General displacement arch-cantilever element method for stress analysis of arch dam
|
|
- William Parsons
- 5 years ago
- Views:
Transcription
1 Water Scence and Engneerng, 009, (): 3-4 do:0.388/j.ssn e-mal: General dsplacement arch-cantlever element method for stress analyss of arch dam Hao REN*, ong-chun LI, Zh-we NIU, Lan-hao ZHAO College of Water Conservancy and Hydropower Engneerng, Hoha Unversty, Nanjng 0098, Chna Abstract: Based on the general dsplacement method and the basc hypothess of the tral load method, a new advanced tral load method, the general dsplacement arch-cantlever element method, was proposed to derve the transformaton relaton of dsplacements and loads between the surface nodes and mddle plane nodes. hs method consders the nodes on upstream and downstream surfaces of the arch dam to be ext nodes (master nodes), and the mddle plane nodes to be slave nodes. Accordng to the derved dsplacement and load transformaton matrces, the equlbrum equaton treatng the dsplacement of mddle plane nodes as a basc unknown varable s transformed nto one that treats the dsplacement of upstream and downstream nodes as a basc unknown varable. Because the surface nodes have only three degrees of freedom (DOF), ths method can be drectly coupled wth the fnte element method (FEM), whch s used for foundaton smulaton to analyze the stress of the arch dam wth consderaton of dam-foundaton nteracton. Moreover, usng the FEM, the nodal load of the arch dam can be easly obtaned. Case studes of a typcal cylndrcal arch dam and the Wudongde arch dam demonstrate the robustness and feasblty of the proposed method. Key words: arch dam; arch-cantlever element method; general dsplacement method; fnte element method (FEM); coupled analyss; stress analyss; Wudongde arch dam Introducton he tral load and fnte element methods are the man exstng stress analyss methods for arch dams. he assgned load s an unknown varable n the tradtonal tral load method. he paucty of zero-elements n the coeffcent matrx of equatons necesstates a hgh amount of computaton. In addton, a homogenous, half-nfnte, elastc foundaton s always assumed, whereas many arch dams are bult on complex geology. For these reasons, the tradtonal tral load method s not adequate for dynamc analyss of arch dams. herefore, many scholars have mproved the tradtonal tral load method and developed new methods, such as the nternal force equlbrum arch-cantlever method (Chen 988), the strp mode synthess method of arch dam analyss (Ln et al. 985), the load dstrbuton dsplacement method (Ln and Yang 987), the mproved load dstrbuton dsplacement method (Zhu et al. 988, 99), and the arch-cantlever element method (Chen et al. 003). hs work was supported by the Natonal Natural Scence Foundaton of Chna (Grant No ). *Correspondng author (e-mal: renhaohhu@63.com) Receved Jun. 6, 008; accepted Sep., 008
2 In ths paper, the basc hypothess of the tral load method s used along wth the general dsplacement method (Zhong 98; Zhong and L 98; Zhong and Zhu 985) to develop a new general dsplacement arch-cantlever element method, and further to derve the transformaton relaton of dsplacements and loads between the surface nodes and mddle plane nodes. Due to the fact that there are only three DOF of surface nodes, ths method can be drectly coupled wth the FEM and facltate the stress analyss of the arch dam wth consderaton of dam-foundaton nteracton. Formulaton of mproved general dsplacement arch-cantlever element method. Fundamental formulaton of arch-cantlever element method Based on the tral load method, some researchers (Chen et al. 003; Xu et al. 005) have developed an arch-cantlever element method. he arch dam s dvded nto arch-cantlever elements. Fg. shows an arch-cantlever element. Nodes through 8 are the surface nodes. Nodes, j, m and n are the mddle plane nodes. In ths system, the arch drecton s expressed as va, the cantlever drecton s expressed as v b, and the normal drecton of the mddle plane of the element s defned as v r. he equlbrum equaton of an arch-cantlever Fg. Arch-cantlever element element s F Fa Fb K () where and F are the dsplacement and load of the mddle plane nodes, respectvely; Fa and Fb are the nodal loads of the arch and cantlever, respectvely; and K s the element stffness matrx, whch s as follows: K = d d () a a a a a b b b b b where a and b are the transformaton matrces of arch and cantlever coordnate systems, respectvely; Ha and Hb are the nterpolaton functons along the arch and cantlever drectons, respectvely; Ka and K b are the stffness matrces of arch and cantlever slces, respectvely; and d and d are the mcro-sectons n arch and cantlever planes, respectvely. An equaton relatng dsplacements and loads at each node n the arch-cantlever system can be obtaned by assemblage of the around nodes. In ths way, the method resembles the fnte element method. It determnes the dsplacement by transformng loads actng on the dam (e.g., water pressure and temperature) nto nodal forces. he elastc beam and arch theores (Panda and Natarajan 98) are used to calculate stresses. Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No.,
3 . Dsplacement transformaton equaton between surface nodes and mddle plane nodes We assume that the dsplacement vector of the mddle plane node s u, v, w,, x y, and the dsplacement vectors of upstream surface node and downstream surface node are, respectvely, u, v, w and u, v, w, n the local coordnate system x' yz ' ' (Fg. ). x' s the drecton from node to node n, y ' s the outer normal drecton of the cross secton of the arch-cantlever element, and z ' s the outer normal drecton of the mddle plane at node (Fg. 3). Fg. Dsplacements of surface nodes and mddle plane node Fg. 3 Local coordnate system Usng the general dsplacement method, the knematcs formulas are obtaned: u u z' y, v v z' x, w w u u z', v v z', w w (4) y x where z' and z' are the z' coordnates of node and node. From Eqs. (3) and (4), t can be shown that z' u z' u z' v z' v u, v z' z' z' z' w w w, w w (5) v v u u x, y z' z' z' z' Based on Eqs. (3) through (5), the dsplacement transformaton matrx can be expressed as follows: z' z' z' z' z' z' z' z' z' z' z' z' d (6) z' z' z' z' z' z' z' z' he dsplacement transformaton relaton between the mddle plane node and the (3) 34 Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No., 3-4
4 surface nodes and can be expressed as d, and w w (7) For the upstream surface node and downstream surface node, there are two other t t condtons: z ' and z ', n whch t s the dam thckness n the normal drecton of the mddle plane. herefore, can be smplfed as d d (8) t t t t he relatonshps and condtons descrbed above are appled to the other nodes as well, so the dsplacement transformaton matrx of an arch-cantlever element s d d 0 j 0 d (9) 0 0 d m dn and the sze of the matrx d s 0 4. he dsplacement transformaton relaton between master nodes and slave nodes of an arch-cantlever element s expressed as e e (0) e where s the dsplacement column matrx of mddle plane nodes, and e s the dsplacement column matrx of upstream and downstream surface nodes. here are addtonal constrant condtons: w w, w3 w4, w5 w 6, and w 7 w 8. hese condtons are appled based on the fber hypothess of arch-cantlever deformaton..3 Load transformaton equaton between surface nodes and mddle plane nodes It s assumed that the concentrated force at node s F N, Qy, Qz, Mx, M y, and the equvalent loads at upstream and downstream surface ext nodes are, respectvely, F f x, fy, f and. he load transformaton equaton can be z F fx, fy, fz derved wth the statc equvalent prncple and rgd equlbrum equatons as follows: F F f F () d Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No.,
5 z ' z ' z' z' z ' z ' z' z' z' z' f () z ' z' z' z' z' z ' z' z' z' z' t Because of the condtons z ' and z ', can be smplfed as t t f (3) t t Other nodes can be transformed the same way. hen, the load transformaton matrx of an arch-cantlever element wth a sze of 4 0 s obtaned: f fj 0 0 f (4) 0 0 f m f n t he load transformaton relaton between master nodes and slave nodes of an arch-cantlever element s expressed as f f e e F F (5) e where F s the load column matrx of mddle plane nodes, and e F s the load column matrx of surface nodes. Obvously, and are a par of transposed matrces. hey guarantee the symmetry d f and effcency of the augmented stffness matrx of the arch-cantlever element. 36 Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No., 3-4
6 .4 Stffness matrx and balance equaton of mproved arch-cantlever element method Insertng Eqs. (0) and (5) nto Eq. (), the followng equaton s obtaned: e e e K F herefore, the stffness matrx of surface nodes s 3 w4, w5 w6, and w7 w8 K e e f K d Eq. (6) s the balance equaton of an arch-cantlever element that treats the dsplacement of upstream and downstream nodes as a basc unknown varable. Here the element stffness matrx e K s not full-rank; therefore, the addtonal constrant condtons of w w, w can elmnate the ll-condtoned problem of ths matrx..5 Coupled analyss In the conventonal analyss, the nodes n the arch-cantlever system and the foundaton smulated wth the FEM have dfferent DOF. Generally, the node n the arch-cantlever system has fve DOF, but the node n the foundaton has only three. he dfferent DOF makes the couplng of the tral load method wth the FEM relatvely complex and dffcult to realze (Zhao and Ln 990; Ln and Su 00). In the mproved method, both the surface node and the node of the foundaton have three DOF, so they can be coupled drectly. Moreover, at the nterface between the dam and the foundaton, the locally ncompatble mesh s permtted, and the dsplacement coordnaton method can be used to deal wth the locally ncompatble meshes to coordnate the dsplacement feld and stress feld (L et al. 003)..6 Calculaton method of nodal load In the tradtonal tral load method, the formulas for calculatng the nodal loads of the dam mddle plane are complex and the calculaton accuracy s low. Usng Eq. (5), the calculaton of the nodal loads of the dam mddle plane can be converted to the calculaton of those of upstream and downstream surfaces. herefore, n the actual calculaton, t s unnecessary to calculate the nodal loads of the dam mddle plane, and the arch-cantlever element can be consdered an eght-node soparametrc element. he fnte element method s used to obtan the surface nodal loads of the arch-cantlever element, n whch the water load s a surface force, the dead weght of the dam s a body force, and the temperature load can be calculated wth correspondng methods. In fact, the water load acts on the dam surface, so the numercal results are relatvely more accurate..7 Calculaton program In ths study, the calculaton program FEMHmadrd, developed by Pastor et al. (997), was used for 3D fnte element smulaton analyss of the arch dam. he program of the (6) (7) Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No.,
7 general dsplacement arch-cantlever element method, presented n ths paper, was compled by Fortran 95 and added to the program FEMHmadrd as a module. 3 Case study 3. Example As a test of ths method, a typcal smple cylndrcal arch dam of consstent thckness, one that has been studed by many researchers (Znkewcz and Cheung 964), was nvestgated. he shape s descrbed n Fg. 4. he elastc modulus and Posson s rato of the dam materal are 0 GPa and 0.5, respectvely. he densty of the cylndrcal arch dam s 400 kg/m 3. he elastc modulus of the dam foundaton s 0 GPa. For the convenence of comparng the calculated result wth others, only the water-pressure and dead weght of the dam and foundaton were consdered. Fg. 4 Arch and cantlever scheme he dam was dscretzed nto 0 archcantlever elements (0 arch layers and 9 cantlever columns), whle the foundaton of the dam was dscretzed nto 848 soparametrc elements. hen, these two types of elements were combned wth the software GID. he confguraton of the calculaton model s shown n Fg. 5. he computaton results are gven n Fgs. 6 through 8. In Fgs. 7 and 8, the tensle stress s postve and the compressve stress s negatve. Fg. 5 Calculaton model Fg. 6 Radal dsplacement of central cantlever As shown n Fgs. 6 through 8, the radal dsplacement of the central cantlever and hoop and vertcal equvalent stresses of the central cantlever are compared wth the results obtaned by the U.S. Bureau of Reclamaton wth the tradtonal tral load method (Znkewcz and Cheung 964). he radal dsplacement of the central cantlever calculated wth the present method s 38 Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No., 3-4
8 lower than that calculated wth the tradtonal tral load. he reason s that the stffness of the foundaton smulated by the FEM s greater than that of the tradton method, and the stffness of the dam body s ncreased by fully consderng the dmensonal effect of the dam. he stresses calculated n the paper agree well wth those of the tradtonal method. Overall, the varaton patterns of the dsplacement and stresses calculated wth the two methods are bascally dentcal. Fg. 7 Hoop equvalent stress of central cantlever Fg. 8 Vertcal equvalent stress of central cantlever 3. Example he Wudongde arch dam s a 65-m-hgh double-curvature arch dam. he crest elevaton s 988 m. It has a crest length of m, and the thckness of the center cantlever vares from 48 m at the base to 0 m at the crest. he man shape parameters and schematc dagrams are shown n able and Fgs. 9 and 0. able Shape parameters of Wudongde arch dam Elevaton (m) Z 0 (m) c (m) l (m) r (m) R cl (m) R cr (m) l ( ) r ( ) Note: R cl and R cr are rad of left and rght arch abutments. he normal upstream hgh water elevaton of s 975 m and the correspondng downstream water elevaton s 80 m. he sedmentaton elevaton n front of the dam s 863 m, the buoyant unt densty s 750 kg/m 3, and the nternal frcton angle s.5. he perennal mean ar temperature s 0.9. he mean ar temperature s.3 n January and 6.9 n July, respectvely. he annual mean water temperature s 0.9 and the Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No.,
9 depth of the temperature-changng water layer s 80.0 m. he jont closure temperature for the arch dam ranges from to 6 (able ). he materal propertes of the dam are shown n able 3. Fg. 9 Plane of arch rng Fg. 0 Secton of crown cantlever able Jont closure temperature for arch dam Elevaton (m) emperature () Elevaton (m) emperature () Item Modulus of elastcty (GPa) able 3 Materal propertes of dam Posson s rato Densty (kg/m 3 ) hermal dffusvty (m /month) hermal expanson coeffcent (0-5 /) Foundaton Dam concrete he dam was dscretzed nto 6 arch-cantlever elements (0 arch layers and 3 cantlever columns), whle the foundaton of the dam was dscretzed nto soparametrc elements. hese two type elements were combned wth the software GID. he calculaton model of the Wudongde arch dam s shown n Fg.. he computaton results are gven n Fgs. through 5. Comparson of the results Fg. FEM model of Wudongde arch dam calculated usng the present method wth those calculated usng the FEM nternal force method (L et al. 006) shows that the varaton patterns wthn those results are bascally dentcal, whch proves the correctness and applcablty of ths method. 40 Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No., 3-4
10 Fg. Hoop stress upstream a (MPa) Fg. 3 Frst prncpal stress upstream (MPa) Fg. 4 Vertcal stress downstream b (MPa) Fg. 5 hrd prncpal stress downstream 3 (MPa) 4 Conclusons () he general dsplacement proposed n ths paper fully consders the dmensonal effect of the dam, and t can be drectly coupled wth the FEM, whch s used for foundaton smulaton. hs couplng method takes nto consderaton the dam-foundaton nteracton and overcomes the drawbacks of the tradtonal method. Case studes n ths paper demonstrate that ths method s practcal. In addton, because the stresses of the arch dam are calculated based on the nternal forces whch are assumed to be lnearly dstrbuted along the radal drecton, the results correspond to current desgn specfcatons for arch dams. () hrough the ntegraton of arch slces and cantlever slces, the equvalent arch-cantlever element s obtaned. Usng the nodal loads of the upstream and downstream surfaces to replace those of the mddle plane and the FEM to obtan the surface nodal loads, the complex load condton can be easly consdered. (3) hs method potentally provdes a new way to conduct further studes on the sesmc analyss of arch dams wth consderaton of dam-water-foundaton nteracton. References Chen, S. H., Xu, M. Y., Shahrour, I., and Egger, P Analyss of arch dams usng coupled tral load and block element methods. Journal of Geotechncal and Geoenvronmental Engneerng, 9(), Chen, Z. Z. and Lu, L Reactve force parameters method and software of arch dam analyss. Water power, (8), -8. (n Chnese) Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No., 3-4 4
11 L,. C., L, M., Wen, Z. W., and Shen, H. B Applcaton of locally ncompatble meshes to stress analyss of hgh arch dams. Journal of Hoha Unversty (Natural Scences), 3(), (n Chnese) L,. C., Zhao, L. H., and Nu, Z. G FEM statc and dynamc research of Wudongde Arch Dam n Jnsha Rver. Nanjng: Hoha Unversty. (n Chnese) Ln, G., Sun, K. M., and Lou, M. L A strp mode synthess technque for dynamc and statc analyss of arch dam and shell structures. Acta Mechanca Solda Snca, (4), (n Chnese) Ln, S. Z., and Yang, Z. H Load dstrbuton-stffness method for stress analyss of arch dams. Journal of Hydraulc Engneerng, 8(), 7-5. (n Chnese) Ln, S. Z., and Su, H. D. 00. Stress analyss for arch dams on complcated rock foundaton usng tral load method. Journal of Yangtze Rver Scentfc Research Insttute, 9(5), (n Chnese) Panda, S. and Natarajan, R. 98. Analyss of lamnated composte shell structures by fnte element method. Computers & Structures, 4(3-4), [do: 0.06/ (8) ] Pastor, M., L,. C., and Fernández Merodo, J. A Stablzed fnte elements for harmonc sol dynamcs problems near the undraned-ncompressble lmt. Sol Dynamcs and Earthquake Engneerng, 6(3), 6-7. [do:0.06/s067-76(97) ] Xu, M. Y., Xue, L. L., Chen, S. H., and Wang, W. M Coupled analyss of Dahuashu Arch Dam wth tral load method and block element method. Chnese Journal of Rock Mechancs and Engneerng, 4(s), (n Chnese) Zhao, G. H., and Ln, S. Z Couplng of tral load method wth fnte element method. Journal of Yangtze Rver Scentfc Research Insttute, 7(4), 8-7. (n Chnese) Zhong, W. X. 98. On the applcaton of generalzed dsplacement n fnte element method and ts mplementaton. Chnese Journal of Mechancal Engneerng, 7(3), (n Chnese) Zhong, W. X., and L, X. K. 98. On the generalzed dsplacement method n the fnte element analyss of ncompressble materals. Journal of Dalan Insttute of echnology, 0(4), -0. (n Chnese) Zhong, W. X., and Zhu, J. P Generalzed dsplacement method n fnte element analyss of thn-walled beams. Journal of Dalan Insttute of echnology, 4(4), (n Chnese) Zhu, B. F., Rao, B., and Ja, J. S Stress analyss of noncrcular arch dam wth varable thckness. Journal of Hydraulc Engneerng, 9(), 7-8. (n Chnese) Zhu, B. F., Rao, B., and Ja, J. S. 99. Stress analyss of noncrcular arch dam. Dam Engneerng, (3), Znkewcz, O. C., and Cheung, Y. K Fnte element method of analyss for arch dam shells and comparson wth fnte dfference procedure. Proceedngs of Symposum on heory of Arch Dams. London: Pergamon Press. 4 Hao REN et al. Water Scence and Engneerng, Mar. 009, Vol., No., 3-4
COMPOSITE 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 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 informationAPPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam
APPENDIX F A DISPACEMENT-BASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a Non-Prsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development
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 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 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 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 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 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 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 information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
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 informationStudy on Non-Linear Dynamic Characteristic of Vehicle. Suspension Rubber Component
Study on Non-Lnear Dynamc Characterstc of Vehcle Suspenson Rubber Component Zhan Wenzhang Ln Y Sh GuobaoJln Unversty of TechnologyChangchun, Chna Wang Lgong (MDI, Chna [Abstract] The dynamc characterstc
More informationProfessor Terje Haukaas University of British Columbia, Vancouver The Q4 Element
Professor Terje Haukaas Unversty of Brtsh Columba, ancouver www.nrsk.ubc.ca The Q Element Ths document consders fnte elements that carry load only n ther plane. These elements are sometmes referred to
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 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 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 informationIndeterminate pin-jointed frames (trusses)
Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
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 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 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 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 informationAssessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion
Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,
More informationSimulation of 2D Elastic Bodies with Randomly Distributed Circular Inclusions Using the BEM
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
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 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 informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationPlate Theories for Classical and Laminated plates Weak Formulation and Element Calculations
Plate heores for Classcal and Lamnated plates Weak Formulaton and Element Calculatons PM Mohte Department of Aerospace Engneerng Indan Insttute of echnolog Kanpur EQIP School on Computatonal Methods n
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 informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationVisco-Rubber Elastic Model for Pressure Sensitive Adhesive
Vsco-Rubber Elastc Model for Pressure Senstve Adhesve Kazuhsa Maeda, Shgenobu Okazawa, Koj Nshgch and Takash Iwamoto Abstract A materal model to descrbe large deformaton of pressure senstve adhesve (PSA
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 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 informationTransactions of the VŠB Technical University of Ostrava, Mechanical Series. article No. 1907
Transactons of the VŠB Techncal Unversty of Ostrava, Mechancal Seres No., 0, vol. LVIII artcle No. 907 Marek NIKODÝM *, Karel FYDÝŠEK ** FINITE DIFFEENCE METHOD USED FO THE BEAMS ON ELASTIC FOUNDATION
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 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 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 informationInternational Power, Electronics and Materials Engineering Conference (IPEMEC 2015)
Internatonal Power, Electroncs and Materals Engneerng Conference (IPEMEC 2015) Dynamc Model of Wnd Speed Dstrbuton n Wnd Farm Consderng the Impact of Wnd Drecton and Interference Effects Zhe Dong 1, a,
More informationAnalysis of Dynamic Cross Response between Spindles in a Dual Spindle Type Multi-Functional Turning Machine
Journal of Power and Energy Engneerng, 2013, 1, 20-24 http://dx.do.org/10.4236/jpee.2013.17004 Publshed Onlne December 2013 (http://www.scrp.org/journal/jpee) Analyss of Dynamc Cross Response between Spndles
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 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 informationChapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary
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. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
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 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 informationLecture 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 informationStudy on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI
2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: 978-1-60595-416-5 Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN,
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 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 informationApplication to Plane (rigid) frame structure
Advanced Computatonal echancs 18 Chapter 4 Applcaton to Plane rgd frame structure 1. Dscusson on degrees of freedom In case of truss structures, t was enough that the element force equaton provdes onl
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
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 informationMODELLING OF ELASTO-STATICS OF POWER LINES BY NEW COMPOSITE BEAM FINITE ELEMENT Bratislava
ODING OF ASTO-STATICS OF POW INS BY NW COPOSIT BA FINIT NT urín Justín 1 rabovský Jura 1 Gogola oman 1 utš Vladmír 1 Paulech Jura 1 1 Insttute of Automotve echatroncs FI STU n Bratslava Ilkovčova 3 812
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More informationBack Analysis of Self-Compacting Concrete Rheological Parameters Based on H-B Model
Internatonal Conference on Archtectural, Cvl and Hydraulcs Engneerng (ICACHE 2015) Back Analyss of Self-Compactng Concrete Rheologcal Parameters Based on H-B Model Shua Zeng1, a, Janjun Sh1,b, Wenqang
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 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 informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationNONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM
Advanced Steel Constructon Vol. 5, No., pp. 59-7 (9) 59 NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM M. Abdel-Jaber, A.A. Al-Qasa,* and M.S. Abdel-Jaber Department of Cvl Engneerng, Faculty
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 informationCOEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN
Int. J. Chem. Sc.: (4), 04, 645654 ISSN 097768X www.sadgurupublcatons.com COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN R. GOVINDARASU a, R. PARTHIBAN a and P. K. BHABA b* a Department
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 informationSolution Thermodynamics
Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs
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 informationModal Strain Energy Decomposition Method for Damage Detection of an Offshore Structure Using Modal Testing Information
Thrd Chnese-German Jont Symposum on Coastal and Ocean Engneerng Natonal Cheng Kung Unversty, Tanan November 8-16, 2006 Modal Stran Energy Decomposton Method for Damage Detecton of an Offshore Structure
More informationNON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE
October 1-17, 008, Bejng, Chna NON LINEAR ANALYSIS OF SRUCURES ACCORDING O NEW EUROPEAN DESIGN CODE D. Mestrovc 1, D. Czmar and M. Pende 3 1 Professor, Dept. of Structural Engneerng, Faculty of Cvl Engneerng,
More informationGeometrically exact multi-layer beams with a rigid interconnection
Geometrcally exact mult-layer beams wth a rgd nterconnecton Leo Škec, Gordan Jelenć To cte ths verson: Leo Škec, Gordan Jelenć. Geometrcally exact mult-layer beams wth a rgd nterconnecton. 2nd ECCOMAS
More informationLifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model
ECCMR, Prague, Czech Republc; September 3 th, 2015 Lfetme predcton of EP and NBR rubber seal by thermos-vscoelastc model Kotaro KOBAYASHI, Takahro ISOZAKI, Akhro MATSUDA Unversty of Tsukuba, Japan Yoshnobu
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 informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationTHREE-DIMENSION DYNAMIC SOIL-STRUCTURE INTERACTION ANALYSIS USING THE SUBSTRUCTURE METHOD IN THE TIME DOMAIN
The 4 th October 2-7 2008 Bejng Chna THREE-DIENSION DYNAIC SOIL-STRUCTURE INTERACTION ANALYSIS USING THE SUBSTRUCTURE ETHOD IN THE TIE DOAIN X..Yang Y.Chen and B.P.Yang 2 Assocate Professor aculty of Constructon
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 informationBAR & TRUSS FINITE ELEMENT. Direct Stiffness Method
BAR & TRUSS FINITE ELEMENT Drect Stness Method FINITE ELEMENT ANALYSIS AND APPLICATIONS INTRODUCTION TO FINITE ELEMENT METHOD What s the nte element method (FEM)? A technqe or obtanng approxmate soltons
More informationCalculating the Quasi-static Pressures of Confined Explosions Considering Chemical Reactions under the Constant Entropy Assumption
Appled Mechancs and Materals Onlne: 202-04-20 ISS: 662-7482, ol. 64, pp 396-400 do:0.4028/www.scentfc.net/amm.64.396 202 Trans Tech Publcatons, Swtzerland Calculatng the Quas-statc Pressures of Confned
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 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 informationFrame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments.
CE7 Structural Analyss II PAAR FRAE EEET y 5 x E, A, I, Each node can translate and rotate n plane. The fnal dsplaced shape has ndependent generalzed dsplacements (.e. translatons and rotatons) noled.
More informationOrientation Model of Elite Education and Mass Education
Proceedngs of the 8th Internatonal Conference on Innovaton & Management 723 Orentaton Model of Elte Educaton and Mass Educaton Ye Peng Huanggang Normal Unversty, Huanggang, P.R.Chna, 438 (E-mal: yepeng@hgnc.edu.cn)
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 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 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 informationANALYSIS OF PILE EQUIVALENT ANCHORAGE LENGTH FOR ELEVATED PILE CAPS UNDER LATERAL LOAD
The th World Conference on Earthquake Engneerng October -7, 008, Bejng, Chna ANALYSIS OF PILE EQUIVALENT ANCHORAGE LENGTH FOR ELEVATED PILE CAPS UNDER LATERAL LOAD M ZHOU Wancheng YUAN and Yue ZHANG Ph.D
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 informationThe Analysis of Convection Experiment
Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 5) The Analyss of Convecton Experment Zlong Zhang School of North Chna Electrc Power Unversty, Baodng 7, Chna 469567@qq.com Keywords:
More informationMECHANICS OF MATERIALS
Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng
More informationPhysics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.
Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays
More informationANALYSIS OF TIMOSHENKO BEAM RESTING ON NONLINEAR COMPRESSIONAL AND FRICTIONAL WINKLER FOUNDATION
VOL. 6, NO., NOVEMBER ISSN 89-668 6- Asan Research Publshng Network (ARPN). All rghts reserved. ANALYSIS OF TIMOSHENKO BEAM RESTING ON NONLINEAR COMPRESSIONAL AND FRICTIONAL WINKLER FOUNDATION Adel A.
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 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 informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
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 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 informationSTUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES
STUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES Abdelkader Benchou, PhD Canddate Nasreddne Benmoussa, PhD Kherreddne Ghaffour, PhD Unversty of Tlemcen/Unt of Materals
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 informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationArmy Ants Tunneling for Classical Simulations
Electronc Supplementary Materal (ESI) for Chemcal Scence. Ths journal s The Royal Socety of Chemstry 2014 electronc supplementary nformaton (ESI) for Chemcal Scence Army Ants Tunnelng for Classcal Smulatons
More informationA Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations
99 A Tmoshenko Pezoelectrc Beam Fnte Element wth Consstent Performance Irrespectve of Geometrc and Materal Confguratons Abstract The conventonal Tmoshenko pezoelectrc beam fnte elements based on Frst-order
More information