High Order Multi-Moment Constrained Finite Volume Method. Part I: Basic Formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

A load simulation method of piezoelectric actuator in FEM for smart structures

More and more piezoelectric materials and structures have been used for structure control in aviation and aerospace industry. More efficient and convenient computation method for large complex structure with piezoelectric actuation devices is required. A load simulation method of piezoelectric actuation is presented in this paper. By this method, the freedom degree of finite element simulation is significantly reduced, the difficulty in defining in-plane voltage for multi-layers piezoelectric composite is overcome and the transfer computation between material main direction and the element main direction is simplified. The concept of simulation load is comprehensible and suitable for engineers of structure strength in shape and vibration control, thereby is valuable for promoting the application of piezoelectric material and structures in practical aviation and aerospace fields.

Análise de guias de ondas pelos métodos vetorial magnético e dos elementos-finitos

Neste trabalho, é apresentada uma formulação apropriada à análise de guias de ondas eletromagnéticos, cobrindo do espectro de microondas até o da óptica. Nas regiões a partir do ultravioleta, os comprimentos de onda são equivalentes às dimensões atômicas e a formulação necessita de uma abordagem quântica, que não é considerada neste estudo. A formulação é fundamentada nos métodos vetorial magnético e dos elementos finitos (MEF), em meios não homogêneos, anisotrópicos e não dissipativos, embora a dissipação possa ser facilmente introduzida na análise. Deu-se preferência à formulação com o campo magnético em vez do elétrico, pelo fato do campo magnético ignorar descontinuidades elétricas. Ele é contínuo em regiões de permeabilidade homogênea, propriedade dos meios dielétricos em geral ( = 0), independente da permissividade dos respectivos meios, conquanto os campos elétricos sejam descontínuos entre regiões de permissividades diferentes.

A fully-nonlocal energy-based formulation and high-performance realization of the quasicontinuum method

The quasicontinuum (QC) method was introduced to coarse-grain crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. Though many QC formulations have been proposed with varying characteristics and capabilities, a crucial cornerstone of all QC techniques is the concept of summation rules, which attempt to efficiently approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of atoms. In this work we propose a novel, fully-nonlocal, energy-based formulation of the QC method with support for legacy and new summation rules through a general energy-sampling scheme. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. Within this structure, we introduce a new class of summation rules which leverage the affine kinematics of this QC formulation to most accurately integrate thermodynamic quantities of interest. By comparing this new class of summation rules to commonly-employed rules through analysis of energy and spurious force errors, we find that the new rules produce no residual or spurious force artifacts in the large-element limit under arbitrary affine deformation, while allowing us to seamlessly bridge to full atomistics. We verify that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors than all comparable previous summation rules through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions. Due to the unique structure of these summation rules, we also use the new formulation to study scenarios with large regions of free surface, a class of problems previously out of reach of the QC method. Lastly, we present the key components of a high-performance, distributed-memory realization of the new method, including a novel algorithm for supporting unparalleled levels of deformation. Overall, this new formulation and implementation allows us to efficiently perform simulations containing an unprecedented number of degrees of freedom with low approximation error.

Análisis y modelización por FEM de elastómeros para silentblocks.

[ES]El objetivo de este trabajo es analizar el comportamiento de materiales elastómeros mediante el método de elementos finitos. Este análisis es necesario por la complejidad de los elastómeros y su comportamiento no común entre los materiales normalmente utilizados en ingeniería. Se pretende calcular la rigidez del material y modelizar su comportamiento.