Finite Element Method (FEM) by Daryl L. Logan

By Daryl L. Logan

This document provides the 1st whole implementation of the Finite point procedure (FEM) using
the Mathematica language. The file specializes in information buildings, info movement and programming
modules for linear structural mechanics.
The fabric accumulated herein without delay helps lots of the syllabus of the path Finite Element
Programming with Mathematica (ASEN 5519). The programming modules also are used to
support machine homework within the path creation to Finite point equipment (ASEN
5007); even though, the common sense of these modules isn't really studied.

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2 Note that the meaning of ”interior nodes” here does not agree with the usual FEM definition except for 3D elements. A plane stress element with one center node has eFNX=1 and eINX=0 instead of eFNX=0 and eINX=1. In other words, that center node is considered a face node. Similarly a bar or beam element with two nodes at its third-points has eSNX=2, eFNX=eINX=0; that is, those nodes are considered side nodes. As explained next, the reason for this convention is mixability. Why use indices instead of actual node counts?

Familiarity with the concepts and terminology of Chapter 3 is essential. 1 General Description The Master Element Definition Table or MEDT is a flat data structure that list all individual finite elements of a discrete model. The qualifier “flat” means that for example, the element with internal number 42 is the 42th object in the table. The qualifier “Master” means that the other element data structures described in this Chapter: the Visual Element Definition Table or VEDT, and the Local Subdomain to Element Connection Table or LSECT can be built from the MEDT.

5. 12) Note that the full set of indices only applies to elements with intrinsic dimensionality of 3. If dimensionality is 2 or less, eINX is ignored. If dimensionality is 1 or less, eFNX and eINX are ignored. Finally if dimensionality is 0, all except eCNX are ignored. 5 Node configuration in element type descriptor Dim Indices Meaning/remarks 1–3 1–3 2–3 eCNX=0,1 eSNX=0,1,2 eFNX=0,1,2 3 eFNX=0,1,2 0 eCSFIX=1000 element has eCNX nodes per corner element has eSNX nodes per side if eFNX=0, no face nodes if eFNX=1, one node per face if eFNX=2, as many face nodes as face corners if eINX=0, no face nodes if eINX=1, one node per face if eINX=2, as many face nodes as face corners all nodes are treated as corners Some exotic node configurations are omitted; cf.

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