In order to tackle realistic engineering applications where constrained problems such as the NavierStokes equations are encountered, the trend is to employ Uzawa’s algorithm, which consists of computing the momentum equation separately from the constraints. Examples of constraints include the divergence-free constraint and the zero-normal velocity constraint to a boundary (slip boundary conditi...

Presented here is a new total-Lagrangian displacement-based finite-element formulation for plates and shells undergoing large displacements and rotations. The theory fully accounts for geometric nonlinearities, general initial curvatures, and extensionality by using Jaumann stress and strain measures, an exact coordinate transformation, and orthogonal virtual rotations. Moreover, transverse she...

Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...

In this paper we develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electr...

This paper presents an application of Continuum (i.e. Lagrangian) and Finite Element Techniques to flexible manipulator arms for derivation of the corresponding Dynamic Equations of Motion. Specifically a one-link flexible arm is considered for detailed analysis, and the results are extended for the case of a two - link flexible manipulator. Numerical examples are given for the case of both one...

Abstract — In this article, we address the numerical solution of a non-smooth eigenvalue problem, which has implications in plasticity theory and image processing. The smallest eigenvalue of the nonsmooth operator under consideration is shown to be the same for all bounded, sufficiently smooth, domains in two space dimensions. Piecewise linear finite elements are used for the discretization of ...

The finite element procedure is developed for the solution of three-dimensional geometrically nonlinear problems with small strains and large rotational and translational displacements. Updated Lagrangian formulation is used with controlling strains and stresses at local coordinate frames at element integration points. Equilibrium iterations at each step are performed according to the Newton-Ra...

In this paper a stabilizing augmented Lagrangian technique for the Stokes equations is studied. The method is consistent and hence does not change the continuous solution. We show that this stabilization improves the well-posedness of the continuous problem for small values of the viscosity coefficient. We analyze the influence of this stabilization on the accuracy of the finite element solutio...

For variational problems of the form we propose a dual method which decouples the difficulties relative to the functionals f and g from the possible ill-conditioning effects of the linear operator A. The approach is based on the use of an Augmented Lagrangian functional and leads to an efficient and simply implementable algorithm. We study also the finite element approximation of such problems,...

This paper presents a high-order finite element method for calculating elastic-plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1, 2]. In order to handle transition to plastic flow, we formulate the stress-strain relation in rate (or incremental) form...