By Julian A. T. Dow

ISBN-10: 0122214404

ISBN-13: 9780122214400

This booklet presents an in-depth historical past to higher figuring out of finite aspect effects and strategies for bettering accuracy of finite point tools. therefore, the reader is ready to determine and do away with mistakes contained in finite point types. 3 diverse errors research thoughts are systematically constructed from a standard theoretical beginning: 1) modeling erros in person parts; 2) discretization mistakes within the total version; three) point-wise blunders within the ultimate rigidity or pressure results.Thoroughly category demonstrated with undergraduate and graduate scholars. A Unified method of the Finite point process and blunder research strategies is certain to turn into a vital source for college kids in addition to practising engineers and researchers. * New, easier aspect formula concepts, model-independent effects, and mistake measures* New polynomial-based tools for deciding on severe issues* New techniques for comparing sheer/strain accuracy* available to undergraduates, insightful to researchers, and helpful to practitioners* Taylor sequence (polynomial) dependent* Intuitive elemental and point-wise errors measures* crucial historical past info supplied in 12 appendices

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Additional resources for A Unified Approach to the Finite Element Method and Error Analysis Procedures

Example text

Integration by parts. 1 An alternative approach for developing this expression is presented in Appendix B. 7) Lesson 2 9 25 The first expression on the right-hand side of Eq. 7 is part of the boundary term. This is as would be expected because this expression is evaluated at the two boundaries. The integrand of the second expression on the right-hand side of Eq. 7 is a component of the Euler-Lagrange equation. The meaning of these terms is discussed when the functional derivative is simplified.

Lesson 1 Principle of Minimum Potential Energy Purpose of Lesson To introduce the principle of minimum potential energy and the concept of a functional (a function of a function). The equations of statics that govern the behavior of discrete systems result when the potential energy function is minimized using the procedures of differential calculus. When the principle is extended to continuous systems, the potential energy function that must be minimized is found to be a functional. The emergence of the need to minimize a functional provides the motivation for Lesson 2, which introduces the calculus of variations, the branch of mathematics used to identify the conditions required to minimize the potential energy functional.

Admissible virtual displacements. 2. Inadmissible virtual displacements. 2 The idea that a virtual displacement is imaginary does not have any significance in statics applications. However, when the idea of a virtual displacement is extended to dynamics problems, it is necessary that the virtual displacementbe independent of time. , it is a product of the imagination. Lesson 2 9 35 Derivation of the Principle of Virtual Work The principle of virtual work states that the work done by the applied forces must be zero when a virtual displacement is imposed on a system in equilibrium.

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A Unified Approach to the Finite Element Method and Error Analysis Procedures by Julian A. T. Dow

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