Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
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    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 41)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 20)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 21)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 9)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 2)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 11)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 22)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 7)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Computational Mechanics
Journal Prestige (SJR): 1.775
Citation Impact (citeScore): 3
Number of Followers: 11  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0924 - ISSN (Online) 0178-7675
Published by Springer-Verlag Homepage  [2469 journals]
  • On the stability of POD basis interpolation on Grassmann manifolds for
           parametric model order reduction

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      Abstract: Abstract Proper Orthogonal Decomposition (POD) basis interpolation on Grassmann manifolds has been successfully applied to problems of parametric model order reduction (pMOR). In this work we address the necessary stability conditions for the interpolation, all defined from strong mathematical background. A first condition concerns the domain of definition of the logarithm map. Second, we show how the stability of interpolation can be lost if certain geometrical requirements are not satisfied by making a concrete elucidation of the local character of linearization. To this effect, we draw special attention to the Grassmannian exponential map and the optimal injectivity condition of this map, related to the cut–locus of Grassmann manifolds. From this, an explicit stability condition is established and can be directly used to determine the loss of injectivity in practical pMOR applications. A third stability condition is formulated when increasing the number p of POD modes, deduced from the principal angles of subspaces of different dimensions p. Definition of this condition leads to an understanding of the non-monotonic oscillatory behavior of the Reduced Order Model (ROM) error-norm with respect to the number of POD modes, and on the contrary, the well-behaved monotonic decrease of the error-norm in the two numerical examples presented herein. We have chosen to perform pMOR in hyperelastic structures using a non-intrusive approach for inserting the interpolated spatial POD ROM basis in a commercial FEM code. The accuracy is assessed by a posteriori error norms defined using the ROM FEM solution and its high-fidelity counterpart simulation. Numerical studies successfully ascertained and highlighted the implication of stability conditions which are general and can be applied to a variety of other linear or nonlinear problems involving parametrized ROMs generation based on POD basis interpolation on Grassmann manifolds.
      PubDate: 2022-07-01
       
  • A unified reproducing kernel gradient smoothing Galerkin meshfree approach
           to strain gradient elasticity

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      Abstract: Abstract A unified reproducing kernel gradient smoothing formulation is presented for efficient Galerkin meshfree analysis of strain gradient elasticity problems with particular reference to high order basis functions, such as cubic and quartic basis functions. The integration constraint is elaborated for the Galerkin meshfree formulation of strain gradient elasticity, where the possible inconsistency issue associated with the separate first and second order gradient smoothing formalism is completely resolved. In this approach, the first order smoothed gradients of meshfree shape functions are expressed as a reproduced kernel form and the second order smoothed gradients are deduced from their first order counterparts through direct differentiation. Thereafter, the unknown coefficients in the first and second order smoothed gradients are simultaneously solved from the integration constraint. The resulting smoothed gradients automatically meet the integration consistency by construction. Subsequently, it is proven that the reproducing kernel gradient smoothing quadrature rules for the conventional elasticity problems are well suitable for the strain gradient elasticity problems. Numerical results clearly demonstrate the superior performance of the proposed approach regarding convergence, accuracy, as well as efficiency, in comparison with the Gauss integration-based meshfree formulation for strain gradient elasticity problems.
      PubDate: 2022-07-01
       
  • Novel first and second order numerical differentiation techniques and
           their application to nonlinear analysis of Kirchhoff–Love shells

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      Abstract: Abstract Numerical simulation based on FEM/IGA methods is the standard approach for the approximated solution of applied physical problems. In this context, the differentiation of the numerical counterpart of mechanical fields is required. Moreover, the differentiated function can have a complicated shape, depend on many variables and change within the process. Many state-of-the-art numerical differentiation methods are not suitable for this kind of applications and the common way is to exploit analytical differentiation. Thus, an on-the-fly differentiation method is desirable particularly when the process is complicated and when new mechanical models are under development. In this paper, a new method is proposed for a precise computation of the gradient and Hessian. This method has been applied to nonlinear analysis of Kirchhoff–Love shells, which can be considered as an appropriate test bench to prove the reliability in relevant physical context. Numerical experiments show the advantages of the proposed techniques with respect to standard approaches.
      PubDate: 2022-07-01
       
  • A multiscale, data-driven approach to identifying thermo-mechanically
           coupled laws—bottom-up with artificial neural networks

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      Abstract: Abstract In this paper a multiscale data-driven approach is developed to model the effective macro-scale thermo-mechanical properties for isotropic, hyperelastic materials, subjected to finite deformation. Two independent artificial neural networks (ANNs) are designed to describe a stress–strain law with temperature dependence, and a heat-conduction law with gradients informed by updated nodal positions. A dimensionless representative volume element (RVE) is designed to generate training data. The ANNs are thus trained offline with this RVE data, to serve as a reliable replacement of classical constitutive equations and macro-scale homogenization, which systematically bypasses the need for their often daunting mathematical formalisms. Our trained ANNs are thus used to drive the online solution of boundary value problems (BVPs) within a commercial finite element (FEM) package. Illustrative examples for homogeneous and heterogeneous microstructures are herein presented, which demonstrate that our approach yields reliable thermo-mechanical predictions, and obtains accurate results when compared against direct numerical simulation (DNS).
      PubDate: 2022-07-01
       
  • Robust hybrid/mixed finite elements for rubber-like materials under severe
           compression

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      Abstract: Abstract A new family of hybrid/mixed finite elements optimized for numerical stability is introduced. It comprises a linear hexahedral and quadratic hexahedral and tetrahedral elements. The element formulation is derived from a consistent linearization of a well-known three-field functional and related to Simo–Taylor–Pister (STP) elements. For the quadratic hexahedral and tetrahedral elements we derive (static reduced) discontinuous hybrid elements, as well as continuous mixed finite elements with additional primary unknowns for the hydrostatic pressure and the dilation, whereas the linear hexahedral element is of the discontinuous type. The elements can readily be used in combination with any isotropic, invariant-based hyperelastic material model and can be considered as being locking-free. In a representative numerical benchmark test the elements numerical stability is assessed and compared to STP-elements and the family of discontinuous hybrid elements implemented in the commercial finite element code Abaqus/Standard. The new elements show a significant advantage concerning the numerical robustness.
      PubDate: 2022-07-01
       
  • Shape optimization of a linearly elastic rolling structure under
           unilateral contact using Nitsche’s method and cut finite elements

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      Abstract: Abstract The main motivation of this work is to develop a numerical strategy for the shape optimization of a rolling elastic structure under contact with respect to a uniform rolling criterion. A first objective is to highlight the influence on the treatment of the contact terms. To do so, we present a numerical comparison between a penalty-based approach and the use of Nitsche’s method which is known to have good consistency properties. A second task concerns the construction of an objective functional to force the uniform rolling criterion. Here, we present and compare two different strategies that will lead to quite similar results. All the numerical experiments proposed in this paper were performed using a fictitious domain approach coupled with a level set representation of the shape and the use of a cut finite element method to approximate the elastic equation.
      PubDate: 2022-07-01
       
  • Space–time isogeometric analysis of car and tire aerodynamics with road
           contact and tire deformation and rotation

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      Abstract: Abstract We present a space–time (ST) isogeometric analysis framework for car and tire aerodynamics with road contact and tire deformation and rotation. The geometries of the computational models for the car body and tires are close to the actual geometries. The computational challenges include i) the complexities of these geometries, ii) the tire rotation, iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, iv) the turbulent nature of the flow, v) the aerodynamic interaction between the car body and the tires, and vi) NURBS mesh generation for the complex geometries. The computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) method, and the element-based mesh relaxation (EBMR). The ST context provides higher-order accuracy in general, the VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, and the moving-mesh feature of the ST context enables high-resolution flow computation near the moving fluid–solid interfaces. The ST-SI enables moving-mesh computation with the tire rotating. The mesh covering the tire rotates with it, and the SI between the rotating mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-TC enables moving-mesh computation even with the TC created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the tire and road surfaces. It also enables dealing with the tire–road contact location change and contact sliding. By integrating the ST-IGA with the ST-SI and ST-TC, in addition to having a more accurate representation of the tire geometry and increased accuracy in the flow solution, the element density in the tire grooves and in the narrow spaces near the contact areas is kept at a reasonable level. The NSVGMG enables NURBS mesh generation for the complex car and tire geometries, and the EBMR improves the quality of the meshes. The car and tire aerodynamics computation we present shows the effectiveness of the analysis framework we have built.
      PubDate: 2022-07-01
       
  • An efficient numerical scheme for the FE-approximation of magnetic stray
           fields in infinite domains

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      Abstract: Abstract In this contribution we propose an efficient and simple finite-element procedure for the approximation of open boundary problems for applications in magnetostatics. In these problems, the interaction of the solid with external space plays a crucial role because of the magnetic stray fields that arise. For this purpose, the infinite region under consideration is approximated by a sufficiently large domain. This region is then divided into a so-called interior domain and an exterior domain. As an essential prerequisite, we assume linear behavior of the (large) exterior domain. The latter is then reduced to the degrees of freedom of the connecting line (2D)/connecting surface (3D) of both domains via static condensation. The proposed finite element scheme can be seen as an alternative to established methods for infinite domains. These methods often require semi-analytical solutions to describe the behavior in the exterior domain, which can be difficult to obtain if heterogeneous structures are present. The proposed finite element procedure is not subject to any restrictions with regard to the topology of the exterior space. After a general introduction of the numerical scheme, we apply the method to problems of magnetostatics with nonlinear behavior in the interior domain.
      PubDate: 2022-07-01
       
  • A new method based on Taylor expansion and nearest-node strategy to impose
           Dirichlet and Neumann boundary conditions in ordinary state-based
           Peridynamics

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      Abstract: Abstract Peridynamics is a non-local continuum theory which is able to model discontinuities in the displacement field, such as crack initiation and propagation in solid bodies. However, the non-local nature of the theory generates an undesired stiffness fluctuation near the boundary of the bodies, phenomenon known as “surface effect”. Moreover, a standard method to impose the boundary conditions in a non-local model is not currently available. We analyze the entity of the surface effect in ordinary state-based peridynamics by employing an innovative numerical algorithm to compute the peridynamic stress tensor. In order to mitigate the surface effect and impose Dirichlet and Neumann boundary conditions in a peridynamic way, we introduce a layer of fictitious nodes around the body, the displacements of which are determined by multiple Taylor series expansions based on the nearest-node strategy. Several numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.
      PubDate: 2022-07-01
       
  • An image-based multi-level hp FCM for predicting elastoplastic behavior of
           imperfect lattice structure by SLM

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      Abstract: Abstract In metallic additive manufacturing (AM), the process-induced geometrical defects challenge the boundary-conforming mesh-based numerical methods for predicting the as-fabricated mechanical properties of the parts with geometrical deviation from their as-designed counterparts. In this study, a computed tomography (CT) image-based multi-level hp finite cell method (FCM) is proposed to predict elastoplastic behaviors of the imperfect 3D lattice structure by the selective laser melting AM. The voxel data of the CT scans of the build are used to generate the locally refined structured mesh with the composed quadrature points utilizing the refine-by-superposition concept to achieve h and p refinements. Therefore, the struts’ external and internal geometrical defects can be efficiently resolved in the FCM discretization model for an accurate prediction of the mechanical behaviors of the builds. The numerical results obtained by the proposed method have shown a good agreement with the experimental data. It is identified that the effect of external geometrical defects on elastoplastic responses of the AM products is significant, while the effect of the internal voids is relatively minor, partly because of their low volume fraction.
      PubDate: 2022-07-01
       
  • A continuous model for the simulation of manufacturing swarm robotics

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      Abstract: Abstract Manufacturing large and/or complex structural components is today non-trivial and far-too expensive, due to limitations in the state-of-the-art production processes. Swarm robotics could then bring a different perspective and it may promise flexible, autonomous, and highly robust solutions for a large variety of applications; hence, its adoption in industry and construction may change manufacturing rules. The present contribution introduces a continuous model to capture the behavior of a swarm of manufacturing agents (e.g., drones, 3D printers, etc.. ) as well as a very simple, but effective, numerical implementation to simulate the evolution of such a swarm. The paper also presents one- and two-dimensional examples, showing the potentiality of the proposed approach in predicting swarm behaviors.
      PubDate: 2022-07-01
       
  • Modeling arbitrarily oriented and reorienting multiscale cracks in
           composite materials with adaptive multiscale discrete damage theory

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      Abstract: Abstract An adaptive multiscale modeling approach based on the multiscale discrete damage theory (MDDT) is established to describe formation of arbitrarily oriented and progressively reorienting cracks at multiple scales in heterogenous materials. MDDT tracks the fracture process over a set of discrete cohesive failure surfaces in the microstructure and consistently bridges the microscopic cracks to the continuum representation of damage at macroscale based on the reduced-order homogenization method. In this manuscript, the adaptation to arbitrary orientation of a crack is achieved using the idea of effective rotation of microstructure which reorients the prescribed failure path at the direction of crack propagation. The MDDT model representing the microstructure is analytically transformed given a crack nucleation orientation and an identification criterion. The performance of the proposed model is demonstrated at the microscale under multiaxial loading conditions. The predictive capabilities of the model are validated using four-point bending test of concrete beam and delamination migration experiments of fiber-reinforced composite cross-ply laminates. The qualitative and quantitative evaluations of crack propagation and reorientation show good agreement with the experimental results.
      PubDate: 2022-06-26
       
  • Data-driven multiscale method for composite plates

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      Abstract: Abstract Composite plates are widely used in many engineering fields such as aerospace and automotive. An accurate and efficient multiscale modeling and simulation strategy is of paramount importance to improve design and manufacture. To this end, we propose an efficient data-driven computing scheme based on the classical plate theory for the multiscale analysis of composite plates. In order to accurately describe the relationship between the macroscopic mechanical properties and the microscopic architecture, the multiscale finite element method (FE \(^2\) ) is adopted to compute the generalized strain and stress fields. These data are then used to construct a database for data-driven computing. Since the database is offline populated, the data-driven computing scheme allows for a reduced computational cost when compared to the traditional multiscale method, where the concurrent coupling of different scales is still a burden. And data are obtained from a reduced structural model for computational efficiency. The proposed scheme is therefore addressed as Structural-Genome-Driven (SGD) modeling of plates. Compared to the general data-driven computational mechanics modeling of plates, SGD is found to be more efficient since the number of integration points is significantly reduced. This scheme provides a robust alternative computational tool for composite plate structures analysis.
      PubDate: 2022-06-21
       
  • Efficient acoustic topology optimization with the Multifrequency
           Quasi-Static Ritz vector (MQSRV) method

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      Abstract: Abstract This research develops a new acoustic topology optimization scheme with a model order reduction called the Multifrequency Quasi Static Ritz Vector (MQSRV) method which effectively reduces the size of the system matrix for the calculating responses as well as sensitivity values in frequency domain. Computing the accurate acoustic responses and sensitivity values with the finite element (FE) method usually requires a significant amount of computational resources. For an efficient optimization, this research adopts recent developments in computational model order reduction approach having successfully exploited advanced mathematical development for calculating accurate solutions of partial differential equation. Among model order reduction schemes, the present study uses the MQSRV method which calculates the Ritz vector bases at multiple frequencies to minimize the amplitude of sound pressure in objective domain. Through several design examples, the efficiency and reliability of the MQSRV method for the acoustic topology optimization are verified.
      PubDate: 2022-06-18
       
  • Concurrent n-scale modeling for non-orthogonal woven composite

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      Abstract: Abstract Concurrent analysis of composite materials can provide the interaction among scales for better composite design, analysis, and performance prediction. A data-driven concurrent n-scale modeling approach ( \(\text {FExSCA}^\text {n-1}\) ) is adopted in this paper for woven composites utilizing a mechanistic reduced order model (ROM) called Self-consistent Clustering Analysis (SCA). We demonstrated this concurrent multiscale modeling theory with a \(\text {FExSCA}^2\) approach to study the 3-scale woven carbon fiber reinforced polymer (CFRP) laminate structure. \(\text {FExSCA}^2\) significantly reduced expensive 3D nested composite representative volume element (RVE) computation for woven and unidirectional (UD) composite structures by developing a material database. The modeling procedure is established by integrating the material database into a woven CFRP structural numerical model, formulating a concurrent 3-scale modeling framework. This framework provides an accurate prediction for the structural performance (e.g., nonlinear structural behavior under tensile load), as well as the woven and UD physics field evolution. The concurrent modeling results are validated against physical tests that link structural performance to the basic material microstructures. The proposed methodology provides a comprehensive predictive modeling procedure applicable to general composite materials aiming to reduce laborious experiments needed.
      PubDate: 2022-06-18
       
  • Isogeometric blended shells for dynamic analysis: simulating aircraft
           takeoff and the resulting fatigue damage on the horizontal stabilizer

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      Abstract: Abstract Aircraft horizontal stabilizers are prone to fatigue damage induced by the flow separation from aircraft wings and the subsequent impingement on the stabilizer structure in its wake, which is known as a buffet event. In this work, the previously developed isogeometric blended shell approach is reformulated in a dynamic analysis setting for the simulation of aircraft takeoff using varying pitch angles. The proposed Kirchhoff–Love (KL) and continuum shell blending allows the critical structural components of the aircraft horizontal stabilizer to be modeled using continuum shells to obtain high-fidelity 3D stresses, whereas the less critical components are modeled using computationally efficient KL thin shells. The imposed aerodynamic loads are generated from a hybrid immersogeometric and boundary-fitted computational fluid dynamics (CFD) analysis to accurately record the dynamic excitation on the stabilizer external surface. Specifically, the entire aircraft except for the wings and stabilizers is immersed into a non-boundary-fitted fluid domain based on the immersogeometric analysis (IMGA) concept for computational savings, whereas the mesh surrounding the aircraft wing and stabilizers is boundary-fitted to accurately compute the aerodynamic loads on the stabilizer. The obtained time histories of the loads are then applied to dynamic blended shell analysis of the horizontal stabilizer, and the high-fidelity stress response is evaluated for subsequent fatigue assessment. A simple frequency-domain fatigue analysis is then carried out to evaluate the buffet-induced fatigue damage of the stabilizer. The results from both the steady-state and dynamic nonlinear blended shell analyses of a representative horizontal stabilizer demonstrate the numerical accuracy and computational efficiency of the proposed approach.
      PubDate: 2022-06-18
       
  • Reduced-order multiscale modeling of plastic deformations in 3D alloys
           with spatially varying porosity by deflated clustering analysis

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      Abstract: Abstract Aluminum alloys are increasingly utilized as lightweight materials in the automobile industry due to their superior capability in withstanding high mechanical loads. A significant challenge impeding the large-scale use of these alloys in high-performance applications is the presence of manufacturing-induced, spatially varying porosity defects. In order to understand the impacts of these defects on the macro-mechanical properties of cast alloys, multiscale simulations are often required. In this paper, we introduce a computationally efficient reduced-order multiscale framework to simulate the behavior of metallic components containing process-induced porosity under irreversible nonlinear deformations. In our approach, we start with a data compression scheme that significantly reduces the number of unknown macroscale and microscale variables by agglomerating close-by finite element nodes into a limited number of clusters. Then, we use deflation methods to project these variables into a lower-dimensional space where the material’s elastoplastic behaviors are approximated. Finally, we solve for the unknown variables and map them back to the original, high-dimensional space. We call our method deflated clustering analysis and by comparing it to direct numerical simulations we demonstrate that it accurately captures macroscale deformations and microscopic effective responses. To illustrate the effect of microscale pores on the macroscopic response of a cast component, we conduct multi-scale simulations with spatially varying local heterogeneities that are modeled with a microstructure characterization and reconstruction algorithm.
      PubDate: 2022-06-11
       
  • Consistent pressure Poisson splitting methods for incompressible
           multi-phase flows: eliminating numerical boundary layers and inf-sup
           compatibility restrictions

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      Abstract: Abstract For their simplicity and low computational cost, time-stepping schemes decoupling velocity and pressure are highly popular in incompressible flow simulations. When multiple fluids are present, the additional hyperbolic transport equation in the system makes it even more advantageous to compute different flow quantities separately. Most splitting methods, however, induce spurious pressure boundary layers or compatibility restrictions on how to discretise pressure and velocity. Pressure Poisson methods, on the other hand, overcome these issues by relying on a fully consistent problem to compute the pressure from the velocity field. Additionally, such pressure Poisson equations can be tailored so as to indirectly enforce incompressibility, without requiring solenoidal projections. Although these schemes have been extended to problems with variable viscosity, constant density is still a fundamental assumption in existing formulations. In this context, the main contribution of this work is to reformulate consistent splitting methods to allow for variable density, as arising in two-phase flows. We present a strong formulation and a consistent weak form allowing standard finite element spaces. For the temporal discretisation, backward differentiation formulas are used to decouple pressure, velocity and density, yielding iteration-free steps. The accuracy of our framework is showcased through a wide variety of numerical examples, considering manufactured and benchmark solutions, equal-order and mixed finite elements, first- and second-order stepping, as well as flows with one, two or three phases.
      PubDate: 2022-06-11
       
  • A large deformation isogeometric continuum shell formulation incorporating
           finite strain elastoplasticity

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      Abstract: Abstract An isogeometric large-deformation continuum shell formulation incorporating finite strain elastoplasticity is presented in this work. The proposed method is based on the multiplicative decomposition of the deformation gradient into the elastic and plastic contributions in a total Lagrangian framework. The standard return mapping algorithm with the backward Euler time integration technique is adopted to solve the 3D elastoplastic constitutive equations. The classical \(J_2\) von Mises plasticity model with isotropic hardening is implemented to describe the nonlinear material behavior. The results of several benchmark studies are illustrated to showcase the computational accuracy and solution robustness of the proposed formulation.
      PubDate: 2022-06-11
       
  • Finite element methodology for modeling aircraft aerodynamics:
           development, simulation, and validation

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      Abstract: Abstract In this work, we propose and validate a new stabilized compressible flow finite element framework for the simulation of aerospace applications. The framework is comprised of the streamline upwind/Petrov–Galerkin (SUPG)-based Navier–Stokes equations for compressible flows, the weakly enforced essential boundary conditions that act as a wall function, and the entropy-based discontinuity-capturing equation that acts as a shock-capturing operator. The accuracy and robustness of the framework is tested for various Mach numbers ranging from low-subsonic to transonic flow regimes. The aerodynamic simulations are carried out for 2D and 3D validation cases of flow around the NACA 0012 airfoil, RAE 2822 airfoil, ONERA M6 wing, and NASA Common Research Model (CRM) aircraft. The pressure coefficients obtained from the simulations of all cases are compared with experimental data. The computational results show good agreement with the experimental findings and demonstrate the accuracy and effectiveness of the finite element framework presented in this work for the simulation of aircraft aerodynamics.
      PubDate: 2022-06-10
       
 
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