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Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction [article]

Chuong Nguyen, Xiaoying Zhuang, Ludovic Chamoin, Hung Nguyen-Xuan, Xianzhong Zhao, Timon Rabczuk
2019 arXiv   pre-print
Two- and three-dimensional numerical results show the effectiveness of the topology optimization algorithm coupled with the reduced basis approach in designing metamaterials.  ...  The central idea relies on using the isogeometric analysis integrated with the parameterized level set function for numerical homogenization, sensitivity calculation and optimization of the effective elastic  ...  We further design three-dimensional metamaterials with negative Poisson's ratio by considering a cubic unit cell and investigate the efficiency of using reduced modeling when the size of problems is increased  ... 
arXiv:1908.11449v1 fatcat:yab47trbdzggxpyxqcfpjtxpzq

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

Jie Gao, Mi Xiao, Yan Zhang, Liang Gao
2020 Chinese Journal of Mechanical Engineering  
In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided  ...  In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications.  ...  Authors' Contributions JG implemented the numerical process of the ITO method and its many applications, and JG is also the main writer of this manuscript.  ... 
doi:10.1186/s10033-020-00503-w fatcat:cyerffdnnbedlpf2wrilw5k7zu

Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models

J. Niiranen, V. Balobanov, J. Kiendl, S. B. Hosseini
2017 Mathematics and mechanics of solids  
Size-dependency of the effective Young's modulus is demonstrated for an auxetic cellular metamaterial ruled by bending-dominated deformation of cell struts.  ...  behavior -one of these kinds (possessed by three models out of four) provides results in a very good agreement with size effects of experimental tests.  ...  Acknowledgements The first, the second and the fourth author has been supported by Academy of Finland through the project entitled Adaptive isogeometric methods for thin-walled structures (decisions 270007  ... 
doi:10.1177/1081286517739669 fatcat:h2uywyxlgjbqfo3zker5sgwk7m

Microarchitecture-dependent nonlinear bending analysis for cellular plates with prismatic corrugated cores via an anisotropic strain gradient plate theory of first-order shear deformation

Jalal Torabi, Jarkko Niiranen
2021 Engineering structures  
The strain energy formulation is based on the dimension reduction of the first-order shear deformation plate theory along with von Kármán's nonlinear strain relations and anisotropic strain gradient theory  ...  Torabi, Jalal; Niiranen, Jarkko Microarchitecture-dependent nonlinear bending analysis for cellular plates with prismatic corrugated cores via an anisotropic strain gradient plate theory of first-order  ...  of a three-dimensional solid body.  ... 
doi:10.1016/j.engstruct.2021.112117 fatcat:7inwhg3jefbmba3y2vexef2mtm

Homogenization of strain gradient continua: constitutive parameter identification, size effects analysis, and brittle fracture propagation [article]

Hua Yang, Technische Universität Berlin, Wolfgang H. Müller
A scaling rule for strain gradient moduli is given. 2D and 3D numerical examples are conducted and materials parameters are identified for metamaterials including lattice structures, composite materials  ...  The classical stiffness parameters are independent of the microstructural sizes, the higher order ones are influenced by that.  ...  .: Manufacturing oriented topology optimization of 3D structures for carbon emission reduction in casting process. J. Clean. Prod. 225, 755–770 (2019) 56.  ... 
doi:10.14279/depositonce-12553 fatcat:ftkt7xk3lfc7fjtoxfsrlpdjpe

Overcoming stress singularities : combining phase-field modelling of fracture, strain gradient theory, and isogeometric analysis [article]

Resam Makvandi, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Daniel Juhre
In the strain gradient theory, the strain energy functional contains both the strain terms and their gradients, which leads to stresses depending on higher-order derivatives of the displacement field.  ...  One can regularize the stress field and therefore, remove the negative effects of the singularities by exploiting these strain gradient models.  ...  “A higher-order phase- field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework”.  ... 
doi:10.25673/42915 fatcat:7wtrvvp7w5frfc533ido3howwe

Volumetric Subdivision for Efficient Integrated Modeling and Simulation

Christian Altenhofen
Isogeometric Analysis (IGA) tries to overcome this meshing hurdle by using the same representation for describing the geometry and for performing the simulation.  ...  In order to analyze physical properties such as stability, aerodynamics, or heat dissipation, the continuous models are discretized into finite element (FE) meshes.  ...  hexahedral and tetrahedral meshes, used for Finite Element Analysis (FEA) • Trivariate spline models -spline volumes -used for Isogeometric Analysis (IGA) and for multi-material additive manufacturing  ... 
doi:10.26083/tuprints-00014617 fatcat:6dv5eyroyfg4xfvguuzifgslqa

APM 2017. Book of abstracts [article]

"Advanced Problems In Mechanics (APM 2017)", International Conference (45; 2017; St. Petersburg, Russia), Russian Academy Of Sciences. Institute For Problems In Mechanical Engineering, University, Peter The Great St. Petersburg Polytechnic
Here we present a simple model for the dynamics of one dimensional of self-gravitating spherical symmetrical gas and dust cloud.  ...  Statical and dynamical analysis of the presented nonlinear problem of electroelasticity is performed, where the microbeams are modeled as Euler-Bernoulli beams, including the nonlinear electric forces  ...  Third, from that pressure distribution we computed the velocity of the region border and computationally modeled the process of border deformation.  ... 
doi:10.18720/spbpu/2/k17-23 fatcat:us6nhplc3rbhrgowwocdqa2wrq

APM 2016. Book of Abstracts [article]

"Advanced Problems In Mechanics" (APM 2016), International Conference (44; 2016; St. Petersburg), Russian Academy Of Sciences. Institute For Problems In Mechanical Engineering, University, Peter The Great St. Petersburg Polytechnic
The authors kindly acknowledge funding from the project TAMER, Trans-Atlantic Micromechanics Evolving Research "Materials containing inhomogeneities of diverse physical properties, shapes and orientations  ...  The authors acknowledge financial support of the Russian Science Foundation (grant 15-19-10056 The authors acknowledge the support within the framework of IRSES Project TAMER (PIRSES-GA-2013-610547).  ...  The goal of the paper is to describe a methodology, which can be used to solve topology optimization problem in nano-level by defining optimization objectives and constraints imposed on design variables  ... 
doi:10.18720/spbpu/2/k16-40 fatcat:yegzycnwbrco7dwsdnsjxvwbc4