We present a stabilized finite element method for the Hu-Washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node-based uniform strain elements. We show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case.

We present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead. This solution is derived by treating the nonlinearity in bending elasticity through the (topological) Bogomol'nyi decomposition technique and elastic compatibility. We recover the "hat-model" approximation in the limit of a small latex bead and find that the regi...

Abstract In this work we propose an approximate numerical method for pricing of options for the constant elasticity of variance (CEV) diffusion model. We prove firstly the existence and uniqueness of the solution in weighted Sobolev space, and then we propose the finite element method and finite difference method to solve the considered problem. Therefore, we compare the obtained results by the...

In this note we propose a finite element method for incompressible (or compressible) elasticity problems with discontinuous modulus of elasticity (or, if compressible, Poisson’s ratio). The problem is written on mixed form using P 1–continuous displacements and the space of piecewise P 0 pressures, leading to the possibility of eliminating the pressure beforehand in the compressible case. In th...

in this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. this strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. from the best knowledge of author, it is the first time that this theory is used for investigating wave pro...

In this paper, we study new exact solutions of Einstein's field equations with the motivation relativistic elasticity theory. We construct static conformal elastic solution by applying transformations to Reissner-Nordstr\"{o}m-de Sitter solution. The factors for space-time structure an matter are obtained. Further, analyze viability energy conditions. And also discuss matching problem exterior ...

In this article, an analytical approximate solution method is given to provide investors with the means to make optimal consumption and portfolio choices with recursive utility in a complete market. The investment opportunity set is stochastic over time. The method is used to provide an exact determination of the unit elasticity of intertemporal substitution. An approximate solution method is d...

In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus,  it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...

For the continuum and discrete elastic equations, we derive exact artificial boundary conditions (ABCs), often referred to as transparent boundary conditions, that can be applied at a planar interface below which there are no forces. Solution of the elasticity equations can then be performed using this interface as an artificial boundary, often with greatly reduced computational effort, but wit...