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Symbolic software tools in the development of finite elementsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 1999 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 72, no 4, 579-593 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

1999. Vol. 72, no 4, 579-593 p.
##### Keyword [en]

Computational methods, Finite element method, Stiffness, Strain, Nonlinear mechanics, Symbolic software, Computer aided software engineering
##### National Category

Applied Mechanics
##### Identifiers

URN: urn:nbn:se:kth:diva-117941DOI: 10.1016/S0045-7949(98)00333-2OAI: oai:DiVA.org:kth-117941DiVA: diva2:603978
#####

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##### Note

Symbolic software has been used in a number of projects concerned with the development of finite element procedures, primarily aiming at complex, i.e. interacting and higher order instabilities, where high accuracy in formulations is required. The symbolic tools improve the efficiency and documentation of the developed procedures, in order to facilitate comparisons between different element assumptions. Beam formulations for plane and space models were developed, in total displacement and co-rotational contexts, respectively. Symbolic derivation allowed analytical verification of equivalence between certain formulations within these two contexts. Treatment of finite space rotations, based on the rotational vector makes the history-less treatment of rotations easier, which is needed in the evaluation of critical equilibrium subsets in higher-dimensional parameter space. A co-rotational viewpoint, where local element displacements can be obtained from global variables in a systematic manner, allowed different element expressions in a common framework. Different simple, linear elements have been tested with respect to computational efficiency. A field consistence approach was used to develop highly accurate beam and plane stress elements. The common element formulations, based on the matrix multiplications BTDB, is often inefficient, due to the large number of operations needed in the matrix product. Other formulations, based on an analytical integration and differentiation of the strain energy, producing explicit expressions for the stiffness terms, were considerably more efficient for certain elements.

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