A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is...
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is...
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is...
A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in Elastostatics
In this work we consider a stabilized Lagrange multiplier method in order to approximate the Coulomb frictional contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed. We study the existence and the uniqueness of solution of the discrete problem.
A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed...
A theoretical comparison between inner products in the shift-invert Arnoldi method and the spectral transformation Lanczos method.
A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...
A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian....
A unilateral boundary-value problem for the rod
A unilateral boundary-value condition at the left end of a simply supported rod is considered. Variational and (equivalent) classical formulations are introduced and all solutions to the classical problem are calculated in an explicit form. Formulas for the energies corresponding to the solutions are also given. The problem is solved and energies of the solutions are compared in the pertubed as well as the unperturbed cases.
A unilateral thermoelastic Stefan-type problem
A variational model for nonlinear elastic plates.
A variationally consistent generalized variable formulation of the elastoplastic rate problem
The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry...
About the use of the HdHr algorithm group in integrating the movement equation with nonlinear terms.
Adaptive finite element relaxation schemes for hyperbolic conservation laws
We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...
Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws
We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...
Adaptive multiscale scheme based on numerical density of entropy production for conservation laws
We propose a 1D adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). This density is used as an a posteriori error which provides information if the mesh should be refined in the regions where discontinuities occur or coarsened in the regions where the solution remains smooth. As due to the Courant-Friedrich-Levy stability condition the time step is restricted and leads to...
Advancing analysis capabilities in ANSYS through solver technology.
Air entrainment in transient flows in closed water pipes : A two-layer approach
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme...