Download or read book Blended Mesh Methods for Large Deformation written by Vincent Tan Beng Chye and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In many cases, it is advantageous to discretize a domain using several finite element meshes instead of a single mesh. For example, in fluid-structure interaction problems, an Eulerian mesh is advantageous for the fluid domain while a Lagrangian mesh is most suited for the structure. However, the interface conditions between different types of meshes often lead to significant errors. A method of treating different meshes by smoothly varying the description from Lagrangian to Eulerian in an interface or blending domain is presented. The finite element approximation for the material domain is obtained by combining the solutions from the constituent meshes through a blending function. There are no boundary conditions for mesh boundaries inside the material domain because of the way the blending function is defined. The coupled semi-discrete finite element equations are obtained from a weak form of the mass and momentum conservation equations. The resultant interpolant retains the property of linear completeness. The convergence of the method was verified by tests on static problems. An operator splitting method is used for advection terms so the time update is separated into the solution of a symmetric system emanating from a Lagrangian description and the advection of history dependent variables. The method was tested on several fluid-structure interaction and free surface problems. A Lagrangian mesh was used for the structure while two different types of mesh were used for the fluid. Arbitrary Lagrangian Eulerian meshes were used in the regions of the fluid-structure interfaces and free surfaces while Eulerian meshes were used for the remainder of the fluid domain. A blending function was used to couple the ALE and Eulerian meshes to ensure a smooth transition from one mesh to another. The fluid-structure problems include flow past a hinged plate, fluid expansion in a closed container and transient interaction of acoustic plane waves with cylindrical and spherical shells. The free surface problem are free surface wave propagation and the draining of a circular tank. All results are in good agreement with standard finite element and analytical solutions.

Download or read book Meshfree Modelling of Hyperelastic Mechanics written by Chun Meng Goh and published by . This book was released on 2020 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large deformation mechanics faces numerous challenges when simulated using mesh-based methods, notably the finite element method. Firstly, the computational modeler is required to fit a mesh to the body of interest, which is a tedious and time-consuming process. Secondly, these meshes are typically simplex shapes and therefore can resist deformation artificially as their deformation increases, and numerical instability can occur as these simplexes/polygons invert for deformation beyond their resolution. Thirdly, these meshes can be resolved further into smaller pieces, a process called refinement, but the process of robust automatic refinement is still another challenge face by modelers. Therefore, in this thesis, we are motivated to use a meshfree method to simulate large deformations of hyperelastic mechanics without the dependency of a body mesh. The thesis then explores some of the challenges faced by meshfree methods currently and further developing and maturing its strengths of solving PDEs with only random nodal distributions. We found that these meshfree methods often depends on a background mesh for quadrature process, hence currently many meshfree methods are still not as “mesh-independent” as we wish them to be. Therefore we attempted to develop a truly meshfree method is in this thesis, where the quadrature is performed in overlapping support domains of a set of functions that form partition of unity of the body. We manage to improve on the Partition of Unity Quadrature scheme, where polynomial consistency can be restored for the first time in overlapping quadrature schemes, while still conserving energy according to the work conjugacy theory. The methods fall short that the quadrature accuracy must be increased with refinement of particle distributions, a common observation among truly meshfree methods. Another issue that meshfree methods faces is the ability to enforce incompressibility in solid mechanics. Hyperelasticity does not only undergo large deformations, they also exhibit nearly- to-truly incompressible behaviour. Such incompressibility constraints may be enforced using mixed formulations, but this requires the user to define the distribution of particles representing primal and dual variables in a certain fashion, such that a stability criterion known as the inf-sup condition is satisfied. This criterion is, however, normally satisfied through the use of a mesh. A more natural approach would have been to set the distributions to be the same set for meshfree method, such that we may avoid the need of tessellation to satisfy the inf-sup condition. Therefore in this thesis, we further propose a stabilised mixed meshfree formulation based on a stabilisation technique called the Polynomial Pressure Projection (PPP) to penalise the violation of the inf-sup condition caused from using the same distributions of primal and dual variables. Similar to the previous investigation, we continue to improve on the quadrature of our stabilised mixed formulation such that the so-called integration constraint may be satisfied, by means of correcting the classical gradient field. Some of the associated properties of the quadrature scheme and the corrected gradients are given in the appendices, where it theoretically explained on why the use of a background mesh is convergent and the resulting bilinear form using corrected gradient remains stable. The stabilised mixed formulation is tested to be effective in linear elasticity mechanics and non- convective fluids, motivating us to further extend it to large deformation mechanics of hyperelasticity, albeit using a more strengthen form of the PPP. We also unified the gradient correction/quadrature scheme with the stabilised mixed formulation using the Veubeke-Hu- Washizu (VHW) approach. We ran some simple test cases and found that the stabilised mixed formulation continues to converge optimally and being locking free. A simple comparison between stabilised meshfree and finite element methods, however, highlighted that meshfree methods consumes more computational power and yield solution with larger errors, an observation that is consistent with the current literature, mainly due to meshfree basis functions are more costly to be computed, stored and integrated in weak form. Next, we recast the formulation in Eulerian setting to enable us to compute undeformed geometry when given a deformed geometry. We continue to use the enhanced/strengthen PPP stabilisation method in the VHW framework, so that the gradient correction scheme is encompassed naturally. We also showed that our Eulerian formulation can recover the standard Cauchy’s law of equilibrium, with some mesh-dependent conditions that diminish with refinement. When we tested against simple test cases, we observed that the formulation also yields solutions with optimal convergence, besides being free from spurious pressure modes. Besides that, when we re-paramerise the undeformed geometry as unknown variables in the stabilised Lagrangian mixed formulation, we also can demonstrate that the unloaded configuration can be computed, using an example of inflated and extended cylinder. Lastly, a summary of our endeavour in solving some challenges in meshfree method is given in the last chapter.

Download or read book Co rotational Meshfree Formulation for Large Deformation Inelastic Analysis of Two dimensional Structural Systems written by Louis Lee Yaw and published by . This book was released on 2008 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Extended Finite Element Method written by Amir R. Khoei and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples

Download or read book EAS Elements for Solid Mechanics Mesh Distortion Insensitive and Hourglassing Free Formulations with Increased Robustness written by Pfefferkorn, Robin and published by KIT Scientific Publishing. This book was released on 2023-04-04 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proposed in the early 1990s, the enhanced assumed strain (EAS) method is one of the probably most successful mixed finite element methods for solid mechanics. This cumulative dissertation gives a comprehensive overview of previous publications on that method and covers recent improvements for EAS elements. In particular, we describe three key issues of standard EAS elements and develop corresponding solutions.

Download or read book Computational Methods and Experimental Measurements XVII written by G.M. Carlomagno and published by WIT Press. This book was released on 2015-05-05 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing papers presented at the seventeenth in a series of biennial meetings organised by the Wessex Institute and first held in 1984, this book includes the latest research from scientists who perform experiments, researchers who develop computer codes, and those who carry out measurements on prototypes and whose work may interact. Progress in the engineering sciences is dependent on the orderly and concurrent development of all three fields. Continuous improvement in computer efficiency, coupled with diminishing costs and rapid development of numerical procedures have generated an ever-increasing expansion of computational simulations that permeate all fields of science and technology. As these procedures continue to grow in magnitude and complexity, it is essential to be certain of their reliability, i.e. to validate their results. This can be achieved by performing dedicated and accurate experiments. At the same time, current experimental techniques have become more complex and sophisticated so that they require the exploitation of computers, both for running experiments as well as acquiring and processing the resulting data. The papers contained in the book address advances in the interaction between these three areas. They cover such topics as: Computational and Experimental Methods; Fluid Flow; Structural and Stress Analysis; Materials Characterisation; Heat Transfer and Thermal Processes; Advances in Computational Methods; Automotive Applications; Applications in Industry; Process Simulations; Environmental Modelling and Applications; Computer Modelling; Validation of Computer Modelling; Computation in Measurements; Data Processing of Experiments; Virtual Testing and Verification; Simulation and Forecasting; Measurements in Engineering.

Download or read book Advanced Computational Methods in Science and Engineering written by Barry Koren and published by Springer Science & Business Media. This book was released on 2010-04-29 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

Download or read book Dissertation Abstracts International written by and published by . This book was released on 1999 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modelling of Metal Forming Processes written by J.L. Chenot and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physical modelling of metal forming processes has been widely used both in University and in Industry for many years. Relatively simple numerical models, such as the Slab Method and the Upper Bound Method, were first used and many such models are implemented in the industry for practical design or regulation of forming processes. These are also under investigation in the University, mainly for treat models ments which require low cost calculations or very fast answers for on-line integration. More recently, sophisticated numerical methods have been used for the simulation of metal flow during forming operations. Since the early works in 1973 and 1974, mainly in U. K. and U. S. A. , the applications of the finite element method to metal processing have been developed in many laboratories all over the world. Now the numerical approach seems to be widely re cognized as a powerful tool for comprehension oriented studies, for predic ting the main technological parameters, and for the design and the optlmi zation of new forming sequences. There is also a very recent trend for the introduction of physical laws in the thermo-mechanical models, in order to predict the local evolution of internal variable representing the micro structure of the metal. To day more and more practicians of the Industry are asking for compu ter models for design of their forming processes.

Download or read book Meshing Geometric Modeling and Numerical Simulation Volume 2 written by Paul Louis George and published by John Wiley & Sons. This book was released on 2019-01-25 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this vision of meshing. These mesh adaptations are generally governed by a posteriori error estimators representing an increase of the error with respect to a size or metric. Independently of this metric of calculation, compliance with a geometry can also be calculated using a so-called geometric metric. The notion of mesh thus finds its meaning in the metric of its elements.

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Damage Modeling of Composite Structures written by Pengfei Liu and published by Elsevier. This book was released on 2021-03-10 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Damage Modeling of Composite Structures: Strength, Fracture, and Finite Element Analysis provides readers with a fundamental overview of the mechanics of composite materials, along with an outline of an array of modeling and numerical techniques used to analyze damage, failure mechanisms and safety tolerance. Strength prediction and finite element analysis of laminated composite structures are both covered, as are modeling techniques for delaminated composites under compression and shear. Viscoelastic cohesive/friction coupled model and finite element analysis for delamination analysis of composites under shear and for laminates under low-velocity impact are all covered at length. A concluding chapter discusses multiscale damage models and finite element analysis of composite structures. - Integrates intralaminar damage and interlaminar delamination under different load patterns, covering intralaminar damage constitutive models, failure criteria, damage evolution laws, and virtual crack closure techniques - Discusses numerical techniques for progressive failure analysis and modeling, as well as numerical convergence and mesh sensitivity, thus allowing for more accurate modeling - Features models and methods that can be seamlessly extended to analyze failure mechanisms and safety tolerance of composites under more complex loads, and in more extreme environments - Demonstrates applications of damage models and numerical methods

Download or read book IDIHOM Industrialization of High Order Methods A Top Down Approach written by Norbert Kroll and published by Springer. This book was released on 2015-01-02 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes the main findings of the EU-funded project IDIHOM (Industrialization of High-Order Methods – A Top-Down Approach). The goal of this project was the improvement, utilization and demonstration of innovative higher-order simulation capabilities for large-scale aerodynamic application challenges in the aircraft industry. The IDIHOM consortium consisted of 21 organizations, including aircraft manufacturers, software vendors, as well as the major European research establishments and several universities, all of them with proven expertise in the field of computational fluid dynamics. After a general introduction to the project, the book reports on new approaches for curved boundary-grid generation, high-order solution methods and visualization techniques. It summarizes the achievements, weaknesses and perspectives of the new simulation capabilities developed by the project partners for various industrial applications, and includes internal- and external-aerodynamic as well as multidisciplinary test cases.

Download or read book Classical And Computational Solid Mechanics Second Edition written by Yuen-cheng Fung and published by World Scientific Publishing Company. This book was released on 2017-05-25 with total page 861 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition provides an update of the recent developments in classical and computational solid mechanics. The structure of the book is also updated to include five new areas: Fundamental Principles of Thermodynamics and Coupled Thermoelastic Constitutive Equations at Large Deformations, Functional Thermodynamics and Thermoviscoelasticity, Thermodynamics with Internal State Variables and Thermo-Elasto-Viscoplasticity, Electro-Thermo-Viscoelasticity/Viscoplasticity, and Meshless Method. These new topics are added as self-contained sections or chapters. Many books in the market do not cover these topics.This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives the first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions.

Download or read book Advances and Trends in Structures and Dynamics written by Ahmed K. Noor and published by Elsevier. This book was released on 2013-10-22 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances and Trends in Structures and Dynamics contains papers presented at the symposium on Advances and Trends in Structures and Dynamics held in Washington, D.C., on October 22-25, 1984. Separating 67 papers of the symposium as chapters, this book documents some of the major advances in the structures and dynamics discipline. The chapters are further organized into 13 parts. The first three parts explore the trends and advances in engineering software and hardware; numerical analysis and parallel algorithms; and finite element technology. Subsequent parts show computational strategies for nonlinear and fracture mechanics problems; mechanics of materials and structural theories; structural and dynamic stability; multidisciplinary and interaction problems; composite materials and structures; and optimization. Other chapters focus on random motion and dynamic response; tire modeling and contact problems; damping and control of spacecraft structures; and advanced structural applications.

Download or read book Proceedings of the Eighth Annual Thermal and Fluids Analysis Workshop Spacecraft Analysis and Design written by and published by . This book was released on 1997 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Processing Analyzing and Learning of Images Shapes and Forms Part 2 written by and published by Elsevier. This book was released on 2019-10-16 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. - Covers contemporary developments relating to the analysis and learning of images, shapes and forms - Presents mathematical models and quick computational techniques relating to the topic - Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods