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Highly Efficient Implementation of ANS/ EAS ‘Solid‐Shell’ Finite Elements for Explicit Time Integration
Author(s) -
Mattern Steffen,
Schweizerhof Karl
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010088
Subject(s) - fortran , computer science , symbolic computation , programming language , computation , code (set theory) , computational science , shell (structure) , matrix (chemical analysis) , source code , parallel computing , algorithm , mathematics , set (abstract data type) , engineering , mathematical analysis , materials science , composite material , civil engineering
Abstract In an explicit time integration algorithm, the most time‐consuming part of an analysis is the computation of the internal nodal force vector. An implementation concept for element routines for volumetric shell so‐called Solid‐Shell ‐ elements based on the application of the symbolic programming tool ACEGEN, a plug‐in for the computer algebra software MATHEMATICA is presented. Symbolic implementation means that vector and matrix operations and differentiations can be performed symbolically in order to generate program code, which supports the implementation, reduces programming effort and helps to avoid programming errors almost completely. The program code is generated in FORTRAN and simultaneously optimized automatically, which leads to very efficient routines compared to manually implemented code. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)