalies of varying shapes and sizes, even when noisy data is taken into account.
Article
Computer Science, Interdisciplinary Applications
A. J. Torii, J. R. de Faria, A. A. Novotny
Summary: The main issue with existing constraint aggregation and regularization approaches is the significant bias that may affect the quality of the designs obtained, especially when dealing with a large number of active constraints. This paper proposes a novel probabilistic approach that overcomes such issues and allows for sharp regularization of extreme values even in the presence of closely spaced values. The proposed approach is compared with the p-norm regularization method and the results show that the proposed approach is more suitable for regularization and aggregation in such cases.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
A. A. M. da Silva, A. A. Novotny
Summary: In this work, a novel approach for solving a damage identification problem in plate structures is proposed, based on the topological derivative method. The method minimizes a shape function to determine the geometrical support of the unknown damage distribution, and represents the damage size and shape by minimizing the error between measured data and computed data.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Engineering, Multidisciplinary
R. Mattoso, L. H. Gabrielli, A. A. Novotny
Summary: A novel topology optimization method for nanophotonic energy concentrators is proposed in this work. The method maximizes a shape functional to find the best material distribution that concentrates energy in a given target domain, using the topological derivative method. It avoids issues from eigen-mode calculations and can be applied to different design domains. The associated topological gradient is rigorously derived and used to devise a black/white binary topology design algorithm that conforms to practical fabrication constraints.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
Mourad Hrizi, Antonio Andre Novotny, Maatoug Hassine
Summary: This paper discusses an inverse source problem governed by the Poisson equation and proposes a self-regularized topology optimization method to reconstruct multiple anomalies. It uses a least-square functional to measure the misfit between observation data and model values and applies the topological derivative method for the reconstruction process.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
(2022)
Article
Mathematics
M. Hrizi, A. A. Novotny, R. Prakash
Summary: Time-fractional diffusion equations have attracted attention from mathematicians due to their wide applicability. This paper investigates a time-fractional inverse source problem, analyzing it through two interconnected streams. The identifiability of this inverse problem is established by proving the existence of a unique solution based on observed data. Furthermore, the problem is reformulated as a topology optimization problem with a quadratic mismatch functional and a regularization term, leading to the design of a noniterative reconstruction algorithm using the topological derivative method.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Engineering, Multidisciplinary
Jorge M. M. Luz Filho, Marcel Xavier, Antonio A. Novotny, Marcio A. Murad
Summary: We propose a new operator splitting scheme to describe fluid-driven brittle fracture propagation in a Biot medium. The scheme consists of two steps: in the injection step, a fixed stress split scheme is used to solve the hydrodynamic subsystem and the geomechanics, and in the fast time scale step, pore mechanics and fracture propagation are solved with frozen pore pressure and Darcy velocity fields. The evolution of the damaged zone is governed by the sensitivity of the associated shape functional with respect to the nucleation of a small damaged zone, which is computed using the topological derivative method.
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
(2022)
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)
