A vectorized Matlab implementation for the P1 finite element is provided for the twodimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and can describe elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures aroun...

Nonlinear plate bending within Mindlin's strain gradient elasticity theory (SGT) is investigated by employing somewhat non-standard finite element methods. The main goal to compare the results provided geometrically nonlinear three-dimensional (3D) and Reissner–Mindlin theory, i.e., first-order shear deformation (FSDT), SGT. For 3D Green–Lagrange relations are adopted, while von Kármán strains ...

The sol-gel transition is studied on a purely entropic two-dimensional model system consisting of hard spheres (disks) in which a fraction p of neighbors are tethered by inextensible bonds. We use a new method to measure directly the elastic properties of the system. We find that over a broad range of hard sphere diameters a the rigidity threshold is insensitive to a and indistinguishable from ...

The paper deals with the two-dimensional exterior boundary value problems of the steady-state oscillation theory for anisotropic elastic bodies. By means of the limiting absorption principle the fundamental matrix of the oscillation equations is constructed and the generalized radiation conditions of Sommerfeld–Kupradze type are established. Uniqueness theorems of the basic and mixed type bound...

For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of S; the minimizer u is C and is such that det∇u vanishes at one point. Mathematics Subject Classification. — Please, give AMS classification codes —. Received October 28, 2005. Revised March 31, 2006.

We study the mechanical property of a two-dimensional filament with constant spontaneous curvature and under uniaxial applied force. We derive the equation that governs the stable shape of the filament and obtain analytical solutions for the equation. We find that for a long filament with positive initial azimuth angle (the azimuth angle is the angle between x axis and the tangent of the filame...