Computer-based manipulation of systems of equations in elasticity problems with Gröbner bases

Ioakimidis, NI; Anastasselou, EG

dc.contributor.author	Ioakimidis, NI	en
dc.contributor.author	Anastasselou, EG	en
dc.date.accessioned	2014-03-01T01:09:20Z
dc.date.available	2014-03-01T01:09:20Z
dc.date.issued	1993	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10911
dc.subject	System of Equations	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Boolean algebra	en
dc.subject.other	Computational methods	en
dc.subject.other	Computer aided analysis	en
dc.subject.other	Differential equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Polynomials	en
dc.subject.other	Structural analysis	en
dc.subject.other	Systems analysis	en
dc.subject.other	Trusses	en
dc.subject.other	Grobner bases	en
dc.subject.other	Multivariate polynomial equations	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Elasticity	en
dc.title	Computer-based manipulation of systems of equations in elasticity problems with Gröbner bases	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0045-7825(93)90022-P	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0045-7825(93)90022-P	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	The classical method of Buchberger's Gröbner bases for multivariate polynomial equations with a variety of applications in computer algebra is applied to three problems in elasticity concerning (i) a simple elastic truss, (ii) an elementary plane elasticity problem in rectangular coordinates, and (iii) the derivation of a compatibility partial differential equation for the stress components and the proof of biharmonicity of the same components also in plane elasticity. The present results aim at the practical illustration of the possibility of deriving computer-generated formulae in elasticity problems by using Gröbner bases (as has been done in the case of geometric problems) and the popular and modern computer algebra system Maple V (equipped with a related package) has been used. Further generalizations of the present results are quite possible and some of these are discussed in brief. © 1993.	en
heal.publisher	ELSEVIER SCIENCE SA LAUSANNE	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/0045-7825(93)90022-P	en
dc.identifier.isi	ISI:A1993MP82900008	en
dc.identifier.volume	110	en
dc.identifier.issue	1-2	en
dc.identifier.spage	103	en
dc.identifier.epage	111	en