We consider thin plates whose energy density is a quadratic function of the difference between second fundamental form deformed configuration and natural curvature tensor. This tensor either denotes stress-free configuration, if it exists, or target In latter case, residual stress arises from geometrical frustration involved in attempt to achieve curvature: as result, plate naturally twisted, even absence external forces prescribed boundary conditions. Here, starting this kind energy, we...

We provide a justification of the Reissner–Mindlin plate theory, using linear three-dimensional elasticity as framework and Γ-convergence technical tool. Essential to our developments is selection transversely isotropic material class whose stored energy depends on (first and) second gradients displacement field. Our choices candidate Γ-limit scaling law basic functional in terms thinness parameter are guided by mechanical formal arguments that variational convergence theorem meant validate...

In this paper we report the second part of our results concerning rigorous derivation a hierarchy one-dimensional models for thin-walled beams with rectangular cross-section. Denoting by h and δ ≪ length sides cross-section beam, analyze limit behavior nonlinear elastic energy which scales as [Formula: see text] when ϵ /δ → 0.

Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit are distinguished by the scaling elastic energy and ratio between sides cross-section. In this paper we report first part our results. More precisely, denoting h δ length ≪ h, [Formula: see text] factor bulk energy, analyze cases in which /ε → 0 (subcritical) 1 (critical).

The control of the shape complex metasurfaces is a challenging task often addressed in literature. This work presents class tessellated plates able to deform into surfaces preprogrammed upon activation by any flexural load and that can be controlled single actuator. Quadric are obtained from infinitesimal origami maps monohedral hexagonal tessellations plane, pavings which all tiles congruent each other. Monohedral portions joined together obtain more shapes, locally synclastic or...

1. Fischer A., 1995. Bending instabilities of thin-walled transversely curved metallic strips, Report cued/d-struct/tr 154. Google Scholar

The equations of a plate for linearly elastic monoclinic material with residual stress are here derived the first time. By using techniques Γ-convergence we show that also in case displacements Kirchhoff-Love type. An improvement result Man and Carlson on existence solution three-dimensional problem linear elasticity is obtained.

A two-dimensional model which describes the evolution of a crack in plate is deduced from three-dimensional lin- early elastic Griffith's type model. The result achieved by adopting framework energetic solutions for rate-independent processes, to fracture evolution, conjunction with variational dimension reduction procedure.

Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of former. Basically, this is feature three-dimensional bodies. At variance, two-dimensional bodies have more freedom to deform than ones. Here, we exploit peculiarity propose honeycomb structure with auxetic opposite one. With suitable choice lattice constitutive parameters, in its continuum description such can achieve whole range values for...

In this paper we study a one-dimensional model simulating the shear in two-dimensional body. We analyse discrete system and deduce continuum limit of lattice as parameter goes to zero. Different energies are introduced linked together.