Grzegorz Lenda*, Marcin Ligas** Splines and Kriging. the use of two methods for shell structures shape analysis
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1 Grzegorz Lenda* Marcn Lga** Splne and rgng he ue o wo mehod or hell rucure hape analy Unvery o Scence and Technology AGH * Deparmen o Cvl Engneerng and Conrucon **Deparmen o Geomac FIG Worng Wee Marraech Morocco 8-22 May 2 G. Lenda M. Lga - Splne and rgng... Thn hell rucure A hn hell dened a an obec wh a hcne whch mall compared o oher dmenon. They are uually el upporng whch ac condoned by proper re drbuon n a hell endng o preerve he ae o mnmal poenal energy. In her cae very dengerou hng are local and abrup hape change whch dor he drbuon o ree. Thereore approxmang her hape mporan o ue mahemacal ool ha wll llurae hee deormaon properly. Splne are uable choce becaue hey are mahemacal equvalen o beam beng ben whn rellency lm and end o preerve he ae o mnmal poenal energy wha conneced wh mnmzaon o oal curvaure. FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2
2 G. Lenda M. Lga - Splne and rgng... G. Lenda M. Lga - Splne and rgng... Fng quadrc drawbac: gve an deal mage o obec ayng nohng abou local deormaon. I dcul o ue hem n order o compare 2 meauremen carred ou a deren pon. plne allow local decrpon need o now he mahemacal uncon by whch he obec wa conruced. Approxmaon by mproper uncon yeld large error. plne do no carry h problem repoonng a ngle pon aec he enre quadrc parameer. by ung plne local mpac lmed only o urroundng pon. Advanage: Unrerced amplng Small number o pon neceary o quadrc FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2 2
3 FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2 3 G. Lenda M. Lga - Splne and rgng... x x 2 x F F 2 F x 3 x 4 3 F 4 EJ M x x z 2 3 / 2 ' " ] [ ρ Bernoull Euler ormula How plne are derved G. Lenda M. Lga - Splne and rgng... The mo popular and he mo common orm o plne - B - plne d S m m n }.. { n [ [ dla dla u d u S n r }.. { n }.. { r u u u
4 G. Lenda M. Lga - Splne and rgng... ey acor deermnng he qualy o nerpolaon by plne: Proper amplng he more regular he beer a n cae o all nerpolaon mehod global acor Parameerzaon no elecon global acor Boundary condon local acor True Dance Square roo Conan dance G. Lenda M. Lga - Splne and rgng... The dome o RMF rado n eporaz Poland How wa meaured? Relecorle oal aon Leca TCRA 2 3 mm 2 ppm or he range up o 8 m and 5 mm 2 ppm or range exceedng 8 m. The dance rom he aon o he obec dd no exceed m. Acue ncdence angle or upper par o he rucure. Pon gven blue Pon o be reored red op vew FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2 4
5 G. Lenda M. Lga - Splne and rgng... Splne curve creaed on he ba o gven pon. Envelope hghlgh area wh he greae doron o amplng. The graph o curvaure G. Lenda M. Lga - Splne and rgng... Spaal drbuon o devaon obaned by plne nerpolaon The magnude o devaon obaned by plne nerpolaon FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2 5
6 FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2 6 G. Lenda M. Lga - Splne and rgng... The prncple o rgng: Unbaedne o he predcor emaor.e.: Mnmzaon o he mean quare error o predcon emaon.e.: ] ˆ [ E mn ˆ 2 o o E a a a ˆ G. Lenda M. Lga - Splne and rgng... Aer ome mah... Unveral rgng yem.... γ µ γ
7 G. Lenda M. Lga - Splne and rgng... Spaal drbuon o devaon obaned by rgng nerpolaon The magnude o devaon obaned by rgng nerpolaon Than you or your aenon Grzegorz Lenda Marcn Lga Unvery o Scence and Technology AGH * Deparmen o Cvl Engneerng and Conrucon **Deparmen o Geomac FIG Worng Wee 2 Brdgng he Gap beween Culure Marraech Morocco 8 22 May 2 7
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