LEADER 05229nam 22005534a 450 001 9910810539203321 005 20200520144314.0 010 $a9781848163072 010 $a184816307X 035 $a(MiAaPQ)EBC1679350 035 $a(CKB)2490000000001680 035 $a(EXLCZ)992490000000001680 100 $a20100520d2010 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cn$2rdamedia 183 $anc$2rdacarrier 200 00$aMultiscale modeling in solid mechanics $ecomputational approaches /$feditors, Ugo Galvanetto, M.H. Ferri Aliabadi 205 $a1st ed. 210 $aLondon $cImperial College ;$aLondon ;$aNew York $cDistributed by World Scientific$d2010 215 $axiii, 334 pages;$d24 cm 225 1 $aComputational and experimental methods in structures ;$vvol. 3 320 $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 $aThis unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approa. 410 0$aComputational and experimental methods in structures ;$vv. 3. 606 $aSolids$xMathematical models 606 $aSolid state physics 606 $aMechanics 606 $aMultiscale modeling 615 0$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$01102751 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910810539203321 996 $aMultiscale modeling in solid mechanics$94100064 997 $aUNINA