The meccano method for finite element and isogeometric analysis

The Meccano Me hod o Fini e Elemen and Isogeome ic Analysis R. Mon eneg o (1)*, J.M. Cascón(2), E. Rod íguez(1), J.M. Escoba (1), M. B o ka(1), J.I. López(1), J. Ramí ez(1) (1) Uni e si y Ins i u e o In elligen Sys ems and Nume ical Applica ions in Enginee ing, SIANI, Uni e si y o Las Palmas de G an Cana ia, Las Palmas de G an Cana ia, Spain, { mon eneg o,e od iguez,jmescoba }@siani.es, [email p o ec ed], josei [email protected], [email p o ec ed], h p://www.dca.iusiani.ulpgc.es/p oyec o2012-2014. (2) Depa men o Economics and His o y o Economics, Facul y o Economics and Managemen , Uni . o Salamanca, Spain, [email p o ec ed], h p://campus.usal.es/~sinumcc. Abs ac In his wo k we p esen he applica ion o he meccano me hod [1] o solid modelling o be used in ini e elemen and isogeome ic analysis [2]. We will show he esolu ion o ellip ic and pa abolic PDE in h ee-dimensional complex domains. The disc e iza ion o he solid is ob ained by cons uc ing a olume ic pa ame e iza ion o he solid. To do ha , an adap i e e ahed al mesh o he pa ame ic domain is isomo phically ans o med on o he solid by applying a simul aneous mesh un angling and smoo hing p ocedu e. In he case o isogeome ic analysis, he geome ic app oxima ion o he solid and he nume ical solu ion ha e been accomplished by using T-splines ha enables he local e inemen . The con ol poin s o he i a ia e T-spline a e calcula ed by imposing he in e pola ion condi ions on poin s si ed on he inne and he su ace o he solid, and using he olume ic pa ame e iza ion. Th ee-dimensional isogeome ic analysis examples o complex solids a e p esen ed. In addi ion, we compa e ini e elemen and isogeome ic solu ions o se e al wo-dimensional examples by using local adap i e s a egies. Re e ences [1] R. Mon eneg o, J.M. Cascón, J.M. Escoba , E. Rod íguez, G. Mon e o, An au oma ic s a egy o adap i e e ahed al mesh gene a ion, Applied Nume ical Ma hema ics 59 (2009) 2203–2217. [2] J.M. Escoba , J.M. Cascón, E. Rod íguez, R. Mon eneg o, A new app oach o solid modeling wi h i a ia e T-splines based on mesh op imiza ion, Compu . Me hods Appl. Mech. Eng g. 200 (2011) 3210–3222.