Related papers: Effective isometries of periodic shells
The class of differential equations describing pseudospherical surfaces enjoys important integrability properties which manifest themselves by the existence of infinite hierarchies of conservation laws (both local and non-local) and the…
Origami metamaterials made of repeating unit cells of parallelogram panels joined at folds dramatically change their shape through a collective motion of their cells. Here we develop an effective elastic model and numerical method to study…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes…
We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence…
The problem of definition of effective material parameters (permittivity and permeability) for composite layers containing only one-two parallel arrays of complex-shaped inclusions is discussed. Such structures are of high importance for…
This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation,…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…
A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction…
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application,…
The Miura ori is a very classical origami pattern used in numerous applications in Engineering. A study of the shapes that surfaces using this pattern can assume is still lacking. A constrained nonlinear partial differential equation (PDE)…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…