Two-dimensional theory (plane strain)

2019 ◽  
pp. 62-113
Author(s):  
William G. Pariseau
Keyword(s):  
Plane Strain ◽  
Two Dimensional ◽  
Dimensional Theory

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

scholarly journals Symmetry Breakdown in Franckeite: Spontaneous Strain, Rippling and Interlayer Moiré

2019 ◽  
Author(s):  
Riccardo Frisenda ◽  
Gabriel Sanchez-Santolino ◽  
Nikos Papadopoulos ◽  
Joanna Urban ◽  
Michal Baranowski ◽  
...  
Keyword(s):  
Optical Properties ◽  
Plane Strain ◽  
Van Der Waals ◽  
Van Der Waals Interaction ◽  
Spatial Modulation ◽  
Two Dimensional ◽  
Spontaneous Strain ◽  
Strain Profile ◽  
Symmetry Breakdown ◽  
Naturally Occurring

<p>Franckeite is a naturally occurring layered mineral with a structure composed of alternating stacks of SnS<sub>2</sub>-like and PbS-like layers. Although this superlattice is composed of a sequence of isotropic two-dimensional layers, it exhibits a spontaneous rippling that makes the material structurally anisotropic. We demonstrate that this rippling comes hand in hand with an inhomogeneous in-plane strain profile and anisotropic electrical, vibrational and optical properties. We argue that this symmetry breakdown results from a spatial modulation of the van der Waals interaction between layers due to the SnS<sub>2</sub>-like and PbS-like lattices incommensurability.</p>

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