Computational structural mechanics within strain gradient elasticity: mathematical formulations and isogeometric analysis for metamaterial design
| dc.contributor | Aalto-yliopisto | fi |
| dc.contributor | Aalto University | en |
| dc.contributor.advisor | Niiranen, Jarkko, Assistant Prof., Aalto University, Department of Civil Engineering, Finland | |
| dc.contributor.author | Balobanov, Viacheslav | |
| dc.contributor.department | Rakennustekniikan laitos | fi |
| dc.contributor.department | Department of Civil Engineering | en |
| dc.contributor.lab | Computational Structural Engineering | en |
| dc.contributor.school | Insinööritieteiden korkeakoulu | fi |
| dc.contributor.school | School of Engineering | en |
| dc.contributor.supervisor | Niiranen, Jarkko, Assistant Prof., Aalto University, Department of Civil Engineering, Finland | |
| dc.date.accessioned | 2018-06-12T09:02:49Z | |
| dc.date.available | 2018-06-12T09:02:49Z | |
| dc.date.defence | 2018-06-18 | |
| dc.date.issued | 2018 | |
| dc.description.abstract | The dissertation studies the majority of the most relevant and widespread physico-mathematical models of structural mechanics within the theory of strain gradient elasticity: gradient-elastic bars, beams, two- and three-dimensional solids and shells. Hamilton's principle, a variational energy approach, is utilized for deriving the strong, weak and finite element formulations of the related problems of statics and dynamics. For the most fundamental problems of the work, existence and uniqueness of weak solutions as well as error estimates for the corresponding conforming Galerkin discretizations are proved within the framework of Sobolev spaces. This theoretical foundation serves as a basis for the development and implementation of isogeometric conforming Galerkin methods within both open source and commercial finite element software packages. A set of benchmark problems for statics and free vibrations is solved for verification purposes and, in particular, for confirming the optimal convergence properties of the methods provided by the theoretical analysis. The numerical shear locking phenomenon for the Timoshenko beam model is studied and, furthermore, two different locking-free formulations are proposed and shown to guarantee optimal convergence results. Various generalized beam models are compared to each other and the most crucial differences between these models, related to the so-called stiffening size effect, are demonstrated by analytical and numerical solutions. The importance of higher-order rotatory inertia terms is highlighted in the context of gradient elasticity. Boundary layers arising due to the presence of the parameter-dependent higher-order terms and non-standard boundary conditions of the gradient-elastic Euler–Bernoulli beams are addressed. All the considered beam models, the Euler–Bernoulli, Timoshenko and the higher-order shear deformable ones, are extended for a case of anisotropic materials. Another advantage of the strain and velocity gradient elasticity theory, regularization of stress singularities, is demonstrated in the context of shell structures, in particular. The ability of the generalized beam models to capture size effects of microstructured continua at different length scales from nano- to macro-scale is demonstrated by comparisons to experimental results for nano- and micro-beams and by comparisons to computational results obtained from fine-scale models for lattice structures and auxetic metamaterials. The computational results cover engineering sandwich lattice beams as well. Extending these results to plates and shells, especially, unlocks a door for utilizing the theoretical results and computational methods of the dissertation for designing microarchitectured materials or mechanical metamaterials with predefined properties. | en |
| dc.format.extent | 63 + app. 157 | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.isbn | 978-952-60-8053-6 (electronic) | |
| dc.identifier.isbn | 978-952-60-8052-9 (printed) | |
| dc.identifier.issn | 1799-4942 (electronic) | |
| dc.identifier.issn | 1799-4934 (printed) | |
| dc.identifier.issn | 1799-4934 (ISSN-L) | |
| dc.identifier.uri | https://aaltodoc.aalto.fi/handle/123456789/31840 | |
| dc.identifier.urn | URN:ISBN:978-952-60-8053-6 | |
| dc.language.iso | en | en |
| dc.opn | Altenbach, Holm, Prof., Otto-von-Guericke-Universität Magdeburg, Germany | |
| dc.publisher | Aalto University | en |
| dc.publisher | Aalto-yliopisto | fi |
| dc.relation.haspart | [Publication 1]: Jarkko Niiranen, Sergei Khakalo, Viacheslav Balobanov, Antti H. Niemi. Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems. Computer Methods in Applied Mechanics and Engineering, 308:182–211, August 2016. DOI: 10.1016/j.cma.2016.05.008 | |
| dc.relation.haspart | [Publication 2]: Jarkko Niiranen, Viacheslav Balobanov, Josef Kiendl, S. Bahram Hosseini. Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models. Mathematics and Mechanics of Solids, 24 pages. November 2017. DOI: 10.1177/1081286517739669 | |
| dc.relation.haspart | [Publication 3]: Saba Tahaei Yaghoubi, Viacheslav Balobanov, S. Mahmoud Mousavi, Jarkko Niiranen. Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler–Bernoulli and shear-deformable beams. European Journal of Mechanics - A/Solids, 69:113–123, May–June 2018. DOI: 10.1016/j.euromechsol.2017.11.012 | |
| dc.relation.haspart | [Publication 4]: Sergei Khakalo, Viacheslav Balobanov, Jarkko Niiranen. Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics. International Journal of Engineering Science, 127:33–52, June 2018. DOI: 10.1016/j.ijengsci.2018.02.004 | |
| dc.relation.haspart | [Publication 5]: Viacheslav Balobanov, Jarkko Niiranen. Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity. Computer Methods in Applied Mechanics and Engineering, 339:137–159, September 2018. DOI: 10.1016/j.cma.2018.04.028 | |
| dc.relation.haspart | [Publication 6]: Viacheslav Balobanov, Josef Kiendl, Sergei Khakalo, Jarkko Niiranen. Kirchhoff-Love shells within strain gradient elasticity: weak and strong formulations and an H3-conforming isogeometric implementation. Computer Methods in Applied Mechanics and Engineering, Under revision, 32 pages, 2018. | |
| dc.relation.haspart | [Errata file]: Errata Viacheslav Balobanov DD-121/2018 publications P2 and P4 | |
| dc.relation.ispartofseries | Aalto University publication series DOCTORAL DISSERTATIONS | en |
| dc.relation.ispartofseries | 121/2018 | |
| dc.rev | Oterkus, Erkan, Assoc. Prof., University of Strathclyde, UK | |
| dc.rev | Rosi, Giuseppe, Assoc. Prof., Université Paris-Est Créteil Val de Marne, France | |
| dc.subject.keyword | strain gradient elasticity | en |
| dc.subject.keyword | structural models | en |
| dc.subject.keyword | variational formulations | en |
| dc.subject.keyword | isogeometric analysis | en |
| dc.subject.keyword | convergence | en |
| dc.subject.keyword | shear locking | en |
| dc.subject.keyword | size effects | en |
| dc.subject.keyword | microstructure | en |
| dc.subject.keyword | architectured materials | en |
| dc.subject.keyword | metamaterials | en |
| dc.subject.other | Civil engineering | en |
| dc.title | Computational structural mechanics within strain gradient elasticity: mathematical formulations and isogeometric analysis for metamaterial design | en |
| dc.type | G5 Artikkeliväitöskirja | fi |
| dc.type.dcmitype | text | en |
| dc.type.ontasot | Doctoral dissertation (article-based) | en |
| dc.type.ontasot | Väitöskirja (artikkeli) | fi |
| local.aalto.acrisexportstatus | checked | |
| local.aalto.archive | yes | |
| local.aalto.formfolder | 2018_06_12_klo_09_07 |
