Structural Analysis with the Finite Element Method

Abstract

Aims and Scope of the SeriesThis series publishes text books on topics of general interest in the field of computational engineering sciences.The books will focus on subjects in which numerical methods play a fundamental role for solving problems in engineering and applied sciences. Advances in finite element, finite volume, finite differences, discrete and particle methods and their applications to classical single discipline fields and new multidisciplinary domains are examples of the topics covered by the series.The main intended audience is the first year graduate student. Some books define the current state of a field to a highly specialised readership; others are accessible to final year undergraduates, but essentially the emphasis is on accessibility and clarity.The books will be also useful for practising engineers and scientists interested in state of the art information on the theory and application of numerical methods. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Volume 1 of the book presents the basis of the FEM and its application to structures that can be modelled as two-dimensional (2D), axisymmetric and three-dimensional (3D) solids using the assumptions of general linear elasticity theory. Volume 2 covers the FEM analysis of beam, plate, folded plate, axisymmetric shell and arbitrary shape shell structures. Emphasis is put in the treatment of structures with composite materials. Each chapter of the book presents the main theoretical concepts on the particular structural model considered, such as the kinematic description, the constitutive relationship between stresses and strains and the equilibrium equations expressed by the Principle of Virtual Work. This is followed by a detailed derivation of the FEM equations and some applications to academic and practical examples of structural analysis. Complementary topics such as error estimation, adaptive mesh refinement, mesh generation and visualization of FEM results and computer programming of the FEM are also covered in the last chapters of Volume 1. The book is particularly addressed to those interested in the analysis and design of solids and structures, understood here in a broad sense. The FEM concepts explained in the book are therefore applicable to the analysis of structures in civil engineering constructions, buildings and historical constructions, mechanical components and structural parts in automotive, naval and aerospace engineering, among many other applications. The background knowledge required for study of the book is the standard one on mathematics, numerical analysis, elasticity and strength of materials, matrix structural analysis and computer programming covered in the...

A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores

“…(1) is a continuous function that is interpolated from the nodal values in the finite element fashion [14,23,24].…”

“…Eqs. (14) are integrated in time in order to compute the motion of the particles. An explicit Forward Euler scheme has been used with substeppping.…”

“…In our work we will choose simple 3-noded linear triangles (n e = 3) for 2D problems and 4-noded tetrahedra (n e = 4) for 3D problems with local linear shape functions N e i defined for each node i of element e [14,23,25]. The velocity components, the weighting functions and the pressure are interpolated over the mesh in terms of their nodal values in the same manner using the global linear shape functions, N j , spanning over the elements sharing node j (j = 1, N ) [14,23,25].…”

“…The coupling effects between the particles and the fluid are introduced via an immersed technique [3][4][5]. The fluid motion is modelled either with an Eulerian stabilized FEM formulation using a fixed mesh, or using a Lagrangian formulation using the Particle Finite Element Method (PFEM) [4,[6][7][8][9][10][11][12][13][14][15][16] for which the mesh evolves in time. For both the Eulerian and the Lagrangian formulations we use a mixed finite element formulation with an equal order linear interpolation for the velocities and the pressure variables.…”

“…Another source of instability, however, remains in the numerical solution of Lagrangian flows such as PFEM, that due to the treatment of the incompressibility constraint which still requires using a stabilized numerical method. In this work we use a PFEM formulation based on a residual-based stabilized expression of the mass balance equation [10][11][12][13][14][15][16]. The excellent mass preservation feature of this formulation has been demonstrated previously [7,16].…”