Contact problems in computational mechanics are of significant importance for a variety of practical applications. Examples are metal forming processes, crash analysis, the design of gear boxes, bearings, car tires or implants in biomechanics. Here, we focus on Signorini’s problem in linear elasticity [10, 21, 22, 29] describing the linearized frictionless contact of an elastic body with a rigi...

In the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions, the main difficulty in the analysis is to prove that an appropriate discrete version of Korn's second inequality is valid. Such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears. Op...

A standard finite element method and a finite element truncation method are applied to solve the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff materials. Finite element solutions are proved to exist and to be in the form of minimizers in appropriate sets of admissible finite element functions for both methods...

Finite element modelling of three dimensional elasticity problems gives rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two level hierarchical basis are developed. Various techniques for ensuring that the incomplete fac...

PURPOSE We aimed to determine the correlations between the elasticity values of solid breast masses and histopathological findings to define cutoff elasticity values differentiating malignant from benign lesions. MATERIALS AND METHODS A total of 115 solid breast lesions of 109 consecutive patients were evaluated prospectively using shear wave elastography (SWE). Two orthogonal elastographic i...

PURPOSE The aim of this study is to evaluate structural alterations of thyroid tissue after microwave ablation using elastography and scintigraphic imaging to investigate the applicability of these diagnostic methods for follow-up.  MATERIALS AND METHODS 35 patients with 39 thyroid nodules were evaluated using elastography and scintigraphic imaging before and after ultrasound-guided microwave...

Material property has great importance in deformable body simulation and medical robotics. The elasticity parameters, such as Young's modulus of the deformable bodies, are important to make realistic animations. Further in medical applications the (recovered) elasticity parameters can assist surgeons to perform better pre-op surgical planning and enable medical robots to carry out personalized ...

An approximate Riemann solver is developed for the equations of nonlinear elasticity in a heterogeneous medium, where each grid cell has an associated density and stress-strain relation. The nonlinear flux function is spatially varying and a wave decomposition of the flux difference across a cell interface is used to approximate the wave structure of the Riemann solution. This solver is used in...

This work presents how approximate solution methods were introduced in a graduate level course of Theory of Elasticity. The three methods introduced are the finite difference method, the finite element method, and the boundary element method. All methods are exemplified by the problem of a thick-walled cylinder subject to internal pressure with an axisymmetric response. Choosing a single proble...

We consider multigrid methods for problems in linear elasticity which are robust with respect to the Poisson ratio. Therefore, we consider mixed approximations involving the displacement vector and the pressure, where the pressure is approximated by discontinuous functions. Then, the pressure can be eliminated by static condensation. The method is based on a saddle point smoother which was intr...