We introduce a nonlinear model for the evolution of biomembranes driven by the L2-gradient flow of a novel elasticity functional describing the interaction of a director field on a membrane with its curvature. In the linearized setting of a graph we present a practical finite element method (FEM), and prove a priori estimates. We derive the relaxation dynamics for the nonlinear model on closed ...

In this paper the effect of random geometric imperfections on the critical load of isotropic, thin-walled, cylindrical shells under axial compression with rectangular cutouts is presented. Second moment characteristics of geometric imperfections are estimated by data of available measurements, a simulation procedure based on the Karhunen-Loève expansion is applied for generating realizations of...

This paper develops and analyzes a finite element method for a nonlinear singular elliptic equation arising from the black hole theory in the general relativity. The nonlinear equation, which was derived and analyzed by Huisken and Ilmanen in [14], represents a level set formulation for the inverse mean curvature flow describing the evolution of a hypersurface whose normal velocity equals the r...

The paper has describes the complete design and investigation processes of permanent magnetic bearing. The passive magnetic bearing (PMB) rotor suspension rig employing no active control components was calculated, designed, constructed and tested. In order to increase the radial passive magnetic bearing stiffness, the Halbach-array configuration was used. The main purpose of the work was develo...

In this paper, we introduce an implementation of the extended finite element method for fracture problems within the finite element software ABAQUSTM. User subroutine (UEL) in Abaqus is used to enable the incorporation of extended finite element capabilities. We provide details on the data input format together with the proposed user element subroutine, which constitutes the core of the finite ...

it is well-known that dam-reservoir interaction has significant effects on the response of dams to the earthquakes. this phenomenon should be considered more exactly in the seismic design of dams with a rational and reliable dynamic analysis method. in this research, seismic analysis of the dam-reservoir is studied as a wave propagation problem by using legendre spectral element method (sem). t...