LEADER 05780nam 22007334a 450 001 9910455577203321 005 20200520144314.0 010 $a1-282-75981-7 010 $a9786612759819 010 $a1-84816-308-8 035 $a(CKB)2490000000001680 035 $a(EBL)1679350 035 $a(OCoLC)729020328 035 $a(SSID)ssj0000423613 035 $a(PQKBManifestationID)11929689 035 $a(PQKBTitleCode)TC0000423613 035 $a(PQKBWorkID)10439684 035 $a(PQKB)11530469 035 $a(MiAaPQ)EBC1679350 035 $a(WSP)00002050 035 $a(Au-PeEL)EBL1679350 035 $a(CaPaEBR)ebr10422189 035 $a(CaONFJC)MIL275981 035 $a(EXLCZ)992490000000001680 100 $a20100520d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aMultiscale modeling in solid mechanics$b[electronic resource] $ecomputational approaches /$feditors, Ugo Galvanetto, M.H. Ferri Aliabadi 210 $aLondon $cImperial College ;$aLondon ;$aNew York $cDistributed by World Scientific$d2010 215 $a1 online resource (352 p.) 225 1 $aComputational and experimental methods in structures ;$vvol. 3 300 $aDescription based upon print version of record. 311 $a1-84816-307-X 320 $aIncludes bibliographical references and index. 327 $aCONTENTS; Preface; Contributors; Computational Homogenisation for Non-Linear Heterogeneous Solids V. G. Kouznetsova, M. G. D. Geers and W. A. M. Brekelmans; 1. Introduction; 2. Basic Hypotheses; 3. Definition of the Problem on the Microlevel; 4. Coupling of the Macroscopic and Microscopic Levels; 4.1. Deformation; 4.2. Stress; 4.3. Internal work; 5. FE Implementation; 5.1. RVE boundary value problem; 5.1.1. Fully prescribed boundary displacements; 5.1.2. Periodic boundary conditions; 5.2. Calculation of the macroscopic stress; 5.2.1. Fully prescribed boundary displacements 327 $a5.2.2. Periodic boundary conditions5.3. Macroscopic tangent stiffness; 5.3.1. Condensation of the microscopic stiffness: Fully prescribed boundary displacements; 5.3.2. Condensation of the microscopic stiffness: Periodic boundary conditions; 5.3.3. Macroscopic tangent; 6. Nested Solution Scheme; 7. Computational Example; 8. Concept of an RVE within Computational Homogenisation; 9. Extensions of the Classical Computational Homogenisation Scheme; 9.1. Homogenisation towards second gradient continuum; 9.2. Computational homogenisation for beams and shells 327 $a9.3. Computational homogenisation for heat conduction problemsAcknowledgements; References; Two-Scale Asymptotic Homogenisation-Based Finite Element Analysis of Composite Materials Qi-Zhi Xiao and Bhushan Lal Karihaloo; 1. Introduction; 2. Mathematical Formulation of First- and Higher-Order Two-Scale Asymptotic Homogenisation; 2.1. Two-scale expansion; 2.2. O(?.2) equilibrium: Solution structure of ui(0); 2.3. O(?.1) equilibrium: First-order homogenisation and solution structure of u(1)m; 2.4. O(?0) equilibrium: Second-order homogenisation; 2.4.1. Solution structure of u(2) 327 $a2.4.2. Solution of u(0) m2.4.3. Solution of ?mno k (y); 2.4.4. Constraints from higher-order solutions; 2.5. O(?1) equilibrium: Third-order homogenisation; 2.5.1. Solution of u(3) k; 2.5.2. Constraints from higher-order terms; 3. Variational Formulation of Problem (29); 4. Finite Element Methods; 4.1. Displacement compatible elements from the potential principle; 4.2. Element-free Galerkin method from the potential principle; 4.2.1. MLS interpolant; 4.2.2. Imposition of the essential boundary conditions; 4.2.3. Discontinuity in the displacement field 327 $a4.2.4. Interfaces with discontinuous first-order derivatives4.3. Displacement incompatible element from the potential principle; 4.3.1. 2D 4-node incompatible element; 4.3.2. 3D 8-node incompatible element; 4.4. Hybrid stress elements from the Hellinger-Reissner principle; 4.4.1. Plane 4-node Pian and Sumihara (PS) 5? element; 4.4.2. 3D 8-node 18? hybrid stress element; 4.5. Enhanced-strain element based on the Hu-Washizu principle; 4.5.1. Plane 4-node enhanced-strain element; 4.5.2. 3D 8-node enhanced-strain element; 4.6. Comments on the various methods 327 $a5. Enforcing the Periodicity Boundary Condition and Constraints from Higher-Order Equilibrium in the Analysis of the RUC 330 $a This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approa 410 0$aComputational and experimental methods in structures ;$vv. 3. 606 $aSolids$xMathematical models 606 $aSolid state physics 606 $aMechanics 606 $aMultiscale modeling 608 $aElectronic books. 615 0$aSolids$xMathematical models. 615 0$aSolid state physics. 615 0$aMechanics. 615 0$aMultiscale modeling. 676 $a531.015118 701 $aGalvanetto$b Ugo$0724369 701 $aAliabadi$b M. H$0884692 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910455577203321 996 $aMultiscale modeling in solid mechanics$92206440 997 $aUNINA LEADER 01256nam0 22002771i 450 001 UON00019142 005 20231205102009.903 100 $a20020107g13501971 |0itac50 ba 101 $aper 102 $aIR 105 $a|||| 1|||| 200 1 $aJasnha va a'yad-e melli va mazhabi dar Iran qabl az Eslam$fHabibollah Bozorgvar 210 $aEsfahan$c[s.n.]$d1350 H. 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