Showing papers on "Finite element method published in 2014"

Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

Abstract: The intended readership includes graduate students and researchers in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing. The publisher describes the book as follows: * An excellent introduction to finite elements, iterative linear solvers and scientific computing * Contains theoretical problems and practical exercises * All methods and examples use freely available software * Focuses on theory and computation, not theory for computation * Describes approximation methods and numerical linear algebra

Ultrasonic Guided Waves in Solid Media

Abstract: Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

The Hitchhiker's Guide to the Virtual Element Method

Abstract: We present the essential ingredients in the Virtual Element Method for a simple linear elliptic second-order problem. We emphasize its computer implementation, which will enable interested readers to readily implement the method.

Finite Element Solution of Boundary Value Problems: Theory and Computation

Abstract: Finite Element Solution of Boundary Value Problems: Theory and Computation provides a thorough, balanced introduction to both the theoretical and the computational aspects of the finite element method for solving boundary value problems for partial differential equations. Although significant advances have been made in the finite element method since this book first appeared in 1984, the basics have remained the same, and this classic, well-written text explains these basics and prepares the reader for more advanced study. Useful as both a reference and a textbook, complete with examples and exercies, it remains as relevant today as it was when originally published. This book is written for advanced undergraduate and graduate students in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined practitioners in engineering and the physical science.

A weak Galerkin mixed finite element method for second order elliptic problems

Abstract: . A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. Allowing the use of discontinuous approximating functions on arbitrary shape of polygons/polyhedra makes the method highly flexible in practical computation. Optimal order error estimates in both discrete H and L norms are established for the corresponding weak Galerkin mixed finite element solutions.

Localization of elliptic multiscale problems

Abstract: This paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches. Hence, on a uniform mesh of size $ H$, patches of diameter $ H\log (1/H)$ are sufficient to preserve a linear rate of convergence in $ H$ without pre-asymptotic or resonance effects. The analysis does not rely on regularity of the solution or scale separation in the coefficient. This result motivates new and justifies old classes of variational multiscale methods. - See more at: http://www.ams.org/journals/mcom/2014-83-290/S0025-5718-2014-02868-8/#sthash.z2CCFXIg.dpuf

Cavity Expansion Methods in Geomechanics

Abstract: Foreword. Preface. 1. Introduction. Part I: Fundamental Solutions. 2. Elastic Solutions. 3. Elastic-Perfectly Plastic Solutions. 4. Critical State Solutions. 5. Further Elastoplastic Solutions. 6. Time-Dependent Solutions. 7. Finite Elements Solutions. Part II: Geotechnical Applications. 8. In-Situ Soil Testing. 9. Pile Foundations and Earth Anchors. 10. Underground Excavations and Tunnelling. 11. Wellbore Instability. Index.

Unified form language: A domain-specific language for weak formulations of partial differential equations

Abstract: We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies for multifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted.

Projective dynamics: fusing constraint projections for fast simulation

Abstract: We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuum-based potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation.

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells

Abstract: Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations The properties estimated using an analytical solution based on the Euler–Bernoulli theory markedly deviated from experimental results for large apparent density values The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations

Finite Element Analysis of Structures through Unified Formulation

Abstract: This book deals with the Finite Element Method for the analysis of elastic structures such as beams, plates, shells and solids. The modern approach of Unified Formulation (UF), as proposed by the lead author, deals with the consideration of one-dimensional (beams), two-dimensional (plates and shells) and three-dimensional (solids) elements. Applications are given for structures which are typically employed in civil, mechanical, and aerospace engineering fields. Additional topics include mixed order elements, extension to layered composite structures, and the analysis of multifield problems involving mechanical, electrical and thermal loadings.

Basic principles of mixed Virtual Element Methods

Abstract: The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H (div)-conforming vector fields (or, more generally, of (n − 1) − Cochains ). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim of making the basic philosophy clear. However, we consider an arbitrary degree of accuracy k (the Virtual Element analogue of dealing with polynomials of arbitrary order in the Finite Element Framework).

Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations

Abstract: Aeroelastic systems achieve the best performance when the aerodynamic shape and structural sizing are optimized concurrently, but such an optimization is challenging when high-fidelity aerodynamic and structural models are required. This paper addresses this challenge through several significant improvements. Fully coupled Newton–Krylov methods are presented for the solution of aerostructural systems and for the corresponding adjoint systems. The coupled adjoint method presented can compute gradients with respect to thousands of multidisciplinary design variables accurately and efficiently. This is enabled by several improvements in the computation of the multidisciplinary terms in the coupled adjoint. The parallel scalability of the methods is demonstrated for a full aircraft configuration using an Euler computational fluid dynamics model with more than 8×106 state variables and a detailed structural finite element model of the wing with more than 1×106 degrees of freedom. The coupled Newton–Krylov metho...

Introduction to finite and spectral element methods using MATLAB

Abstract: The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media

Abstract: SUMMARY A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading-history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large-scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross-scale understanding of granular media. The developed framework is first benchmarked by a simulation of single-element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non-coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band. Copyright © 2014 John Wiley & Sons, Ltd.

Accordion-like Actuators of Multiple 3D Patterned Liquid Crystal Polymer Films

Abstract: This work describes the fabrication, characterization, and modelling of liquid crystalline polymer network films with a multiple patterned 3D nematic director profile, a stimuli-responsive material that exhibits complex mechanical actuation under change of temperature or pH. These films have a discrete alternating striped or checkerboard director profile in the plane, and a 90-degree twist through the depth of the film. When actuated via heating, the striped films deform into accordion-like folds, while the film patterned with a checkerboard microstructure buckles out-of-plane. Furthermore, striped films are fabricated so that they also deform into an accordion shaped fold, by a change of pH in an aqueous environment. Three-dimensional finite element simulations and elasticity analysis provide insight into the dependence of shape evolution on director microstructure and the sample's aspect ratio.