Article
Mathematics, Interdisciplinary Applications
N. Climent, I. D. Moldovan, E. D. Bendea
Summary: This paper derives the formulation of hybrid-Trefftz displacement finite elements for transient problems in three-dimensional elastic media. The formulation is implemented as a new module in FreeHyTE, an open-source and user-friendly Trefftz platform. Numerical tests show satisfactory results for the new 3D FreeHyTE module implemented with the functions derived in this paper.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Christoph Lehrenfeld, Paul Stocker
Summary: A new variant called embedded Trefftz discontinuous Galerkin method is proposed, which is the Galerkin projection of an underlying discontinuous Galerkin method onto a subspace of Trefftz-type. This method allows for convenient extension to general cases, reduces globally coupled unknowns significantly, and improves accuracy in the Helmholtz problem.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Sanjib Kumar Acharya, Kamana Porwal
Summary: This manuscript explores a primal hybrid finite element method for the two-dimensional linear elasticity problem. It provides a priori error estimates for both primal and hybrid variables. The method is robust as its convergence rate is independent of the Lame parameters. Numerical experiments are conducted to validate the theoretical findings.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mechanics
Meral Tuna, Patrizia Trovalusci
Summary: The study compared the micropolar and Eringen's models with classical model on infinite plates weakened by elliptic holes, showing that non-local effects reduce maximum stress more prominently with increasing aspect ratio of the ellipse.
COMPOSITE STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
J. P. Moitinho de Almeida, Jonatha Reis
Summary: We propose a methodology to define the matrices used in stress based finite element approximations for three-dimensional problems. By rotating the global reference frame, the increased complexity of the 3D case is greatly simplified. This rotation can also be applied to the 2D case. The focus of this work is on the matrices used in the implementation of the hybrid equilibrium approach, but we also present a complementary displacement-based methodology for efficiently defining the matrices required for dual analysis.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Philippe R. B. Devloo, Agnaldo M. Farias, Sonia M. Gomes, Weslley Pereira, Antonio J. B. dos Santos, Frederic Valentin
Summary: The work introduces a family of multiscale hybrid-mixed methods for the two-dimensional linear elasticity problem on general polygonal meshes. These methods approximate displacement, stress, and rotation using two-scale discretizations, with stability and convergence proved in a unified framework. The methods are shown to be optimal and high-order convergent, with super-convergent properties in the L-2-norm for the approximate displacement and stress divergence.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2021)
Article
Mechanics
S. El Shawish, T. Mede
Summary: A simple analytical model is proposed to describe the intergranular normal stresses in elastic polycrystalline materials. The model provides algebraic expressions for the local grain-boundary-normal stress and uncertainties as a function of various parameters. Understanding intergranular normal stresses is important in predicting damage and failure in structural materials. The model is derived through a perturbative approach and validated against finite element simulations.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Mechanics
Tobias Kaiser, Samuel Forest, Andreas Menzel
Summary: This contribution presents a finite element implementation of the stress gradient theory by introducing a generalised displacement field variable to reformulate the governing set of partial differential equations. The associated weak formulation stipulates boundary conditions in terms of the normal projection of the generalised displacement field or the stress tensor. The proposed formulation is validated through analytical solutions for a cylindrical bar under tension and torsion, showing a smaller size effect in stress gradient elasticity solutions compared to strain gradient elasticity solutions.
Article
Engineering, Multidisciplinary
Ionut Dragos Moldovan, Natalia Climent, Elena Daniela Bendea, Ildi Cismasiu, Antonio Gomes Correia
Summary: Hybrid-Trefftz finite elements are suitable for modeling materials under highly transient loading, embedding physical information and removing sensitivity to high solution gradients. However, there is currently no public software using this method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics
Todd Arbogast, Chuning Wang
Summary: This paper introduces new families of direct serendipity and direct mixed finite elements defined on general planar, strictly convex polygons. The finite elements provide optimal approximation while using the minimal degrees of freedom. The paper proposes alternative ways to construct supplemental functions on the element, resulting in better accuracy and robustness in numerical tests.
Article
Mathematics, Applied
Jakob Leck
Summary: Lower bounds are demonstrated for a specific quotient of differences of Taylor polynomials of functions whose inverse Fourier transform is non-negative and additionally may be isotropic or decreasing. This provides insight on the spectra of differential operators obtained by using truncated moment expansions, especially their definiteness. Physical applications include the approximation of nonlocal elasticity or nonlocal electrostatics by gradient theories, and the Kramers-Moyal expansion.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Engineering, Multidisciplinary
Tom Gustafsson, Peter Raback, Juha Videman
Summary: The purpose of this work is to investigate mortar methods for linear elasticity using standard low order finite element spaces. A stabilized mortar method for linear elasticity is introduced based on residual stabilization and compared with the unstabilized mixed mortar method. Numerical results demonstrate the stability and convergence of the methods for tie contact problems, as well as the successful extension of the mixed method to three dimensional problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Jeffrey S. Ovall, Samuel E. Reynolds
Summary: H-1-conforming Galerkin methods on polygonal meshes employ local finite element functions to solve Poisson problems with polynomial source and boundary data. These methods have recently been extended to handle curvilinear polygons in mesh cells. We propose an integration approach that reduces integrals on cells to integrals along their boundaries, and demonstrate the practical performance of our methods through numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Hongliang Li, Pingbing Ming, Huiyu Wang
Summary: This paper establishes a new H2-Korn's inequality and its discrete analog, simplifying the construction of nonconforming elements for a linear strain gradient elastic model. Analysis of the Specht triangle and NZT tetrahedron as representatives demonstrates robust nonconforming elements with convergence rate independent of small material parameter. Construction of regularization interpolation operators and enriching operators for both elements is achieved with error estimates under minimal smoothness assumption on the solution. Numerical results for smooth solution and solution with boundary layer are consistent with theoretical predictions.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
C. Carstensen, S. Sauter
Summary: In this paper, we prove that Crouzeix-Raviart finite elements of polynomial order p >= 5, p odd, are inf-sup stable for the Stokes problem on triangulations. By introducing a new representation and deriving all possible critical functions, we show that they belong to the range of the divergence operator, resulting in the stability of the discretization.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Environmental Sciences
Lixin Li, Xiaolu Zhou, Marc Kalo, Reinhard Piltner
INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH
(2016)
Article
Environmental Sciences
L. Li, X. Zhang, R. Piltner
JOURNAL OF ENVIRONMENTAL INFORMATICS
(2008)
Article
Environmental Sciences
Lixin Li, Travis Losser, Charles Yorke, Reinhard Piltner
INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH
(2014)
Article
Engineering, Multidisciplinary
Reinhard Piltner
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2019)
Proceedings Paper
Computer Science, Hardware & Architecture
Travis Losser, Lixin Li, Reinhard Piltner
2014 FIFTH INTERNATIONAL CONFERENCE ON COMPUTING FOR GEOSPATIAL RESEARCH AND APPLICATION (COM.GEO)
(2014)
Article
Computer Science, Interdisciplinary Applications
R Piltner
COMPUTERS & STRUCTURES
(2002)
Article
Construction & Building Technology
T Celestino, R Piltner, PJM Monteiro, CP Ostertag
JOURNAL OF MATERIALS IN CIVIL ENGINEERING
(2001)
Article
Engineering, Multidisciplinary
R Piltner, DS Joseph
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING
(2001)
Article
Mathematics, Interdisciplinary Applications
R Piltner, DS Joseph
COMPUTATIONAL MECHANICS
(2001)
Article
Materials Science, Multidisciplinary
R Piltner
MATHEMATICS AND MECHANICS OF SOLIDS
(2001)
Article
Mathematics, Interdisciplinary Applications
R Piltner
COMPUTATIONAL MECHANICS
(2000)
Article
Construction & Building Technology
R Piltner, PJM Monteiro
CEMENT AND CONCRETE RESEARCH
(2000)
Letter
Engineering, Multidisciplinary
R Piltner
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2001)
Letter
Engineering, Multidisciplinary
R Piltner
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2001)
Article
Mathematics, Applied
Guo Zheng, Zengqiang Cao, Yuehaoxuan Wang, Reza Talemi
Summary: This study introduces two novel methods for predicting the fatigue response of Dynamic Cold Expansion (DCE) and Static Cold Expansion (SCE) open-hole plates. The accuracy of the prediction is enhanced by considering stress distributions and improving existing methods. The study also discusses the mechanisms behind fatigue life enhancement and fatigue crack propagation modes in cold expansion specimens.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Eric Heppner, Tomohiro Sasaki, Frank Trommer, Elmar Woschke
Summary: This paper presents a modeling approach for estimating the bonding strength of friction-welded lightweight structures. Through experiments and simulations, a method for evaluating the bonding strength of friction-welded lightweight structures is developed, and the plausibility and applicability of the model are discussed.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Piermario Vitullo, Alessio Colombo, Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Summary: Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. Traditional projection based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Chanh Dinh Vuong, Xiaofei Hu, Tinh Quoc Bui
Summary: In this paper, we present a dynamic description of the smoothing gradient-enhanced damage model for the simulation of quasi-brittle failure localization under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of the dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Alexandre D. C. Amaro, A. Francisca Carvalho Alves, F. M. Andrade Pires
Summary: This study focuses on analyzing various deformation mechanisms that affect the behavior of PC/ABS blends using computational homogenization. By establishing a representative microstructural volume element, defining the constitutive description of the material phases, and modeling the interfaces and matrix damage, accurate predictions can be achieved. The findings have important implications for broader applications beyond PC/ABS blends.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
David Hoffmeyer, A. R. Damanpack
Summary: This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. The efficacy of the method is validated by numerical examples and a benchmark example, and the analysis on a real sawn timber cross-section reveals significant disparities in the maximum stresses compared to conventional engineering approaches.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Vladimir Stojanovic, Jian Deng, Dunja Milic, Marko D. Petkovic
Summary: The present paper investigates the dynamic analysis of a coupled Timoshenko beam-beam or beam-arch mechanical system with geometric nonlinearities. A modified p-version finite element method is developed for the vibrations of a shear deformable coupled beam system with a discontinuity in an elastic layer. The main contribution of this work is the discovery of coupled effects and phenomena in the simultaneous vibration analysis of varying discontinuity and varying curvature of the newly modelled coupled mechanical system. The analysis results are valuable and have broader applications in the field of solids and structures.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Gihwan Kim, Phill-Seung Lee
Summary: The phantom-node method is applied in the phase field model for mesh coarsening to improve computational efficiency. By recovering the fine mesh in the crack path domain into a coarse mesh, this method significantly reduces the number of degrees of freedom involved in the computation.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Souhail Chaouch, Julien Yvonnet
Summary: In this study, an unsupervised machine learning-based clustering approach is developed to reduce the computational cost of nonlinear multiscale methods. The approach clusters macro Gauss points based on their mechanical states, reducing the problem from macro scale to micro scale. A single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster, using a linear approximation of the macro stress. Anelastic macro strains are used to handle internal variables. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Hoang-Giang Bui, Jelena Ninic, Christian Koch, Klaus Hackl, Guenther Meschke
Summary: With the increasing demand for underground transport infrastructures, it is crucial to develop methods and tools that efficiently explore design options and minimize risks to the environment. This study proposes a BIM-based approach that connects user-friendly software with effective simulation tools to analyze complex tunnel structures. The results show that modeling efforts and computational time can be significantly reduced while maintaining high accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Aslan Nasirov, Xiaoyu Zhang, David Wagner, Saikumar R. Yeratapally, Caglar Oskay
Summary: This manuscript presents an efficient model construction strategy for the eigenstrain homogenization method (EHM) for the reduced order models of the nonlinear response of heterogeneous microstructures. The strategy relies on a parallel, element-by-element, conjugate gradient solver, achieving near linear scaling with respect to the number of degrees of freedom used to resolve the microstructure. The linear scaling in the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. The developed framework has been verified using an additively manufactured polycrystalline microstructure of Inconel 625.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Atticus Beachy, Harok Bae, Jose A. Camberos, Ramana V. Grandhi
Summary: Emulator embedded neural networks leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. However, training the ensemble models can be costly and pose computational challenges. This work presents a new type of emulator embedded neural network using the rapid neural network paradigm, which trains near-instantaneously without loss of prediction accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Arash Hajisharifi, Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: This paper introduces three reduced order models for reducing computational time in atmospheric flow simulation while preserving accuracy. Among them, the PODI method, which uses interpolation with radial basis functions, maintains accuracy at any time interval.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
D. Munoz, S. Torregrosa, O. Allix, F. Chinesta
Summary: The Proper Generalized Decomposition (PGD) is a Model Order Reduction framework used for parametric analysis of physical problems. It allows for offline computation and real-time simulation in various situations. However, its efficiency may decrease when the domain itself is considered as a parameter. Optimal transport techniques have shown exceptional performance in interpolating fields over geometric domains with varying shapes. Therefore, combining these two techniques is a natural choice. PGD handles the parametric solution while the optimal transport-based methodology transports the solution for a family of domains defined by geometric parameters.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Jothi Mani Thondiraj, Akhshaya Paranikumar, Devesh Tiwari, Daniel Paquet, Pritam Chakraborty
Summary: This study develops a diffused interface CPFEM framework, which reduces computational cost by using biased mesh and provides accurate results using non-conformal elements in the mesh size transiting regions. The accuracy of the framework is confirmed through comparisons with sharp and stepped interface results.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)