Computer Methods in Applied Mechanics and Engineering

nonlinear finite elements for continua and structures is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the nonlinear finite elements for continua and structures is universally compatible with any devices to read.

Nonlinear Finite Elements For Continua And Structures

We present a new family of stabilized methods for the Stokes problem. The focus of the paper is on the lowest order velocity-pressure pairs. While not LBB compliant, their simplicity and attractive computational properties make these pairs a popular choice in engineering practice. Our stabilization approach is motivated by terms that characterize the LBB 'deficiency' of the unstable spaces. The stabilized methods are defined by using these terms to modify the saddle-point Lagrangian associated with the Stokes equations. The new stabilized methods offer a number of attractive computational properties. In contrast to other stabilization procedures, they are parameter free, do not require calculation of higher order derivatives or edge-based data structures, and always lead to symmetric linear systems. Furthermore, the new methods are unconditionally stable, achieve optimal accuracy with respect to solution regularity, and have simple and straightforward implementations. We present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods.

Stabilization of low-order mixed finite elements for the stokes equations.

Thank you very much for downloading mathematical foundations of elasticity. As you may know, people have search numerous times for their favorite books like this mathematical foundations of elasticity, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their laptop. mathematical foundations of elasticity is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the mathematical foundations of elasticity is universally compatible with any devices to read.

Mathematical Foundations Of Elasticity

A broad class of engineering problems including penetration, impact and large rotations of solid bodies causes severe numerical problems. For these problems, the constitutive equations are history dependent so material points must be followed; this is difficult to implement in an Eulerian scheme. On the other hand, purely Lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement. Remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables, a process which can introduce errors. Proposed here is an extension of the particle-in-cell method in which particles are interpreted to be material points that are followed through the complete loading process. A fixed Eulerian grid provides the means for determining a spatial gradient. Because the grid can also be interpreted as an updated Lagrangian frame, the usual convection term in the acceleration associated with Eulerian formulations does not appear. With the use of maps between material points and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history. Example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced. Also, it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity.

/pdf/a-particle-method-for-history-dependent-materials-17k7rkc0xq.pdf

A particle method for history-dependent materials

An excavation process is a nonlinear dynamic problem that includes geometrical, material, and contact nonlinearities. The simulation of ground excavation has to face contact interaction in a changing geometry composed by several solid domains. The particle finite-element method (PFEM) is based on a Lagrangian description for modeling the motion of a continuum medium. The PFEM is particularly suitable for modeling a fluid motion with free surfaces. The application of the PFEM in ground excavation includes the use of the remeshing process, α-shape concepts for detecting the domain boundary, contact mechanics laws, material constitutive models, and surface wear models. Everything is correctly matched to quantify the excavation and the corresponding damage caused to the ground. The erosion and wear parameters of the soil/rock material govern the evolution of the excavation process. The preliminary results presented in this paper show that the PFEM it is a very suitable tool for the simulation of ground excavation processes.

/pdf/modeling-of-ground-excavation-with-the-particle-finite-4qmykhruwf.pdf

Modeling of ground excavation with the particle finite element method

Numerical simulation of undrained insertion problems in geotechnical engineering with the Particle Finite Element Method (PFEM)

Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method

Unified Lagrangian formulation for solid and fluid mechanics and FSI problems

SUMMARY
We present a Lagrangian formulation for finite element analysis of quasi-incompressible fluids that has excellent mass preservation features. The success of the formulation lays on a new residual-based stabilized expression of the mass balance equation obtained using the finite calculus method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities and the pressure. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D quasi-incompressible free-surface flow problems using the particle FEM (www.cimne.com/pfem). Examples include the sloshing of water in a tank, the collapse of one and two water columns in rectangular and prismatic tanks, and the falling of a water sphere into a cylindrical tank containing water. Copyright © 2014 John Wiley & Sons, Ltd.

Josep Maria Carbonell

Papers

Modeling of ground excavation with the particle finite element method

Numerical simulation of undrained insertion problems in geotechnical engineering with the Particle Finite Element Method (PFEM)

Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method

Unified Lagrangian formulation for solid and fluid mechanics and FSI problems

Lagrangian formulation for finite element analysis of quasi‐incompressible fluids with reduced mass losses