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Упит dcterms_creator_txt:Milanka N. Negovanović

793 items

  • The number of unimodular roots of some reciprocal polynomials

    Dragan Stankov (2020)
    We introduce a sequence P2n of monic reciprocal polynomials with integer coefficients having the central coefficients fixed. We prove that the ratio between number of nonunimodular roots of P2n and its degree d has a limit when d tends to infinity. We present an algorithm for calculation the limit and a numerical method for its approximation. If P2n is the sum of a fixed number of monomials we determine the central coefficients such that the ratio has the minimal limit. ...
    Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, Schinzel-Zassenhaus conjecture, Mahler measure, method of least squares, cyclotomic polynomials

  • Soil oscillation law parameter determination with the application of Lagrange’s theorem at “Kovilovača“ open pit

    Suzana Lutovac, Nebojša Vidanović, Čedomir Beljić, Zoran Gligorić (2015)
    ... (8) is reduced to: 1-n- c 1 -n 1 -n s Rn-k R- Rk-R sR k , (9) namely to: 1-n- c 1 -n 1 -n s R-n R- R-R sR , R1 < Rc < Rs. (10) No. 3, 2015 Mining & Metallurgy Engineering Bor 56 From the equation (10) the following is obtained: 1 1 1 1 n n s n s c RR RRn R , R1 ...
    ... (5), for- mula (8) se svodi na: 1-n- c 1 -n 1 -n s Rn-k R- Rk-R sR k , (9) tj. na: 1-n- c 1 -n 1 -n s R-n R- R-R sR , R1 < Rc < Rs. (10) Broj 3, 2015. Mining & Metallurgy Engineering Bor 66 Iz jednačine (10) dobijamo: 1 1 1 1 n n s n s c RR RRn R , R1 < Rc < Rs. ...
    ... .., N, are used from the table of experimental data, so that: n 111 RvK n 222 RvK ... n NNN RvK , whereby, for parameter K, the arithmetic mean is used, namely: N KKK K N...21 . (19) In this way, the model for solving the rock mass oscillation law is determined, taking: n RKv ...

  • A necessary and sufficient condition for an algebraic integer to be a Salem number

    Dragan Stankov (2019)
    We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a Salem number. This condition requires that the minimal polynomial of some power of the algebraic integer has a linear coefficient that is relatively large. We also determine the probability that an arbitrary power of a Salem number, of certain small degrees, satisfies this condition.
    Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, Schinzel-Zassenhaus conjecture, Mahler measure, method of least squares, cyclotomic polynomials

  • The use of biological markers in determination of origin and type of organic matter in the Tisza river sediments

    Snežana Štrbac, Gordana Gajica, Aleksandra Šajnović, Nebojša Vasić, Ksenija Stojanović, Branimir Jovančićević (2013)
    The objective of the study was to determine the origin and type of organic matter (OM) of the Tisza recent sediments along the distance of 153 km through the territory of Serbia. For this purpose group organic-geochemical parameters and biomarker compositions were used. All samples contain approximately same amount of OM, which was deposited under uniform, slightly reducing conditions. Based on the distribution of n-alkanes, the origin and type of OM could not be precisely estimated. However, n-alkane patterns ...
    sediments, Tisza River, organic matter, biomarkers, oil pollutants
    ... n-C20)+Σodd(n-C17–n-C21) / Σeven(n-C18–n-C22)]; cCPI deter- mined for distribution of n-alkanes C23–C35 (mass chromatogram m/z 71), CPI (C23–C35) = 1/2 [Σodd(n-C23– –n-C35) / Σeven(n-C22–n-C34)+Σodd(n-C23–n-C35) / Σeven(n-C24–n-C36)]; dPr/Ph = pristane/phytane Tricyclic and pentacyclic terpanes. The ...
    ... n of n-alkanes C16–C35 (mass chromatogram m/z 71), CPI (C16–C35) = 1/2 [Σodd(n-C17–n-C35) / Σeven(n-C16–n-C34) + Σodd(n-C17–n-C35) / Σeven(n-C18–n- –C36)]; bCPI determined for the distribution of n-alkanes C16–C22 (mass chromatogram m/z 71), CPI (C16– –C22) = 1/2 [Σodd(n-C17–n-C21) / Σeven(n-C16– ...
    ... such as gaso- line and diesel, have different n-alkane distributions, which range from n-C6 to n-C12, and n-C12 to n-C25, respectively. Moreover, these derivatives do not con- tain polycyclic biomarkers of the sterane and terpane types.7,8 Similarly to n-alkanes, the distributions of polycyclic alkanes ...

  • On the distribution modulo 1 of the sum of powers of a Salem number

    Dragan Stankov (2016)
    It is well known that the sequence of powers of a Salem number θ, modulo 1, is dense in the unit interval, but is not uniformly distributed. Generalizing a result of Dupain, we determine, explicitly, the repartition function of the sequence , where P is a polynomial with integer coefficients and θ is quartic. Also, we consider some examples to illustrate the method of determination.
    Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, Schinzel-Zassenhaus conjecture, Mahler measure, method of least squares, cyclotomic polynomials

  • Development of the Availability Concept by Using Fuzzy Theory with AHP Correction, a Case Study: Bulldozers in the Open-Pit Lignite Mine

    Stevan Đenadić, Dragan Ignjatović, Miloš Tanasijević, Uglješa Bugarić, Ivan Janković, Tomislav Šubaranović (2019)
    Availability is one of the most used terms in maintainability engineering. This concept is used to denote: The quality of service of an engineering system, i.e., machines, weak points’ analysis, asset management, as well as making decisions in the process of life cycle management. Availability is an overall indicator and contains partial indicators that are oriented towards reliability, maintenance, and logistical support. Availability presents a variable value and changes in time and space. Usually, availability is shown as the ...
    raspoloživost, fazi teorija, AHP višekriterijumska analiza, eksperska ocena, buldozer
    ... example: λ1 = (a11·WRB1−N)+(a12·WMB1−N)+(a13·WSB1−N) WRB1−N = (1·0.1630)+(0.5·0.2968)+(0.33·0.5401) 0.1630 = 3.01492 λ2 = (a21·WRB1−N)+(a22·WMB1−N)+(a23·WSB1−N) WMB1−N = (2·0.1630)+(1·0.2968)+(0.5·0.5401) 0.2968 = 3.00825 λ3 = (a31·WRB1−N)+(a32·WMB1−N)+(a33·WSB1−N) WSB1−N = (3·0.1630)+(2·0.2968)+(1·0 ...
    ... specific example: _ (a11-Wrpi-n)+(412-Wopi-n)+(413-Wspi-n) __ (1-0.1630)+(0.5-0.2968) + (0.33-0.5401) __ A= = = 3.01492 Wrsi-N 0.1630 -Wrepi- -W; _ -Weopi— 2-0.1630 1-0.2968 0.5-0.5401 A> = (421:Wrpi-n)+(422-Wopi-n) +(423-Wsp1-N) ( )+( )+( ) 3.00825 Wupi_n 0.2968 -Wrpi- -W; _ -Wopi- 3-0.1630 2-0.2968 1-0 ...
    ... ranking of the R, M, S indicators is given for the new (B1-N, B2-N, and B3-N have the same ranking) and old machines. Table 6. The ranking of partial indicators of the availability of new and old machines. AHP Preferences B1-N (B2-N, B3-N) B1-O B2-O B3-O R M S R M S R M S R M S R 1 1/2 1/3 1 1 1 ...

  • DNA/BSA interactions and cytotoxic studies of tetradentate N,N,O,O Schiff base copper(II) complexes

    Aleksandar Mijatović, Angelina Caković, Aleksandar Lolić, Snezana Sretenović, Marko Živanović, Dragana Seklić, Jovana Bogojeski, Biljana Petrović (2023)
    Three Schiff base Cu(II) complexes, (N,N’-bis(acetylacetone)propylenediimine)copper(II) complex, [Cu(acac2pn)] (1), (N,N'-bis-(benzoylacetone)propylenediimine)copper(II) complex, [Cu(phacac2pn)] (2) and (N,N’-bis-(trifluoroacetylacetone)propylenediimine)copper(II) complex, [Cu(tfacac2pn)] (3), were used to investigate the interactions with calf thymus DNA (ct-DNA) and bovine serum albumin (BSA) using the electronic absorption and spectroscopic fluorescence methods. UV-Vis absorption studies showed that studied complexes interact with DNA molecule and exhibit moderate binding affinity. Fluorescence studies of complexes 1-3 also showed a possibility for DNA intercalation as well as a relatively high binding ability ...
    General Chemistry

  • Some models for determination of parameters of the soil oscillation law during blasting operations

    Suzana Lutovac, Dragan Medenica, Branko Gluščević, Rade Tokalić, Čedomir Beljić (2018)
    ... Equation (4) into Equation (3), we obtain: v “ Kv ¨ ˝ 3 b 3¨Q 4¨π r ˛ ‚ n “ Kv ¨ ˜ 3 c 3 4 ¨ π ¸n ¨ ˆ 3 ? Q r ˙n “ Kv ¨ K1 ¨ ˆ r 3 ? Q ˙´n “ K ¨ ˆ r 3 ? Q ˙´n “ K ¨ R´n (5) where as: ˜ 3 c 3 4 ¨ π ¸n “ K1; Kv “ K K1 ; r 3 ? Q “ R (6) where: R—reduced distance is the distance ...
    ... marked ´n, meaning that: ∆v v ∆R R « ´n (7) Thereby it can be considered that: lim∆RÑ0 ∆v v ∆R R “ ´n, which means: dv v dR R “ ´n (8) Equation (8) can be written in the form: dv v “ ´n ¨ dR R , where by integration is obtained: ż dv v “ ´n ¨ ż dR R , namely: logv “ logR´n ` logC (9) ...
    ... (1) we obtain the equation: v “ v1 ¨ ˆ R1 R ˙n (14) From Equation (14), for R = R1 there is obtained v = v1 for any n, in our case n > 0. For R = Ri, i = 2, 3, ..., N, from Equation (14), we can take that: vi “ v1 ¨ ´ R1 Ri ¯n , i = 2, 3, ..., N, from there the relation is obtained: v1 ¨ v2 ...

  • Parameter determination of soil oscillation law using quotient of the relative growth increments of oscillation velocity and reduced distances at “Nepričava“ open pit mine

    Suzana Lutovac, Sanja Bajić, Marina Ravilić, Radmila Gaćina (2015)
    ... obtained: 1 1 2 1 1 2 ... ... n N N N N R v v v v R R R             (10) From the relation (10), we can determine parameter n. By logharithm operation of relation (10) we obtain: 1 21 1 2 1 ... log log ... N N N N v v vR n R R R v          ...
    ... .. N N N N v v v v n R R R R                (11) By the replacement of the value for the parameter n in the equation (11), found in this way, we obtain the relation for the oscillation velocity of rock mass in the monitored environment: 1 1 n R v ...
    ... obtain the equation: 1 1 n R v v R        (9) From the equation (9), for R = R1 there is obtained v = v1 for any n, in our case n > 0. For R = R1, i = 2, 3, ..., N, from the equation (9), we can take that: 1 1 2,3,..., n i i R v v i N R         ...

  • Rezultati probnog ispitivanja geotehničkih prenapregnutih sidara u Užicu (Stari grad)

    Vladimir Kovačević (2024)
    Za potrebe izrade završnog rada na četvrtoj godini Rudarsko-geološkog fakulteta, studijskog programa Geotehnika, pod mentorstvom doc. dr Zorana Berisavljevića, odabrana je tema „Rezultati probnog ispitivanja geotehničkih prenapregnutih sidara u Užicu (Stari grad)“. Osnovni metodološki pristup koji je korišćen za rešavanje postavljenog problema predstavlja kabinetsko istraživanje dostupne dokumentacije, analiza i interpretacija rezultata izvedenih geoloških,geotehničkih i geomehaničkih istraživanja. Predstavljene su osnovne informacije,karakteristike i upotreba prednapregnutih geotehničkih sidara.Analiziran je tok testiranja granične nosivosti prednapregnutih sidara. Na osnovu izvršenih geotehničkih istraživanja terena i ispitivanja ...
    geotehnička istraživanja, prednapregnuta sidra, nosivost sidra, standard SIA V 191
    ... M O H O N V 3O O N L L S S L L A L I O V d V O ĐONIMHVHH - Q O M I O H O N V Đ N L L S M . L / L I S O A I S O N M N Q I N V N M S O I S M L - V I V G I S f N V A L L I d S I I W O N T O H . L N O X O X I N S I d V Z Đ N I S S H N . L S H N H G G N V gauMn,LOniLLS ...
    ... A Y O H O N V O O N L L S I L L A.LIOVdV' O Đ N I D H V H H - Q 1 O D 0 i 1 O H O N V Đ N L L S ? L L / L L S O A I S O N M N N O I N V ? H D .LSŠLL – V M V G I S O f N V A L L I d S I T W O N T O H . L N O N M O M I N S I d V Z ĐNISSHNH.LSHNHd G N V SMMn.LOnbiLLS ...
    ... + i i = + - + ++ o 5 ( N O d d S r N a Z n O Z I - V1IS I N W H O V T I G ĐONISSiHHLSSHHd G N V g S d H n i O n H 1 I S HO34 H 3 1 N 3 O - S r N v V Z d H d v N G d b H d | 3 r I O 5 n H . L S N O y N VZ H V 1 L N 3 O B8B8B8BPEB8BSBBRB wl {v= CENTAR ...

  • Clockwise vertical-axis rotation in the West Vardar zone of Serbia: Tectonic implications

    Vesna Lesić, Emo Márton, Violeta Gajić, Dragana Jovanović, Vesna Cvetkov (2018)
    The Vardar-Tethyan mega-suture between the Eurasian and Adria (Gondwana) margins comprises remnants of oceanic lithosphere of Neotethys and distal parts of the adjacent continental margins including unconformable Late Cretaceous sedimentary cover and Cenozoic igneous rocks of post-obduction age. This study provides kinematic constraints for displacements and rotations affecting the Serbian part of the West Vardar and Jadar-Kopaonik units after the closure of the Neotethyan (= Sava) Ocean. The targets of the paleomagnetic research were Late Cretaceous sediments representing an ...
    Paleomagnetism, Clockwise rotation, Dinarides, West Vardar zone
    ... T u ro n ia n S u m m ar y o f lo ca li ty m ea n p al eo m ag n et ic d ir ec ti o n s b as ed o n th e re su lt s o f p ri n ci p al co m p o n en t an al y si s (K ir sc h v in k 1 9 8 0 ). K ey : L at . N an d L o n . E : g eo g ra p h ic co o rd in at es (W G S 8 4 ), n /n o : n u m b er ...
    ... /4 1 U p p e r C e n o m a n ia n -T u ro n ia n 5 G aj ić q u ar ry 4 2 8 3 – 2 9 8 4 4 � 0 6 0 2 6 00 2 0 � 0 9 0 5 9 00 L im es to n e p in k is h g re y 1 5 /1 6 3 8 .8 4 7 .4 2 1 1 2 .6 3 6 .2 2 6 .7 2 1 1 2 .6 2 8 /2 1 S a n to n ia n -C a m p a n ia n 6 B o g d an o v ić ...
    ... er ca rb o n at es w it h n eg at iv e su sc ep ti b il it y ei th er sc at te re d d ir ec ti o n s o r b ad d em ag n et iz at io n cu rv es . * L ef t o u t fr o m te ct o n ic in te rp re ta ti o n d u e to cl o se n es s to th e d ir ec ti o n o f p re se n t E ar th m ag n et ic fi el ...

  • Biosorpcija-nekonvencionalni metod u prečišćavanju otpadnih voda

    Radulović Milanka, Ilić Marija, Živić Miroslav, Marković Zoran (2010)

  • Mean-based iterative methods for finding multiple roots in nonlinear chemistry problems

    Dejan Ćebić, Nebojša M. Ralević (2021)
    нелинеарне једначине, поступци засновани на срединама, вишеструки корени,

  • Towards Automatic Definition Extraction for Serbian

    Ranka Stanković, Cvetana Krstev, Rada Stijović, Mirjana Gočanin, Mihailo Škorić (2021)
    U radu su prikazani preliminarni rezultati automatske ekstrakcije kandidata za definicije rečnika iz nestrukturiranih tekstova na srpskom jeziku u cilju ubrzanja razvoja rečnika. Definicije u rečniku Srpske akademije nauka i umetnosti (SANU) korišćene su za modelovanje različitih tipova definicija (opisnih, gramatičkih, referentnih i sinonimskih) koje imaju različite sintaksičke i leksičke karakteristike. Korpus istraživanja sastoji se od 61.213 definicija imenica, koje su analizirane korišćenjem morfoloških e-rečnika i lokalnih gramatika implementiranih kao pretvarači konačnih stanja u paketu za obradu korpusa otvorenog ...
    ... акушерка N в.бабица (accoucheuse N v. midwife) 2 (1) surname 3672 3670 (100%) Андрић N презиме (Andrić N surname) 3 (1) verbal noun 913 912 (100%) плакање N гл. им. од плакати (crying N verb. n. from to cry) 4 (3) type of 1435 1250 (87%) бисер N врста пенушавог вина (pearl N a kind ...
    ... 1575 (97%) ветрић N дем. и хип. од ветар; (small wind N dim. and hyp. of wind) 6 (1) first name or a nickname 914 857 (94%) Пачавра N лични надимак (Pačavra N personal nickname) 7 (3) women 596 483 (81%) бедевуша N танка, висока незграпна жена. (bedevuša N a thin, tall clumsy woman) ...
    ... Вечерњача N народни назив за планету Венеру (Večernjača N folk name of the planet Venus) 14 (1) collective nouns 103 101 (98%) браћа N зб. им. од брат (brothers N col. noun derived from brother) 15 (3) animals 2115 1564 (74%) арнаут N назив за помамна, љута коња; (arnaut N name for a ...

  • Influence of paleoenvironmental conditions on distribution and relative abundance of saturated and aromatic hydrocarbons in sediments from the NW part of the Toplica basin, Serbia

    Nikola Burazer, Aleksandra Šajnović, Nebojša Vasić, Milica Kašanin-Grubin, Dragana Životić, João Graciano Mendonça Filho, Predrag Vulić, Branimir Jovančićević (2020)
    Stratigraphy,Economic Geology,Geology,Geophysics,Oceanography

  • Одређивање резерви нафтног лежишта „Х“ методом материјал баланса

    Александра Петровић (2024)
    Метода материјалног баланса је кључна техника у процени резерви нафте и гаса у лежиштима која омогућава системско прорачунавање доступних резерви. Циљ ове методе је да се прецизно израчунају количине флуида у лежишту на основу доступних PVT података, података о лежишту и производњи. Резултати примене методе материјалног баланса показују да је она ефикасна у пружању кавнтитативних процена, међутим њена тачност зависи од квалитета улазних података. Метода материјалног баланса пружа основу за процену резерви, али може бити подложна грешкама због непрецизности ...
    материјални баланс, прорачун, енергетски режим, притисак, аквифер
    ... JoOujeHe y HHTCPBAa]JIy tn-1 OJIHOCHO: CApn — (We)n-i(Pp)n (We)n = (W.)n-i + [(tp)a — (ta)n-il (Pp), — (tp)n_i(p5)n (58) Ine cy: C – Barn EnepniHreH-XypcToBa KOHCTaHTa BOJIČHOr yTOKa tp — Oc3J1HMCH3HOHAaJIHO BDCMC n — TDeHyTHH BpeČMeCHCKH KOpaK n-] — rpeTXojHH BpeMCHCKH KOpaK Apn – ykyrnHu najni ...
    ... 2019): • EKcHaH3HOHH pe;KHM: N=—_P— 3.27 BoiceAp ( ) • Pe»MHM pacTBopeHor raca: N„|B R, – Rs)B N= P[ 0+( p 5) g] (328) Bt — Bti • PeMM racHe Kame: N= NP[BO + (Rp _— RS)Bg] Bg (3.29) (B. – Ba) + mBii (T_ 1) gi • BojoHanopHH pe)KMM Oe3 racHe Kate: N _Np[BO+(Rp—RS)Bg]+WpBW—We (3.30) ...
    ... THIOueTaK KaO IIITO je IIpHka3aHO Ha CJIHIH . 37 | N E(„·•·Eu Canuka 4.8. Fy dynkuuju Eo+Ey (Okotie u Ikporo, 2019) • HenoaHara BenauuHHa racHe Kane m, N, G F = N|E, + mE„,| = NE, + mNE, (4.33) FE_ N+mN Fa 4.34 DN 3) Ine cy: F = N,|B, + (R, — R.)B,| (4.35) Eo = [(Bo — Boi) + (Rsi — ...

  • Models of Determining the Parameters of Rock Mass Oscillation Equation with Experimental and Mass Blastings

    Suzana Lutovac, Branko Gluščević, Rade Tokalić, Jelena Majstorović, Čedomir Beljić (2018)
    ... Equation (4), in the Equation (3), we obtain: v = Kv   3 √ 3Q 4π r   n = Kv· ( 3 √ 3 4π )n · ( 3 √ Q r )n = Kv·K1· ( r 3 √ Q )−n = K· ( r 3 √ Q )−n = K·R−n, (5) whereas: ( 3 √ 3 4π )n = K1; Kv = K K1 ; r 3 √ Q = R; (6) whereby: R—the reduced distance is the distance ...
    ... velocity of the soil v will decrease (increase) by approximately n% [8]. Indeed, for h = ± R 100 = ±1%R, from (12) we obtain: v ( R ± R 100 ) ≈ v(R)∓ n· R 100 · v(R) R , v ( R ± R 100 ) ≈ v(R)∓ n· v(R) 100 , v(R ± 1%R) ≈ v(R)∓ n%·v(R). (14) 3.3. Models to Determine the Parameters of Equation ...
    ... vm) the following relations are valid: vm = K·Rm −n, m = 1, 2, . . . , N, (15) Minerals 2018, 8, 70 6 of 18 from where we obtain the relation: v1·v2· . . . ·vs vs+1·vs+2· . . . ·v2s = Ks·(R1·R2· . . . ·Rs) −n Ks·(Rs+1·Rs+2· . . . ·R2s) −n , (16) i.e., relation: v1·v2· . . . ·vs vs+1·vs+2· ...

  • An optimal sixteenth order family of methods for solving nonlinear equations and their basins of attraction

    Dejan Ćebić, Nebojša Ralević, Marina Marčeta (2020)
    нелинеарна једначина, 16.ред конвергенције, оптималне методе, подељене разлике

  • A comparative study of the molecular and isotopic composition of biomarkers in immature oil shale (Aleksinac deposit, Serbia) and its liquid pyrolysis products (open and closed systems)

    Gordana Gajica, Aleksandra Šajnović, Ksenija Stojanović, Jan Schwarzbauer, Aleksandar Kostić, Branimir Jovančićević (2021)
    The molecular and isotopic composition of biomarkers in initial bitumen isolated from immature (0.41% Rr) oil shale samples (Aleksinac deposit) and liquid products obtained by pyrolysis in open (OS) and closed (CS) systems are studied. The influence of pyrolysis type and variations of kerogen type on biomarkers composition and their isotopic signatures in liquid products is determined. The applicability of pyrolysis type, numerous biomarkers and carbon isotopic compositions (δ13C) of n-alkanes in liquid pyrolysates is established. Pyrolysis experiments were ...
    Uljni šejl, Aleksinac, organska supstanca, otvoreni i zatvoreni sistem pirolize, biomarkeri, izotopski sastav ugljjenika

  • Mapping and classifying large deformation from digital imagery: application to analogue models of lithosphere deformation

    Taco Broerse, Nemanja Krstekanić, Cor Kasbergen, Ernst Willingshofer (2021)
    kontinentalna tektonika: kompresija, kontinentalna tektonika: ekstenzija, kontinentalna tektonika: transkurentni i transformni rasedi, pukotine, rasedi, zone snažnih deformacija, kinematika deformacija kore i omotača, teorijska mehanika, modelovanje
    ... two orthogonal stretches with different magnitude, but the same sign. 3 A P P L I C AT I O N : S T R A I N T Y P E F O R RO TAT I N G E L E M E N T S U N D E R D I F F E R E N T T Y P E S O F D E F O R M AT I O N As a first test, we apply our strain type classification to individual square elements that ...
    ... than missing material) should be directed to the corresponding author for the paper. A P P E N D I X A : S H A P E F U N C T I O N S F O R D E T E R M I N I N G T H E D I S P L A C E M E N T G R A D I E N T We use linear shape functions to determine the displacement gradient ∂u ∂X for quadrilaterals ...
    ... quadrilateral deformation and that described by F the elements should be chosen sufficiently small. A P P E N D I X B : P O L A R D E C O M P O S I T I O N O F T H E D E F O R M AT I O N G R A D I E N T I N 2 D Analytic solutions exist for the decomposition of the deformation gradient F into the rotation tensor ...