Simulation of 2D Elastic Bodies with Randomly Distributed Circular Inclusions Using the BEM
|
|
- Gabriel Robbins
- 5 years ago
- Views:
Transcription
1 Smulaton of 2D Elastc Bodes wth Randomly Dstrbuted Crcular Inclusons Usng the BEM Zhenhan Yao, Fanzhong Kong 2, Xaopng Zheng Department of Engneerng Mechancs 2 State Key Lab of Automotve Safety and Energy Tsnghua Unversty Bejng, Chna Abstract Based on the Rzzo s drect boundary ntegral equaton formulaton for elastcty problems, elastc bodes wth randomly dstrbuted crcular nclusons are smulated usng the boundary element method. The gven numercal examples show that the boundary element method s more accurate and more effcent than the fnte element method for such type of problems. The presented approach can be successfully appled to estmate the equvalent elastc propertes of many composte materals. Introducton As composte materals are appled more and more to many mportant engneerng projects, researchers have pad much more attenton to the smulaton of the composte materals and to the estmaton of ther equvalent elastc propertes. To estmate the equvalent elastc propertes of composte materals, many theoretcal models have been developed, such as the composte cylnder model [], the dlute or non-nteractng soluton [2], the self-consstent method [3], the generalzed self-consstent method [4~7] and the Mor-Tanaka method [8~]. At the same tme, only few data obtaned from numercal smulatons can be found n lterature. A numercal procedure, based on the seres expanson of complex potentals, was proposed n Ref. [2], but only several knds of perodc arrays of holes were consdered. A sprng force model has been used to smulate a sheet contanng crcular holes arranged as trangular and hexagonal arrays [3]. A numercal equvalent ncluson method was presented [4], whch can be appled to analyze stress felds n and around nclusons of varous shapes by the fnte element method. But ths approach can only be appled to smulate the elastc body wth only one ncluson. The smulaton of the sheet wth randomly or normally dstrbuted crcular holes was nvestgated n our group several years ago [5]. Based on Rzzo s drect BEM [6] for elastcty problem, a new BEM approach for the smulaton of elastc bodes wth randomly dstrbuted crcular nclusons s proposed n ths paper. Several numercal examples are presented to menstruate the advantages of ths new BEM approach over the doman-based FEM approach. 270
2 BEM for smulaton of 2D elastc body wth a crcular ncluson The model of 2D elastc body wth a crcular ncluson s shown n Fgure, where Ω ΙΙ denote the doman of matrx and ncluson respectvely, Ω Ι, Γ the matrx-ncluson nterface boundary, and t u ΓI, Γ I ndcate the gven tracton part and gven dsplacement part of the outer boundary of matrx materal doman Γ Ι. Fg.. Model of 2D elastc body wth a crcular ncluson The boundary ntegral equatons can be wrtten for the matrx and ncluson subdoman respectvely: Ι I Γ I+Γ Γ I+Γ ΙΙ II = (, ) d Γ (, ) dγ Γ Γ C p u p = U p, q t q d Γ T p, q u q dγ αβ β αβ β αβ β C p u p U p q t q T p q u q αβ β αβ β αβ β Where superscrpts Ι and ΙΙ ndcate matrx and ncluson subdoman respectvely, p and q stand for the source pont of fundamental soluton and feld pont on the boundary respectvely, Cαβ ( p) s a free term determned from the shape of the Ι ΙΙ boundary at source pont p, Uαβ ( p, q), Tαβ ( p, q) and Tαβ ( p, q) are fundamental solutons of 2D elastcty problem, and uβ, tβ are boundary dsplacement and boundary tracton respectvely. After dscretzaton usng lnear or quadrc boundary elements, equatons () can be rewrtten nto matrx form as follows: () I I I I I I I I A A2 A 3 U B B2 B 3 T I I I I I I I I A2 A22 A23 T = B2 B22 B23 U I I I I I I I A3 A32 A33 U B3 B32 B33 T (2a) II II II GT = HU (2b) 27
3 Ι where U and T Ι represent the unknown nodal dsplacement vector and the gven t Ι nodal tracton vector respectvely on the gven tracton boundary Γ I, T and U Ι, the unknown nodal tracton vector and the gven nodal dsplacement vector on the gven u dsplacement boundary Γ I, U, the unknown nodal dsplacement vector on the Ι matrx-ncluson nterface boundary Γ. Whle T and T ΙΙ stand for the unknown nodal tracton vector on the matrx-ncluson nterface boundary for the matrx and ncluson materal respectvely. For the matrx materal, the subdoman s a multply connected doman, the nodal number and the correspondng sequence of boundary varables can be arranged sequentally n the postve drecton of the boundary. When advancng n the postve drecton of boundary, the nner doman surrounded by the boundary s always at the left sde. For the ncluson, the nodal number of the matrx-ncluson nterface should keep n lne wth that of matrx materal subdoman. So the nodal number and the correspondng sequence of boundary varables should be arranged sequentally n the negatve drecton of the boundary for the ncluson tself. In equatons (2), the dsplacement contnuty on the matrx-ncluson nterface has been taken nto account. The nterface condton for the tractons can be wrtten as: II I T = T (3) Substtutng equaton (3) nto the equaton (2b), we can obtan the relaton between the tractons and dsplacements of the matrx on the nterface: I II II T = G H U (4) Substtutng equaton (4) nto equaton (2a), we can obtan the fnal system of equatons for the 2D elastc body wth a crcular ncluson as follows: I I I I II II A A2 A3 + B3 G H I I I U B B 2 I I I I I II II I I I T A2 A22 A23 + B23 G H T = B2 B22 I I I I I I I II U II U B3 B32 A 3 A32 A33 + B33 G H BEM for smulaton of 2D elastc body wth randomly dstrbuted crcular nclusons The model of 2D elastc body wth randomly dstrbuted dentcal crcular nclusons s shown n Fgure 2. Where Ω 0 s the subdoman of matrx materal, Ω, Ω2, L, Ω, L, Ωn, the subdomans of ncluson materal, Γ the matrx-ncluson nterface boundares, and Γ 0 the outer boundary of the matrx materal subdoman. (5) 272
4 Fg. 2. Model of 2D elastc body wth randomly dstrbuted dentcal crcular nclusons If the conventonal subdoman boundary element method s adopted, n + equaton systems for the n + subdomans should be solved. As the number of nclusons ncreases, the computng tme wll ncrease sgnfcantly. If we notce that the relatons between the tractons and dsplacements of each dentcal ncluson are just the same and smlar as shown n equaton (4), we can reduce the full computaton to the soluton of the equaton for the matrx materal doman wth nner boundary condtons smlar to equaton (4), whch can be descrbed as follows: where n A A2 3 L 3 L 3 U B B 2 n A2 A L L 23 T B2 B22 n A 3 A32 33 L 33 L U 33 B3 B 32 T M M M O M O M M = M M n A U 3 A32 33 L 33 L U 33 B 3 B 32 M M M O M O M M M M n n n n nn n A3 A32 33 L 33 L n n 33 U B3 B32 j j j = A3 + B3 G H 23 = A23 + B23 G H = A + B G H The frst and the second subscrpt ndcate the boundary where the source pont node p and the feld pont node q located, and, 2, 3 denote the tracton gven part, dsplacement gven part of outer boundary and the nner boundares respectvely. To dstngush dfferent nner boundares, the superscrpts are used. The frst and the second (f there s a second one) superscrpt ndcate the number of nner boundary where the (6) (7) 273
5 source pont node p and the feld pont node q located. Matrces G and H n equaton (7) are coeffcent matrxes for the ncluson materal subdomans. As all the randomly dstrbuted crcular nclusons are dentcal, t needs to form the coeffcent matrxes G and H for a certan ncluson only one tme. In equaton (6), U, T and U ndcate the unknown dsplacement vector on the tracton gven part of outer boundary, the unknown tracton vector on the dsplacement gven part of outer boundary and the unknown dsplacement vector on the -th nner nterface boundares respectvely. On the other hand, T and U stand for the gven tracton vector and the gven dsplacement vector on the outer boundary respectvely. For the case of 2D elastc body wth randomly dstrbuted crcular nclusons of dfferent sze, the above-presented approach can be generalzed no dffculty, provded the number of dfferent sze s much less than the number of nclusons. In such case, the equaton (7) should be modfed as follows: k () 3 = k () k() 23 = k() j j j k () 33 = k A B G H A B G H () A B G H where k =, 2, L, m denote dfferent ncluson sze, k() can be also a random functon, and for the ncluson of each sze the matrces G and H should be computed once. Numercal examples ) A square sheet wth a crcular ncluson at the center subjected to unform tenson on two opposte edges (8) Fg. 3. Model of a square sheet wth a crcular ncluson at the center subjected to unform tenson on two opposte edges 274
6 Fgure 3 shows the computatonal model. The sde length a = 00 mm, the radus of the crcular ncluson r = 2 mm, the tracton q = 0 MPa, the materal propertes of the matrx E = 0 MPa, v = 0.3, and that of the ncluson E2 = ke and v 2 = 0.3. The rgd body dsplacement s constraned properly. In the computaton, the matrx-ncluson nterface s dvded nto 0 quadratc elements. Fgure 4 shows the absolute value of crcumferental stress σ θ on the matrxncluson nterface obtaned by BEM n comparson wth the analytcal soluton, for the specal case of crcular hole. The sold lne s the analytcal soluton, and the sold dots show the BEM results. As to the case of an nfnte sheet wth a crcular hole at the center, the analytcal soluton can be wrtten as: σθ = q 2cos2θ (9) It s obvous that the maxmum of the crcumferental stress σ θ s 3q = 30MPa when θ s equal to π 2 or 3π 2, and the mnmum s zero when θ s equal to π 6, 5π 6, 7π 6 or π 6. It can be found that the present numercal results agree wth the analytcal soluton very well. The maxmum error of BEM results s less than 0.02%. σ θ (MPa) Theoretcal soluton BEM soluton θ( ) Fg. 4. Comparson of the crcumferental stress σ θ on the matrx- ncluson nterface obtaned by the BEM and the analytcal soluton 275
7 3.5 Stress concentraton factor Modulus rato of ncluson and matrx materals Fg. 5. Relaton between stress concentraton factor and the ncluson-matrx modulus rato obtaned from BEM scheme Fgure 5 shows that the stress concentraton factor obtaned by BEM vares wth the ncluson-matrx modulus rato, the sold dots show the numercal results, and the sold lne s nterpolated curve. It can be found from Fgure 5 that the stress concentraton factor decreases quckly wth the ncrease of ncluson-matrx modulus rato when ncluson materal s softer than matrx materal. Furthermore, stress concentraton factor ncreases slowly wth the ncrease of the ncluson-matrx modulus rato when ncluson materal s harder than matrx materal. As to the analytcal soluton of an nfnte sheet wth a crcular hole or a crcular rgd core at the center, the stress concentraton factor s equal to 3.0 or.5 from elastc theory respectvely. The correspondng results obtaned by BEM are and.5002 respectvely. It s obvous that the present numercal results agree wth the elastc theory very well. 2) A square sheet wth two very close nclusons subjected to unform dsplacement on one edge Fgure 6 shows the computatonal model. The sde length a = 00 mm, the radus of two very close crcular nclusons R = 5 mm, the mnmum dstance between the matrx-ncluson nterface boundares b = 0.5 mm, the gven unform dsplacement on the rght edge d =.0 mm, the materal property of the matrx E = 0 MPa, v = 0.3, and that of the ncluson E2 = ke, v 2 = 0.3. It s obvous that the stress concentraton factor ncreases to the maxmum when the ncluson-matrx modulus rato approaches zero. So the stress gradent around the matrx-ncluson nterface wll reach the maxmum for the case of two crcular holes. To ensure hgh accuracy, t s necessary to take fner mesh around the two nclusons for ether the BEM or FEM computaton. Fgure 7 shows the varaton of Von-Mses stress on one quarter of the matrx-ncluson 276
8 nterface by usng 0 quadratc boundary elements and 20 quadratc boundary elements. It can be found that the varaton s very small, whch ndcates a convergent soluton has been obtaned by usng only 0 quadratc boundary elements n BEM computaton. a=00mm R=5mm E =0 v =0.3 b=0.5mm E 2 =ke v 2 =0.3 d=.0mm Fg. 6. The model of a square sheet wth two very close nclusons under gven unform dsplacement on one edge Mses stress quadrc elements 20 quadrc elements Fg. 7. Comparson of the Von-Mses stress on the quarter of the matrx-ncluson boundares by dfferent boundary element number θ 277
9 Mses stress BEM(0 quadrc elements) MSC.Marc(46356 quadrc elements) MSC.Marc(96 quadrc elements) θ Fg. 8. Comparson of Von-Mses stress on the quarter of the matrx-ncluson nterface boundary obtaned from BEM and the famous MSC.Marc software Fgure 8 shows the comparson of Von-Mses stress on one quarter of matrx-ncluson nterface obtaned by the presented BEM and the FEM usng MSC/Marc software, for the case of two crcular holes. It can be found that the Von-Mses stress ncreases slowly to the results obtaned by BEM wth the mmense ncrease of fnte elements. It s obvous that the accuracy reached by MSC/Marc usng quadratc elements s far lower than by BEM usng 0 quadratc boundary elements on the nterface. The presented BEM s much more effectve than FEM for such knd of problems. Furthermore, for 2D elastc body wth randomly dstrbuted crcular nclusons, there wll be plenty of very close nclusons. Thus, the presented scheme of BEM s very sutable to such smulaton problems, and t has obvous advantage over the FEM. 3) A square sheet wth 00 randomly dstrbuted dentcal crcular nclusons subjected to unform tenson on the opposte edges Fgure 9 shows the computatonal model. The sde length of ths square sheet s 00mm, the tracton on the opposte edges s 0Mpa, the thckness of ths square sheet s mm, and the volume rato of all 00 nclusons s 0.4. Then the radus of the crcular ncluson can be determned automatcally. The model s taken as a plane stress problem. In addton, doman mesh s only needed for plottng results. After BEM computaton, we can obtan the deformaton pattern and stress dstrbuton. As examples, Fgure 0 shows the deformaton pattern for the case of 00 crcular holes, E 2 = 0, Fgure and Fgure 2 shows the Von-Mses stress dstrbuton of a square sheet wth 00 randomly dstrbuted dentcal crcular hole under the unform tenson on two opposte edges for the case of E2/ E =
10 Fg. 9. Model of a square sheet wth 00 randomly dstrbuted dentcal crcular nclusons under unform tenson on two opposte edges Fg. 0. Deformaton pattern of a square sheet wth 00 randomly dstrbuted dentcal crcular hole under the unform tenson on two opposte edges (E 2 = 0) 279
11 Fg.. Deformaton pattern of a square sheet wth 00 randomly dstrbuted dentcal crcular nclusons under the unform tenson on two opposte edges ( E2 E = 0.5 ) Fg.2. Von-Mses stress dstrbuton of a square sheet wth 00 randomly dstrbuted dentcal crcular holes under unform tenson on two opposte edges ( E2/ E = 0.5 ) 280
12 Concludng Remarks ) A scheme of the BEM for the smulaton of 2D elastc bodes wth randomly dstrbuted crcular nclusons has been presented n ths paper. The gven numercal examples ndcate ts hgh accuracy and hgh effcency. 2) As for the elastc bodes wth randomly dstrbuted dentcal crcular nclusons, the presented BEM scheme has a dstnctve advantage over the FEM due to hgh stress gradent resulted from the presence of many very close nclusons. 3) The presented BEM scheme can be generalzed wthout dffculty to the elastc bodes wth randomly dstrbuted nclusons of dfferent geometrcal szes, dfferent shapes (ellptcal ncluson wth dfferent shape and prncpal drecton, cracks wth dfferent drecton, etc.) and dfferent elastc modulus. 4) The presented BEM scheme can be appled to estmate the equvalent elastc propertes of correspondng composte materals. 5) The presented BEM can be combned wth some knd of fast multpole algorthms. It s possble to effcently smulate the elastc bodes wth much more dfferent nclusons wth such fast algorthms. Snce ths manuscrpt was submtted two years ago, some related nvestgatons n the authors group have been publshed [7-20]. In those nvestgatons, a large number of numercal examples of the 2D elastc solds wth randomly dstrbuted nclusons, usng repeated smlar sub-doman BEM, have shown that ths method has hgher accuracy and hgher effcency, and provdes an effcent tool for the numercal smulatons of correspondng composte materals. Ths method can be appled to smulate not only the 2D solds wth nclusons of dfferent shapes, szes and materals, but also the nclusons wth nterphases layers. By applyng the fast multpole BEM nto ths feld, the scale of the computaton can be ncreased. In a prelmnary nvestgaton, the number of nclusons smulated was ncreased from 00 to 600. Further nvestgatons wll be carred out n two drectons: on the one hand, t wll be developed from 2D to 3D problems; on the other hand from the smulaton of effectve elastc modul to smulatons of the falure process of such composte materals. Acknowledgements Fnancal support for the project from the Natonal Natural Scence Foundaton of Chna under grant No and No s gratefully acknowledged. References [] Hashn Z. The elastc modul of heterogeneous materals. J Appl Mech., 962; 29: 43~50. [2] Budansky Y. On the elastc modul of heterogeneous materals. J Mech Phys Solds, 965; 3: 223~
13 [3] Hll R. A self-consstent mechancs of composte materals. J Mech Phys Solds, 965; 3: 23~222. [4] Chrstensen RM, Lo KH. Solutons for effectve shear propertes n three phase sphere and cylnder models. J Mech Phys Solds, 979; 27: 35~330. [5] Aboud J, Benvenste Y. The effectve modul of cracked bodes n plane deformaton. Engng Fracture Mech., 987; 26: 7~84. [6] Huang Y, Hu KX, We X, Chandra A. A generalzed self-consstent mechancs method for composte materals wth multphase nclusons, J Mech Phys Solds, 994; 42: 49~504. [7] Huang Y, Hu KX, Chandra A. A generalzed self-consstent mechancs method for mcrocracked solds, J Mech Phys Solds, 994; 42: 273~29. [8] Mor T, Tanaka K. Average stress n matrx and average elastc energy of materals wth ms-fttng nclusons. Acta Metal, 973; 2: 57~583. [9] Taya M, Chou T-W. On two knds of ellpsodal nhomogenetes n an nfnte elastc body: an applcaton to a hybrd composte. Int J Solds Structure, 979; 27: 35~330. [0] Weng GJ. Some elastc propertes of renforced solds, wth specal reference to sotropc ones contanng sphercal nclusons. Int J Engng Sc., 984; 22: 845~856. [] Benvenste Y. A new approach to the applcaton of Mor-Tanaka theory n composte materals. Mech Mater, 987; 6: 47~57. [2] Isda M, Igawa H. Analyss of zgzag array of crcular holes n an nfnte sold under unaxal tenson. Int J Solds Structure, 99; 27: 849~864. [3] Day AR, Snyder KA, Garbocz EJ, Thorpe MF. The elastc modul of a sheet contanng crcular holes. J Mech Phys Solds 992; 40: [4] Yuj Nakasone, Hrotada Nshyama, Tetsuharu Nojr. Numercal equvalent ncluson method: a new computatonal method for analyzng stress felds n and around nclusons of varous shapes, Materals Scence and Engneerng, 2000; A285: 229~238. [5] Hu N, Wang B, Tan GW, Yao ZH, Yuan WF. Effectve elastc propertes of 2-D solds wth crcular holes: numercal smulatons, Compostes Scence and Technology, 2000; 60: [6] Rzzo FJ. An ntegral equaton approach to boundary value problems of classcal elastostatcs. Quart. J. of Appl. Math., 967; 5(). [7] Kong Fanzhong, Yao Zhenhan, Zheng Xaopng. BEM for smulaton of a 2D elastc body wth randomly dstrbuted crcular nclusons. Acta Mechanca Solda Snca, 2002; 5(): 8~88. [8] Yao, Zhenhan, Kong, Fanzhong, Wang Pengbo. Smulaton of 2D elastc solds wth randomly dstrbuted nclusons by boundary element method, n Proc. of WCCM V. Venna: [9] Yao Zhenhan, Wang Pengbo, Kong Fanzhong. Smulaton of 2D elastc solds wth randomly dstrbuted nclusons wthout or wth nterphases by BEM. In Proc. of the 3 rd Int. Conf. on Boundary Technques. Bejng: [20] Wang Hatao, Yao Zhenhan. Applcaton of fast multpole BEM for smulaton of 2D elastc body wth large number of nclusons. In Proc. of the 3 rd Int. Conf. on Boundary Technques. Bejng:
Lecture Note 3. Eshelby s Inclusion II
ME340B Elastcty of Mcroscopc Structures Stanford Unversty Wnter 004 Lecture Note 3. Eshelby s Incluson II Chrs Wenberger and We Ca c All rghts reserved January 6, 004 Contents 1 Incluson energy n an nfnte
More informationA comprehensive study: Boundary conditions for representative volume elements (RVE) of composites
Insttute of Structural Mechancs A comprehensve study: Boundary condtons for representatve volume elements (RVE) of compostes Srhar Kurukur A techncal report on homogenzaton technques A comprehensve study:
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationOFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES
ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty
More informationOn Pressure Distributions of Drum Brakes
Yuan Mao Huang Professor e-mal: ymhuang@ccmsntuedutw J S Shyr Research Assstant Department of Mechancal Engneerng, Natonal Tawan Unversty, Tape, Tawan, Republc of hna On Pressure Dstrbutons of Drum Brakes
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationNumerical Nonlinear Analysis with the Boundary Element Method
Blucher Mechancal Engneerng Proceedngs May 2014, vol. 1, num. 1 www.proceedngs.blucher.com.br/evento/10wccm Numercal Nonlnear Analyss wth the Boundary Element Method E. Pneda 1, I. Vllaseñor 1 and J. Zapata
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationAPPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS
6th ICPT, Sapporo, Japan, July 008 APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS James MAINA Prncpal Researcher, Transport and Infrastructure Engneerng, CSIR Bult Envronment
More informationGeneral displacement arch-cantilever element method for stress analysis of arch dam
Water Scence and Engneerng, 009, (): 3-4 do:0.388/j.ssn.674-370.009.0.004 http://kkb.hhu.edu.cn e-mal: wse@hhu.edu.cn General dsplacement arch-cantlever element method for stress analyss of arch dam Hao
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationANALYSIS OF CONTACT PROBLEM USING IMPROVED FAST MULTIPOLE BEM WITH VARIABLE ELEMENTS LENGTH THEORY
Journal of Marne Scence and Technology, Vol., No., pp. -7 () DOI:.69/JMST--7- NLYSIS OF CONTCT PROBLEM USING IMPROVED FST MULTIPOLE BEM WITH VRIBLE ELEMENTS LENGTH THEORY Ha-Lan Gu, Qang L, Qng-Xue Huang,
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationBuckling analysis of single-layered FG nanoplates on elastic substrate with uneven porosities and various boundary conditions
IOSR Journal of Mechancal and Cvl Engneerng (IOSR-JMCE) e-issn: 78-1684,p-ISSN: 30-334X, Volume 15, Issue 5 Ver. IV (Sep. - Oct. 018), PP 41-46 www.osrjournals.org Bucklng analyss of sngle-layered FG nanoplates
More informationTopology Optimization of Elastic Material Microstructures with Classic Models of Micromechanics
COMPUTATIONAL MECHANICS WCCM VI n conjuncton wth APCOM 4, Sept. 5-1, 24, Bejng, Chna 24 Tsnghua Unversty Press & Sprnger-Verlag Topology Optmzaton of Elastc Materal Mcrostructures wth Classc Models of
More informationNUMERICAL RESULTS QUALITY IN DEPENDENCE ON ABAQUS PLANE STRESS ELEMENTS TYPE IN BIG DISPLACEMENTS COMPRESSION TEST
Appled Computer Scence, vol. 13, no. 4, pp. 56 64 do: 10.23743/acs-2017-29 Submtted: 2017-10-30 Revsed: 2017-11-15 Accepted: 2017-12-06 Abaqus Fnte Elements, Plane Stress, Orthotropc Materal Bartosz KAWECKI
More informationRelaxation Methods for Iterative Solution to Linear Systems of Equations
Relaxaton Methods for Iteratve Soluton to Lnear Systems of Equatons Gerald Recktenwald Portland State Unversty Mechancal Engneerng Department gerry@pdx.edu Overvew Techncal topcs Basc Concepts Statonary
More informationConstitutive Modelling of Superplastic AA-5083
TECHNISCHE MECHANIK, 3, -5, (01, 1-6 submtted: September 19, 011 Consttutve Modellng of Superplastc AA-5083 G. Gulano In ths study a fast procedure for determnng the constants of superplastc 5083 Al alloy
More informationOne-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationModule 3: Element Properties Lecture 1: Natural Coordinates
Module 3: Element Propertes Lecture : Natural Coordnates Natural coordnate system s bascally a local coordnate system whch allows the specfcaton of a pont wthn the element by a set of dmensonless numbers
More informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationAn identification algorithm of model kinetic parameters of the interfacial layer growth in fiber composites
IOP Conference Seres: Materals Scence and Engneerng PAPER OPE ACCESS An dentfcaton algorthm of model knetc parameters of the nterfacal layer growth n fber compostes o cte ths artcle: V Zubov et al 216
More informationCHAPTER 9 CONCLUSIONS
78 CHAPTER 9 CONCLUSIONS uctlty and structural ntegrty are essentally requred for structures subjected to suddenly appled dynamc loads such as shock loads. Renforced Concrete (RC), the most wdely used
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More information4DVAR, according to the name, is a four-dimensional variational method.
4D-Varatonal Data Assmlaton (4D-Var) 4DVAR, accordng to the name, s a four-dmensonal varatonal method. 4D-Var s actually a drect generalzaton of 3D-Var to handle observatons that are dstrbuted n tme. The
More informationThree-dimensional eddy current analysis by the boundary element method using vector potential
Physcs Electrcty & Magnetsm felds Okayama Unversty Year 1990 Three-dmensonal eddy current analyss by the boundary element method usng vector potental H. Tsubo M. Tanaka Okayama Unversty Okayama Unversty
More informationSimulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests
Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth
More informationHigh resolution entropy stable scheme for shallow water equations
Internatonal Symposum on Computers & Informatcs (ISCI 05) Hgh resoluton entropy stable scheme for shallow water equatons Xaohan Cheng,a, Yufeng Ne,b, Department of Appled Mathematcs, Northwestern Polytechncal
More informationNumerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method
Appled Mathematcs, 6, 7, 5-4 Publshed Onlne Jul 6 n ScRes. http://www.scrp.org/journal/am http://.do.org/.436/am.6.77 umercal Solutons of a Generalzed th Order Boundar Value Problems Usng Power Seres Approxmaton
More informationGEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE
GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of cvl engneerng, IIT Bombay, Powa, Mumba 400076, Inda. Tel.022-25767328 emal: cejnm@cvl.tb.ac.n Module - 9 LECTURE - 48
More informationGrid Generation around a Cylinder by Complex Potential Functions
Research Journal of Appled Scences, Engneerng and Technolog 4(): 53-535, 0 ISSN: 040-7467 Mawell Scentfc Organzaton, 0 Submtted: December 0, 0 Accepted: Januar, 0 Publshed: June 0, 0 Grd Generaton around
More informationNew Method for Solving Poisson Equation. on Irregular Domains
Appled Mathematcal Scences Vol. 6 01 no. 8 369 380 New Method for Solvng Posson Equaton on Irregular Domans J. Izadan and N. Karamooz Department of Mathematcs Facult of Scences Mashhad BranchIslamc Azad
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationEVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES
EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge
More informationHEAT TRANSFER THROUGH ANNULAR COMPOSITE FINS
Journal of Mechancal Engneerng and Technology (JMET) Volume 4, Issue 1, Jan-June 2016, pp. 01-10, Artcle ID: JMET_04_01_001 Avalable onlne at http://www.aeme.com/jmet/ssues.asp?jtype=jmet&vtype=4&itype=1
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More information2016 Wiley. Study Session 2: Ethical and Professional Standards Application
6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton
More informationEffect of anisotropy on laminated composite plates containing circular holes
Indan Journal of ngneerng & Materals Scences Vol. 1, June 005, pp. 07-13 ffect of ansotropy on lamnated composte plates contanng crcular holes H Murat Arslan Cukurova Unversty, Cvl ngneerng Department,
More informationA Frequency-Domain Approach for Transient Dynamic Analysis using Scaled Boundary Finite Element Method (I): Approach and Validation
COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 2-23, 26, Sanya, Hanan, Chna 26 Tsnghua Unversty Press & Sprnger A Frequency-Doman Approach for Transent Dynamc Analyss usng Scaled Boundary
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationarxiv: v1 [math.co] 12 Sep 2014
arxv:1409.3707v1 [math.co] 12 Sep 2014 On the bnomal sums of Horadam sequence Nazmye Ylmaz and Necat Taskara Department of Mathematcs, Scence Faculty, Selcuk Unversty, 42075, Campus, Konya, Turkey March
More informationAdjoint Methods of Sensitivity Analysis for Lyapunov Equation. Boping Wang 1, Kun Yan 2. University of Technology, Dalian , P. R.
th World Congress on Structural and Multdscplnary Optmsaton 7 th - th, June 5, Sydney Australa Adjont Methods of Senstvty Analyss for Lyapunov Equaton Bopng Wang, Kun Yan Department of Mechancal and Aerospace
More informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
More informationBOUNDARY ELEMENT ANALYSIS OF THIN STRUCTURAL PROBLEMS IN 2D ELASTOSTATICS
Journal of Marne Scence and Technology, Vol. 19, No. 4, pp. 409-416 (011) 409 BOUNDARY ELEMENT ANALYSIS OF THIN STRUCTURAL PROBLEMS IN D ELASTOSTATICS Yao-Mng Zhang,, Yan Gu, and Jeng-Tzong Chen Key words:
More informationTHE STURM-LIOUVILLE EIGENVALUE PROBLEM - A NUMERICAL SOLUTION USING THE CONTROL VOLUME METHOD
Journal of Appled Mathematcs and Computatonal Mechancs 06, 5(), 7-36 www.amcm.pcz.pl p-iss 99-9965 DOI: 0.75/jamcm.06..4 e-iss 353-0588 THE STURM-LIOUVILLE EIGEVALUE PROBLEM - A UMERICAL SOLUTIO USIG THE
More informationFUZZY FINITE ELEMENT METHOD
FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationPower law and dimension of the maximum value for belief distribution with the max Deng entropy
Power law and dmenson of the maxmum value for belef dstrbuton wth the max Deng entropy Bngy Kang a, a College of Informaton Engneerng, Northwest A&F Unversty, Yanglng, Shaanx, 712100, Chna. Abstract Deng
More informationResearch on the Fuzzy Control for Vehicle Semi-active Suspension. Xiaoming Hu 1, a, Wanli Li 1,b
Advanced Materals Research Onlne: 0-0- ISSN: -9, Vol., pp -9 do:0.0/www.scentfc.net/amr.. 0 Trans Tech Publcatons, Swterland Research on the Fuy Control for Vehcle Sem-actve Suspenson Xaomng Hu, a, Wanl
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationREAL-TIME DETERMINATION OF INDOOR CONTAMINANT SOURCE LOCATION AND STRENGTH, PART II: WITH TWO SENSORS. Beijing , China,
REAL-TIME DETERMIATIO OF IDOOR COTAMIAT SOURCE LOCATIO AD STREGTH, PART II: WITH TWO SESORS Hao Ca,, Xantng L, Wedng Long 3 Department of Buldng Scence, School of Archtecture, Tsnghua Unversty Bejng 84,
More informationA new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems
Home Search Collectons Journals About Contact us My IOPscence A new ntegrated-rbf-based doman-embeddng scheme for solvng flud-flow problems Ths artcle has been downloaded from IOPscence. Please scroll
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More information2010 Black Engineering Building, Department of Mechanical Engineering. Iowa State University, Ames, IA, 50011
Interface Energy Couplng between -tungsten Nanoflm and Few-layered Graphene Meng Han a, Pengyu Yuan a, Jng Lu a, Shuyao S b, Xaolong Zhao b, Yanan Yue c, Xnwe Wang a,*, Xangheng Xao b,* a 2010 Black Engneerng
More informationInterconnect Modeling
Interconnect Modelng Modelng of Interconnects Interconnect R, C and computaton Interconnect models umped RC model Dstrbuted crcut models Hgher-order waveform n dstrbuted RC trees Accuracy and fdelty Prepared
More informationACTM State Calculus Competition Saturday April 30, 2011
ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward
More informationFormulas for the Determinant
page 224 224 CHAPTER 3 Determnants e t te t e 2t 38 A = e t 2te t e 2t e t te t 2e 2t 39 If 123 A = 345, 456 compute the matrx product A adj(a) What can you conclude about det(a)? For Problems 40 43, use
More informationComputer Based Porosity Design by Multi Phase Topology Optimization
Computer Based Porosty Desgn by Mult Phase Topology Optmzaton Andreas Burbles and Matthas Busse Fraunhofer-Insttut für Fertgungstechnk und Angewandte Materalforschung - IFAM Wener Str. 12, 28359 Bremen,
More informationOne Dimensional Axial Deformations
One Dmensonal al Deformatons In ths secton, a specfc smple geometr s consdered, that of a long and thn straght component loaded n such a wa that t deforms n the aal drecton onl. The -as s taken as the
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationAmplification and Relaxation of Electron Spin Polarization in Semiconductor Devices
Amplfcaton and Relaxaton of Electron Spn Polarzaton n Semconductor Devces Yury V. Pershn and Vladmr Prvman Center for Quantum Devce Technology, Clarkson Unversty, Potsdam, New York 13699-570, USA Spn Relaxaton
More informationDESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS
Munch, Germany, 26-30 th June 2016 1 DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Q.T. Guo 1*, Z.Y. L 1, T. Ohor 1 and J. Takahash 1 1 Department of Systems Innovaton, School
More informationReport on Image warping
Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.
More informationLecture 8 Modal Analysis
Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal
More informationFree vibration analysis of a hermetic capsule by pseudospectral method
Journal of Mechancal Scence and echnology 6 (4) (0) 0~05 wwwsprngerlnkcom/content/78-494x DOI 0007/s06-0-06-y Free vbraton analyss of a hermetc capsule by pseudospectral method Jnhee ee * Department of
More informationSTAT 511 FINAL EXAM NAME Spring 2001
STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationFINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION
VOL. 6, NO. 3, MARCH 0 ISSN 89-6608 006-0 Asan Research Publshng Network (ARPN). All rghts reserved. FINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION Adel A. Al-Azzaw and Al S. Shaker
More informationOperating conditions of a mine fan under conditions of variable resistance
Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationThis column is a continuation of our previous column
Comparson of Goodness of Ft Statstcs for Lnear Regresson, Part II The authors contnue ther dscusson of the correlaton coeffcent n developng a calbraton for quanttatve analyss. Jerome Workman Jr. and Howard
More informationThe Geometry of Logit and Probit
The Geometry of Logt and Probt Ths short note s meant as a supplement to Chapters and 3 of Spatal Models of Parlamentary Votng and the notaton and reference to fgures n the text below s to those two chapters.
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationSpeeding up Computation of Scalar Multiplication in Elliptic Curve Cryptosystem
H.K. Pathak et. al. / (IJCSE) Internatonal Journal on Computer Scence and Engneerng Speedng up Computaton of Scalar Multplcaton n Ellptc Curve Cryptosystem H. K. Pathak Manju Sangh S.o.S n Computer scence
More informationAppendix B. The Finite Difference Scheme
140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton
More informationTemperature. Chapter Heat Engine
Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the
More informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More information2 Finite difference basics
Numersche Methoden 1, WS 11/12 B.J.P. Kaus 2 Fnte dfference bascs Consder the one- The bascs of the fnte dfference method are best understood wth an example. dmensonal transent heat conducton equaton T
More informationTHE EFFECT OF BEAM TO COLUMN CONNECTION IN ARC PORTAL FRAME
THE EFFECT OF BEAM TO COLUMN CONNECTON N ARC PORTAL FRAME Asko Keronen Rakenteden Mekankka, Vol. 26 No 2 1993, ss. 35-5 SUMMARY A full scale rc (renforced concrete) portal frame has been bult n order to
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationMoments of Inertia. and reminds us of the analogous equation for linear momentum p= mv, which is of the form. The kinetic energy of the body is.
Moments of Inerta Suppose a body s movng on a crcular path wth constant speed Let s consder two quanttes: the body s angular momentum L about the center of the crcle, and ts knetc energy T How are these
More informationChapter 3 Differentiation and Integration
MEE07 Computer Modelng Technques n Engneerng Chapter Derentaton and Integraton Reerence: An Introducton to Numercal Computatons, nd edton, S. yakowtz and F. zdarovsky, Mawell/Macmllan, 990. Derentaton
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationEffects of Boundary Conditions on Cross-Ply Laminated Composite Beams
Internatonal Journal of Engneerng Research And Advanced Technology (IJERAT) DOI: http://dx.do.org/0.734/ijerat.344 E-ISSN : 454-635 Vol.3 (0) Oct -07 Effects of Boundary Condtons on Cross-Ply Lamnated
More informationImplement of the MPS-FEM Coupled Method for the FSI Simulation of the 3-D Dam-break Problem
Implement of the MPS-FEM Coupled Method for the FSI Smulaton of the 3-D Dam-break Problem Youln Zhang State Key Laboratory of Ocean Engneerng, School of Naval Archtecture, Ocean and Cvl Engneerng, Shangha
More informationP R. Lecture 4. Theory and Applications of Pattern Recognition. Dept. of Electrical and Computer Engineering /
Theory and Applcatons of Pattern Recognton 003, Rob Polkar, Rowan Unversty, Glassboro, NJ Lecture 4 Bayes Classfcaton Rule Dept. of Electrcal and Computer Engneerng 0909.40.0 / 0909.504.04 Theory & Applcatons
More information