We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

Under some generic assumptions we prove the unique continuation property for the two-dimensional inhomogeneous anisotropic elasticity system. Having established the unique continuation property, we then investigate the inverse problem of reconstructing the inclusion or cavity embedded in a plane elastic body with inhomogeneous anisotropic medium by infinitely many localized boundary measurements.

A simple method to obtain the highest and lowest Young’s modulus for a material of the hexagonal class is presented. It is based upon the use of tensor invariants of plane anisotropic elasticity; in fact, the cylindrical symmetry of the elastic tensor allows for transforming the 3D original problem into a planar one, with a considerable simplification.

A collocation-quadrature method is proposed and studied for the numerical solution of a singular integral equation concerned with the two-dimensional elasticity problem of a crack at a circular cavity surface. These investigations are based on an C∗-algebra approach presented in a recent paper [5] on the numerical solution of an integral equation for the notched half-plane problem.

21  Abstract—This paper describes a numerical solution for plane elasticity problem. It includes algorithms for discretization by mixed finite element methods. The discrete scheme allows the utilization of Brezzi-Douglas-Fortin-Marini (BDFM2) for the stress tensor and piecewise linear elements for the displacement. The numerical results are compared with some previously published works or with...

Through several numerical experiments, we explore the theoretical properties of a residual based a posteriori error estimator of an augmented mixed method applied to linear elasticity problem in the plane. More precisely, we show numerical evidence confirming the theoretical properties of the estimator, and ilustrating the capability of the corresponding adaptive algorithm to localize the singu...

We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations the absence of exact rotational invariance space. An example is provided by membrane an orientational field, tuned to critical buckling point application in-plane stresses. Through detailed analysis, show that tr...

For a number of materials used in modern practice, calculations according to the classical theory elasticity give incorrect results. To ensure reliable operation structures, there is need for new theories. At present, particular interest practical applications asymmetric moment elasticity. In work, by method hypotheses, three-dimensional equations are reduced plates. The hypotheses plates formu...

For the proper simulation of processes inside microfluidic devices, proper model for blood flow must be used. We use the lattice-Boltzmann method for the blood plasma flow and the immersed boundary method for the description of red blood cells and other components of blood. One of the four key mechanisms governing the elastic behaviour of a red blood cell is the in-plane shear modulus of elasti...