Structural

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

By Julian A. T. Dow

This publication presents an in-depth heritage to higher realizing of finite point effects and methods for making improvements to accuracy of finite aspect equipment. therefore, the reader is ready to establish and dispose of blunders contained in finite point versions. 3 assorted blunders research recommendations are systematically built from a typical theoretical beginning: 1) modeling erros in person components; 2) discretization mistakes within the total version; three) point-wise error within the ultimate pressure or pressure results.Thoroughly type confirmed with undergraduate and graduate scholars. A Unified method of the Finite point strategy and blunder research methods is certain to turn into a necessary source for college kids in addition to practising engineers and researchers. * New, easier aspect formula recommendations, model-independent effects, and blunder measures* New polynomial-based equipment for picking serious issues* New techniques for comparing sheer/strain accuracy* available to undergraduates, insightful to researchers, and priceless to practitioners* Taylor sequence (polynomial) dependent* Intuitive elemental and point-wise blunders measures* crucial history info supplied in 12 appendices

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

Sample text

The finite difference method, a differential approach, finds a solution that satisfies an approximation to the differential equations of equilibrium for the system. The details of these differences are discussed in Part IV. Error Analysis Developments As mentioned earlier, the availability of two different solution techniques is exploited to develop procedures for evaluating the errors in finite element results. This is accomplished by using concepts from the finite difference method to improve existing error analysis methods and to develop new procedures for identifying errors in finite element results.

Thus, this is not an admissible virtual displacement. 2b illustrates an inadmissible virtual displacement applied to a pinned connection. The constraint on the displacement has been violated. The virtual displacements shown in Fig. 2 are inadmissible because they violate the constraints of their respective boundaries. A virtual displacement is denoted here as 5r. The characteristics of a virtual displacement are explicated by deriving the principle of virtual work for discrete systems and by using a virtual displacement in a problem.

Example Problem The principle of virtual work is now applied to a simple problem to demonstrate the use of an admissible virtual displacement. The problem chosen for this demonstration is that of the teeter-totter shown in Fig. 3. A teeter-totter consists of a rigid beam and a pinned connection. A known force is applied to the right end of the rigid beam. The objective of the problem is to find the unknown force on the left end required to produce equilibrium. The system is given an admissible virtual displacement, as shown in Fig.

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