2D ELASTICITY TENSOR INVARIANTS, INVARIANTS DEFINITE POSITIVE CRITERIA

In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.

Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive

In this work, analytical solution of simply supported sandwich arches considering permeation effect of adhesives is presented. The permeation layer is described by the functionally graded material, exponentially graded in the radial direction. The stresses and deformations of each layer are based on the two-dimensional (2D) elasticity theory in the polar coordinate. The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. The solution can be obtained efficiently by means of the recursive matrix method, especially for the arch with many layers. The present solution agrees well with the finite element solution with a fine mesh, while the finite element method is time consuming in mesh division and calculation. The one-dimensional (1D) solution based on the Euler–Bernoulli theory is close to the present one; however, the error increases as the arch becomes thick. The effect of permeation layer thickness on the stresses is studied. It is indicated that the stress distributions tend to be smooth along the radial direction as the permeation layer thickness increases.

ICCM2016: Multi-Patch-Based B-Spline Method for Solid and Structure

In this paper, the solution domain is divided into multi-patches on which B-spline basis functions are used for approximation. The different B-spline patches are connected by a transition region which is described by several elements. The basis functions in different B-spline patches are modified in the transition region to ensure the basic polynomial reconstruction condition and the compatibility of displacements and their gradients. This new method is applied to the stress analysis of 2D elasticity problems in order to investigate its performance. Numerical results show that the present method is accurate and stable.

Transversal Otolithic Membrane Deflections Evoked by the Linear Accelerations

Considered is the model of the transversal utricle membrane deflections evoked by the linear accelerations. The basic idea underlying this consideration is that the linear accelerations can cause both longitudinal and transversal deformations when acting along the membrane in the buckling way. The real 3D utricle membrane structure was simplified by considering its middle section and evaluating its elastic properties in 2D space. The steady state transversal deflections along the membrane are analytically evaluated and numerically simulated using the 2D elasticity theory. The transversal deflections are found to be more expressive and stronger as compared to the conventional longitudinal deformations. The maxima of longitudinal deformations and transversal deflections are observable in different regions of the utricle membrane. The revealed properties could be used for explanation of the transduction processes in the otolith organ. Based on the implemented modeling approach the new otolithic membrane mechanical properties are discussed and new explanations for the available experimental data are given.

Transversal otolithic membrane deflections evoked by the linear accelerations

Considered is the model of the transversal utricle membrane deflections evoked by the linear accelerations. The real 3D utricle membrane structure was simplified by considering its middle section and evaluating its elastic properties in 2D space. The steady state transversal deflections along the membrane are analytically evaluated and numerically simulated using the 2D elasticity theory. The transversal deflections are found to be more expressive and stronger as compared to the conventional longitudinal deformations. The revealed properties could be used for explanation of the transduction processes in the otholith organ. Based on the implemented modeling approach the new otolithic membrane mechanical properties are discussed and new explanations for the available experimental data are given.