We propose an efficient numerical algorithm for computing deformations of “very” soft tissues (such as the brain, liver, kidney etc.), with applications to real time surgical simulation. The algorithm is based on the finite element method using the Total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computi...

This paper presents the development of an algorithm based on the discontinuous Galerkin finite element method (DGFEM) for the Euler equations of gas dynamics. The DGFEM is a mixture of a finite volume and finite element method. In the DGFEM the unknowns in each element are locally expanded in a polynomial series and thus the information about the flow state at the element faces can be directly ...

In this paper, we present a new numerical method, the Immersed Element-Free Galerkin Method (IEFGM), for the solution of fluid-structure interaction problems. The technique is a variation of the Immersed Finite Element Method developed by (L. Zhang et al., Journal of Fluids and Structures, 23(6):836-857 (2007)) in which the fluid-solid interaction force is represented as a volumetric force in t...

Interpolation operators map a function u to an element Iu of a finite element space. Unlike more general approximation operators, interpolants are defined locally. Estimates of the interpolation error, i.e., the difference u− Iu, are of utmost importance in numerical analysis. These estimates depend on the size of the finite elements, the polynomial degree employed, and the regularity of u. In ...

In this article, the prominence has been given to study the influence of skew angle on bending response of functionally graded material shell panels under thermo-mechanical environment. Derivation of governing equations is based on the Reddy’s higher-order shear deformation theory and Sander’s kinematic equations. To circumvent the problem of C1 continuity requirement coupled with the finite el...

Abstract: In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubberlike materials is presented. The element is a triangular shell of anyorder with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the ReissnerMindlin hypothesis. The finite element can represent thickness...

This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...

The aim of this thesis paper, to create a numerical model to examine the residual stresses induced by orthogonal machining in the finished work piece and the model is validated by comparing with experimental result. The finite element method is used to simulate and analyze the residual stresses induced by a orthogonal metal cutting process. A Dynamics explicit time integration technique with Ar...

We study a variant of augmented Lagrangian (AL)-based block triangular preconditioners to accelerate the convergence of GMRES when solving linear algebraic systems arising from finite element discretizations of the 3D Navier-Stokes equations in VelocityVorticity-Helicity form. This recently proposed formulation couples a velocity-pressure system with a vorticity-helicity system, providing a num...