Browsing by Author "Balobanov, Viacheslav"

Now showing 1 - 9 of 9

Computational structural mechanics within strain gradient elasticity: mathematical formulations and isogeometric analysis for metamaterial design
(2018) Balobanov, Viacheslav
School of Engineering | Doctoral dissertation (article-based)
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.
Isogeometric finite element analysis of mode I cracks within strain gradient elasticity
(2017) Niiranen, Jarkko; Khakalo, Sergei; Balobanov, Viacheslav
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
A variational formulation within an H^2 Sobolev space setting is formulated for fourth-order plane strain/stress boundary value problems following a widely-used one parameter variant of Mindlin's strain gradient elasticity theory. A corresponding planar mode I crack problem is solved by isogeometric C^(p-1)-continuous discretizations for NURBS basis functions of order p >= 2. Stress field singularities of the classical elasticity are shown to be removed by the strain gradient formulation.
Kirchhoff–Love shells within strain gradient elasticity : Weak and strong formulations and an H3-conforming isogeometric implementation
(2019-02-01) Balobanov, Viacheslav; Kiendl, Josef; Khakalo, Sergei; Niiranen, Jarkko
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
A strain gradient elasticity model for shells of arbitrary geometry is derived for the first time. The Kirchhoff-Love shell kinematics is employed in the context of a one-parameter modification of Mindlin's strain gradient elasticity theory. The weak form of the static boundary value problem of the generalized shell model is formulated within an H-3 Sobolev space setting incorporating first-, second- and third-order derivatives of the displacement variables. The strong form governing equations with a complete set of boundary conditions are derived via the principle of virtual work. A detailed description focusing on the non-standard features of the implementation of the corresponding Galerkin discretizations is provided. The numerical computations are accomplished with a conforming isogeometric method by adopting C-P(-1)-continuous NURBS basis functions of order p >= 3. Convergence studies and comparisons to the corresponding three-dimensional solid element simulation verify the shell element implementation. Numerical results demonstrate the crucial capabilities of the non-standard shell model: capturing size effects and smoothening stress singularities. (C) 2018 Elsevier B.V. All rights reserved.
Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity
(2018-09-01) Balobanov, Viacheslav; Niiranen, Jarkko
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
The Timoshenko beam bending problem is formulated in the context of strain gradient elasticity for both static and dynamic analysis. Two non-standard variational formulations in the Sobolev space framework are presented in order to avoid the numerical shear locking effect pronounced in the strain gradient context. Both formulations are shown to be reducible to their locking-free counterparts of classical elasticity. Conforming Galerkin discretizations for numerical results are obtained by an isogeometric Cp−1-continuous approach with B-spline basis functions of order p≥2. Convergence analyses cover both statics and free vibrations as well as both strain gradient and classical elasticity. Parameter studies for the thickness and gradient parameters, including micro-inertia terms, demonstrate the capability of the beam model in capturing size effects. Finally, a model comparison between the gradient-elastic Timoshenko and Euler–Bernoulli beam models justifies the relevance of the former, confirmed by experimental results on nano-beams from literature.
Modeling chemical reaction front propagation by using an isogeometric analysis
(2018) Morozov, Alexander; Khakalo, Sergei; Balobanov, Viacheslav; Freidin, Alexander; Müller, Wolfgang H.; Niiranen, Jarkko
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We develop a numerical procedure for solving boundary value problems for elastic solids undergoing chemical transformations. The kinetic equation for the reaction front propagation is based on an expression for the chemical affinity tensor, which allows us to study the influence of stresses and strains on the chemical reaction rate and the normal component of the reaction front velocity. Isogeometric analysis provides a high accuracy when finding the normal to the reaction front, and it is applied with the use of Abaqus to a numerical simulation of the front propagation. In order to test and demonstrate the capabilities of the developed procedure a hollow cylinder undergoing a chemical transformation is considered. First, an axially-symmetric problem is solved and a good agreement between numerical simulations and analytical results is demonstrated. Then a case is considered where the initial front configuration does not have axial symmetry. Reaction front acceleration, retardation, and even reaction blocking due to mechanical stresses are investigated.
Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: applications to sandwich beams and auxetics
(2018-06) Khakalo, Sergei; Balobanov, Viacheslav; Niiranen, Jarkko
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Parametric tools for the analysis of micro-architectured thin structures
(2019-08-19) Capdevila Choy, Cristina
Insinööritieteiden korkeakoulu | Master's thesis
The present work is devoted to a tool for generating lattice structure geometries. A review on lattice structures is performed passing through their definition, history and actual fields of applicability. An overview of software that is currently available for lattice geometries generation and their finite elements analysis is also accomplished, including the software pros and cons in the context of the research purposes of the present work. Based on the review, a scripted tool is developed and implemented boosting user customization and future FEA integration as a software prototype. An explanation of the generalized idea, structure and organization is given. The validation of the tool has been executed through a banch of examples. The applicational potential of the tool in modelling and analysis of different lattice structures made of the different RVEs is demonstrated including the simulation of possible imperfections arising due to manufacturing defects. In addition, it is shown how the tool can help in homogenization of the artificial micro-architectural lattice materials accomplished with the aid of the gradient elasticity theory.
Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear deformable beams
(2018-05-01) Tahaei Yaghoubi, Saba; Balobanov, Viacheslav; Mousavi, S. Mahmoud; Niiranen, Jarkko
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.
Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models
(2019-01) Niiranen, Jarkko; Balobanov, Viacheslav; Kiendl, Josef; Hosseini, Seyyed
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
As a first step, variational formulations and governing equations with boundary conditions are derived for a pair of Euler–Bernoulli beam bending models following a simplified version of Mindlin’s strain gradient elasticity theory of form II. For both models, this leads to sixth-order boundary value problems with new types of boundary conditions that are given additional attributes singly and doubly, referring to a physically relevant distinguishing feature between free and prescribed curvature, respectively. Second, the variational formulations are analyzed with rigorous mathematical tools: the existence and uniqueness of weak solutions are established by proving continuity and ellipticity of the associated symmetric bilinear forms. This guarantees optimal convergence for conforming Galerkin discretization methods. Third, the variational analysis is extended to cover two other generalized beam models: another modification of the strain gradient elasticity theory and a modified version of the couple stress theory. A model comparison reveals essential differences and similarities in the physicality of these four closely related beam models: they demonstrate essentially two different kinds of parameter-dependent stiffening behavior, where one of these kinds (possessed by three models out of four) provides results in a very good agreement with the size effects of experimental tests. Finally, numerical results for isogeometric Galerkin discretizations with B-splines confirm the theoretical stability and convergence results. Influences of the gradient and thickness parameters connected to size effects, boundary layers and dispersion relations are studied thoroughly with a series of benchmark problems for statics and free vibrations. The size-dependency of the effective Young’s modulus is demonstrated for an auxetic cellular metamaterial ruled by bending-dominated deformation of cell struts.