By Paul M. Kurowski
Many books were written approximately Finite point research (FEA), notwithstanding little or no FEA literature takes a center floor technique and particularly addresses the desires of layout engineers who use FEA as a regular layout device. This publication makes an attempt to fill that void by way of concentrating on an knowing of FEA basics, that are defined via uncomplicated and intuitive examples that may be utilized by any engineer. This booklet additionally takes a realistic procedure, attribute to the attitudes of layout engineers.
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Additional resources for Finite Element Analysis for Design Engineers
Example text
A warped quadrilateral element shown here with “zebra stripes” to better visualize the warpage. underestimate the displacements. Consequently, the strains and stresses, as being calculatedbased on displacementsresults, also are underestimated. 16, where the degenerated portion of the twosided cantilever underestimates deflections by 60%! 1 6. The left side is modeled with excessively distorted elements; the right side is modeled with properly shaped elements. 17 shows a model erroneously meshed with first-order elements.
What happens if degenerated elements are used? 15. A warped quadrilateral element shown here with “zebra stripes” to better visualize the warpage. underestimate the displacements. Consequently, the strains and stresses, as being calculatedbased on displacementsresults, also are underestimated. 16, where the degenerated portion of the twosided cantilever underestimates deflections by 60%! 1 6. The left side is modeled with excessively distorted elements; the right side is modeled with properly shaped elements.
In direct analogy to the uniform and non-uniform h-convergence processes, the p-convergence process can also be uniform or non-uniform. In a uniform p-convergence process, the order of all elements is upgraded until the desired accuracy is obtained. The advantage of a uniform element upgrade is that the mesh compatibility is automatically assured because functions of the same order are used on all faces and edges of all elements. To assure mesh compatibility in the non-uniform (often called “adaptive”) p-convergence process, shape functions of different orders must be used on different edges and faces of the same element to assure that displacements on adjacent edges and faces of neighboring elements are described by the same shape functions.