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# The finite element method for engineers

01 Jan 1975-

TL;DR: The Finite Element Method as discussed by the authors is a method to meet the Finite Elements Method of Linear Elasticity Theory (LETI) and is used in many of the problems of mesh generation.

Abstract: PART I. Meet the Finite Element Method. The Direct Approach: A Physical Interpretation. The Mathematical Approach: A Variational Interpretation. The Mathematical Approach: A Generalized Interpretation. Elements and Interpolation Functions. PART II. Elasticity Problems. General Field Problems. Heat Transfer Problems. Fluid Mechanics Problems. Boundary Conditions, Mesh Generation, and Other Practical Considerations. Appendix A: Matrices. Appendix B: Variational Calculus. Appendix C: Basic Equations from Linear Elasticity Theory. Appendix D: Basic Equations from Fluid Mechanics. Appendix E: Basic Equations from Heat Transfer. References. Index.

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09 Mar 1989

TL;DR: In this paper, the finite element method was used to analyze the metal forming process and its properties, including plasticity, viscoplasticity, and plane-strain problems.

Abstract: Introduction Metal forming process Analysis and technology in metal forming Plasticity and viscoplasticity Methods of analysis The finite element method (1) The finite element method (2) Plane-strain problems Axisymmetric isothermal forging Steady state processes of extrusion and drawing Sheet metal forming Thermo-viscoplastic analysis Compaction and forging of porous metals Three dimensional problems Preform design in metal forming Solid formulation, comparison of two formulations, and concluding remarks Index.

1,226 citations

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17 Jul 2000TL;DR: In this article, the Fourier series is used to measure the response of a single-degree-of-freedom system to initial and non-periodic oscillations, respectively.

Abstract: 1 Concepts from Vibrations 2 Response of Single-Degree-of-Freedom Systems to Initial Excitations 3 Response of Single-Degree-of-Freedom Systems to Harmonic and Periodic Excitations 4 Response of Single-Degree-of-Freedom Systems to Nonperiodic Excitations 5 Two-Degree-of-Freedom Systems 6 Elements of Analytical Dynamics 7 Multi-Degree-of-Freedom Systems 8 Distributed-Parameter Systems: Exact Solutions 9 Distributed-Parameter Systems: Approximate Mathods 10 The Finite Element Method 11 Nonlinear Oscilations 12 Random Vibrations Appendix A. Fourier Series Appendix B. Laplace Transformation Appendix C. Linear Algebra

1,133 citations

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Virginia Tech

^{1}TL;DR: A comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations that are described by partial differential and integral equations and the simulations that result from their numerical solution.

Abstract: Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

966 citations

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10 Sep 2000

TL;DR: In the present article target cascading is formalized by a process modeled as a multilevel optimal design problem that links all subproblem decisions so that the overall system performance targets are met.

Abstract: Target cascading is a key challenge in the early product development stages of large complex artifacts: how to propagate the desirable top level design specifications (or targets) to appropriate specifications for the various subsystems and components in a consistent and efficient manner. Consistency means that all parts of the designed system should work well together, while efficiency means that the process itself should avoid iterations at later stages, which are costly in time and resources. In the present article target cascading is formalized by a process modeled as a multilevel optimal design problem. Design targets are cascaded down to lower levels using partitioning of the original problem into a hierarchical set of subproblems. For each design problem at a given level, an optimisation problem is formulated to minimize deviations from the propagated targets and thus achieve intersystem compatibility. A coordination strategy links all subproblem decisions so that the overall system performance targets are met. The process is illustrated with an explicit analytical problem and a simple automotive chassis design model that demonstrates how the process can be applied in practice.

605 citations

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01 Aug 1996

TL;DR: Three new ideas for solving the problem of achieving real‐time performance for these models of 3D solid volumetric Finite Element models to surgery simulation are introduced.

Abstract: This paper discusses the application of 3D solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real-time performance for these models. The simulation system we have developed is described and we demonstrate real-time deformation using the methods developed in the paper.

589 citations