Antti H. Niemi

Finite element analysis of the Girkmann problem using the modern hp -version and the classical h -version

We perform finite element analysis of the so called Girkmann problem in structural mechanics. The problem involves an axially symmetric spherical shell stiffened with a foot ring and is approached (1) by using the axisymmetric formulation of linear elasticity theory and (2) by using a dimensionally reduced shell-ring model. In the first approach the problem is solved with a fully automatic hp-adaptive finite element solver whereas the classical h-version of the finite element method is used in the second approach. We study the convergence behaviour of the different numerical models and show that accurate stress resultants can be obtained with both models by using effective post-processing formulas.

Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm

We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view.

Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

Abstract We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the Ṕeclet number in the current application. The e_ectiveness of the algorithm is demonstrated on two problems for the linear advection-di_usion equation.

Discontinuous Petrov–Galerkin method based on the optimal test space norm for steady transport problems in one space dimension

Abstract We revisit the finite element analysis of convection-dominated flow problems within the recently developed Discontinuous Petrov–Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the optimal test space norm. This makes the DPG method not only stable but also robust, that is, uniformly stable with respect to the Peclet number in the current application. We employ discontinuous piecewise Bernstein polynomials as trial functions and construct a subgrid discretization that accounts for the singular perturbation character of the problem to resolve the corresponding optimal test functions. We also show that a smooth B-spline basis has certain computational advantages in the subgrid discretization. The overall effectiveness of the algorithm is demonstrated on two problems for the linear advection–diffusion equation.

Dynamics and Control of Multiple-Effect Evaporator and Drum Washer Plants

After a study of an evaporator model with variable liquor volume, state space models of evaporator and washer plants used in pulp and paper industry are set up. Problems of optimal feedforward control are formulated using these models, and computed solutions are presented for the case of an evaporator plant. A practical control method being tested in a washer plant.

A non-singular spherically symmetric separable copy of the vacuum in SU(2) Landau gauge

Abstract We give a new non-singular spherically symmetric and separable copy of the vacuum in Landau gauge for SU(2) Yang-Mills theories. The solution can be considered as a generalization of Gribovs solution in Coulomb gauge and thus it demonstrates the similarity between vacua in Coulomb and Landau gauges.

Point Load on a Shell

We study the fundamental (normal point load) solution for shallow shells. The solution is expressed as a Fourier series and its properties are analyzed both at the asymptotic limit of zero shell thickness and when the thickness has a small positive value. Some results of benchmark computations using both high- and low-order finite elements are also presented.

Evaluation of some harmonic load models for the vibration analysis of footbridges

We analyze and compare different dynamic load models used for the verification of vibration serviceability of footbridges. The considered models predict the acceleration response of the bridge for random streams of pedestrians as well as for deterministic group of walking or running pedestrians. The analysis is carried out in the context of a model steel-concrete composite bridge. Both moving and stationary loads are studied.

ISOGEOMETRIC GALERKIN METHODS FOR GRADIENT-ELASTIC BARS, BEAMS, MEMBRANES AND PLATES

Isogeometric Galerkin methods are used to analyse plate and beam bending problems as well as membrane and bar models based on Mindlin’s strain gradient elasticity theory for generalized continua. The current strain gradient models include higher-order displacement gradients combined with length scale parameters enriching the strain and kinetic energies of the classical elasticity and hence resulting in higher-order partial differential equations with corresponding non-standard boundary conditions. The problems are first formulated within appropriate higher-order Sobolev space settings and then discretized by utilizing Galerkin methods with isogeometric NURBS basis functions providing appropriate higher-order continuity properties. Example benchmark problems illustrate the convergence properties of the methods.