Strain gradient continuum mechanics: simplified models, variational formulations and isogeometric analysis with applications

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.advisor Niiranen, Jarkko, Assistant Prof., Aalto University, Department of Civil Engineering, Finland Khakalo, Sergei 2017-11-22T10:02:47Z 2017-11-22T10:02:47Z 2017
dc.identifier.isbn 978-952-60-7748-2 (electronic)
dc.identifier.isbn 978-952-60-7747-5 (printed)
dc.identifier.issn 1799-4942 (electronic)
dc.identifier.issn 1799-4934 (printed)
dc.identifier.issn 1799-4934 (ISSN-L)
dc.description.abstract This dissertation is devoted to two families of generalized continuum theories: the first and second strain gradient elasticity theories including the first and second velocity gradient inertia, respectively. First of all, a number of model problems is studied by analytical means revealing the key characters and potential of generalized continuum theories. In particular, the classical Kirsch problem is extended to the case of a simplified first strain gradient elasticity model demonstrating the size dependency of stresses and strains in the vicinity of a round hole in a plate in tension. Within linearly isotropic second strain gradient elasticity theory, instead, a simplified model is proposed, still capable of capturing free surface effects and surface tension, in particular, arising in solids of both nano- and macro-scales. With a series of benchmark problems, including a comprehensive set of stability analyses, the role of higher-order material parameters is revealed. On the way towards computational analysis, the boundary value problems of the fourth- and sixth-order partial differential equations arising in the first and second strain gradient models, respectively, are formulated and analysed in a mathematical variational form within appropriate Sobolev space settings. For numerical simulations, isogeometric Galerkin methods meeting higher-order continuity requirements are implemented in a user element framework of a commercial finite element software. Various benchmarks for statics and free vibrations confirm the optimal convergence properties of the numerical methods, verify the implementation and demonstrate the key properties of the underlying higher-order continuum models. Regarding model validation and applications, thorough analyses of stretching, shearing and vibration phenomena of complex triangular lattices homogenized by the simplified second strain gradient elasticity model reveal the strong size dependency of lattice structures and hence provide pivotal information for practical applications of materials and structures with a microstructure or microarchitecture. en
dc.format.extent 50 + app. 118
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher Aalto University en
dc.publisher Aalto-yliopisto fi
dc.relation.ispartofseries Aalto University publication series DOCTORAL DISSERTATIONS en
dc.relation.ispartofseries 237/2017
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]: Sergei Khakalo, Jarkko Niiranen. Gradient-elastic stress analysis near cylindrical holes in a plane under bi-axial tension fields. International Journal of Solids and Structures, 110–111:351–366, April 2017. DOI: 10.1016/j.ijsolstr.2016.10.025
dc.relation.haspart [Publication 3]: Sergei Khakalo, Jarkko Niiranen. Isogeometric analysis of higher-order gradient elasticity by user elements of a commercial finite element software. Computer-Aided Design, 82:154–169, January 2017. DOI: 10.1016/j.cad.2016.08.005
dc.relation.haspart [Publication 4]: Sergei Khakalo, Jarkko Niiranen. Form II of Mindlin’s second strain gradient theory of elasticity with a simplification: for materials and structures from nano- to macroscales. European Journal of Mechanics - A/Solids, Under revision, 44 pages, 2017
dc.subject.other Civil engineering en
dc.title Strain gradient continuum mechanics: simplified models, variational formulations and isogeometric analysis with applications en
dc.type G5 Artikkeliväitöskirja fi Insinööritieteiden korkeakoulu fi School of Engineering en
dc.contributor.department Rakennustekniikan laitos fi
dc.contributor.department Department of Civil Engineering en
dc.subject.keyword first strain gradient elasticity en
dc.subject.keyword second strain gradient elasticity en
dc.subject.keyword variational formulation en
dc.subject.keyword isogeometric analysis en
dc.subject.keyword abaqus user elements en
dc.subject.keyword stress concentration en
dc.subject.keyword size effects en
dc.subject.keyword surface effects en
dc.subject.keyword nano-structures en
dc.subject.keyword lattice structures en
dc.subject.keyword size dependency en
dc.subject.keyword eigenfrequencies en
dc.identifier.urn URN:ISBN:978-952-60-7748-2
dc.type.dcmitype text en
dc.type.ontasot Doctoral dissertation (article-based) en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.contributor.supervisor Niiranen, Jarkko, Assistant Prof., Aalto University, Department of Civil Engineering, Finland
dc.opn Dell'Isola, Francesco, Prof., Sapienza University of Rome, Italy
dc.contributor.lab Computational Structural Engineering en
dc.rev Eremeyev, Victor A., Prof., Gdansk University of Technology, Poland
dc.rev Placidi, Luca, Assistant Prof., Università Telematica Internazionale Uninettuno, Italy
dc.rev 2017-12-08

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