Supporting FEniCS-based finite element method solver and Docker image used to generate the FEM results in the paper:
Micro-structured materials: inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach. Elena Atroshchenko , Jack S. Hale, Javier A. Videla, Stanislav Potapenko, and Stéphane P.A. Bordas.
This is a permanent archival and DOI citation for the material in the repositories below. It is easiest to use the Bitbucket repository and the Dockerhub to get the supporting materials.

Elasticity

10.6084/m9.figshare.4047462

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Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Computer Methods in Applied Mechanics and Engineering (2019)

Javier Videla Felipe Contreras Hoang X. Nguyen Elena Atroshchenko

Heaviside step function

10.1016/j.cma.2019.112754

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Citations (17)

Variational Formulation of Crack Problems in Three-dimensional Classical Elasticity

Mathematics and Mechanics of Solids (2009)

Elena Atroshchenko S. Potapenko I. Chudinovich G. Glinka

In this paper we consider a crack of arbitrary shape in a homogeneous elastic media in the absence of body forces, formulate variational Dirichlet and Neumann crack problems in a linear three-dimensional elasticity in Sobolev spaces and prove the existence and uniqueness of the corresponding (weak) solutions.

Elasticity

Linear elasticity

Nonlinear elasticity

10.1177/1081286509344260

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Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

International Journal for Numerical Methods in Engineering (2018)

Elena Atroshchenko Satyendra Tomar Gang Xu Stéphane Bordas

Summary This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer‐aided design geometry (for example, given by nonuniform rational B‐splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T‐splines, LR‐splines, (truncated) hierarchical B‐splines, and PHT‐splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer‐aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.

Isogeometric analysis

10.1002/nme.5778

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Citations (109)

Stress intensity factors for elliptical and semi-elliptical cracks subjected to an arbitrary mode l loading

Elena Atroshchenko

Mode (computer interface)

Source

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Citations (10)

Shape Optimization with Adaptive Geometry Independent Field Approximation (Gift) in 3d Time-Harmonic Acoustics

Javier Videla Ahmed Mostafa Shaaban Elena Atroshchenko

In this work, an adaptive shape optimization is developed using Geometry Independent Field approximaTion (GIFT) for 3D acoustics problems.The geometry-independent field approximation, using Non-uniform Rational B-splines (NURBS) to model the geometry, and Polynomial-splines over Hierarchical T-meshes (PHT-splines) to model the field space, are employed for 3D shape optimization problems in the context of time-harmonic acoustics.The adaptive optimization scheme proposed in this work combines a gradient-based optimization method with a local refinement algorithm. In this case, two types of local refinement algorithms are tested: a recovery-based and a residual-based algorithm.Single and multi-patch examples are studied, and it is shown that the proposed adaptive shape optimization scheme can lead to the same results as the uniform optimization, but using less time and fewer degrees of freedom.

Harmonic

10.2139/ssrn.4432674

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