Homogenization of reticulated structures
Author(s)
Bibliographic Information
Homogenization of reticulated structures
（Applied mathematical sciences, v. 136）
Springer, c1999
Available at 45 libraries
Note
Includes bibliographical references and index
Description and Table of Contents
Description
Materials science is an area of growing research as composite materials become widely used in such areas as civil engineering, electrotechnics, and the aerospace industry. This mathematically rigorous treatment of lattice-type structures will appeal to both applied mathematicians, as well as engineers looking for a solid mathematical foundation of the methodology.
Table of Contents
1 Homogenization in Perforated Media.- 1. The General Method of Homogenization.- 1.1 The One-Dimensional Periodic Case.- 1.2 A Model Example: the Thermal Problem.- 1.3 Perforated Domains.- 2. The Homogeneous Neumann Problem.- 2.1 Perforated Domains and Variational Formulation.- 2.2 Multiple-Scale Method.- 2.3 Extension Operators.- 2.4 Convergence Theorems.- 2.5 Domains with Nonisolated Holes.- 2.6 Error Estimates.- 3. Other Boundary Value Problems.- 3.1 The Dirichlet Problem.- 3.2 Fourier Conditions.- 3.3 Eigenvalue Problem.- 2 Lattice-Type Structures.- 1. The Two-Dimensional Case.- 1.1 Statement of the Problem and the Main Theorem.- 1.2 Proof of the Main Theorem: Technique of Dilatations.- 1.3 Superposition Method.- 1.4 Error Estimates.- 2. The Three-Dimensional Case.- 2.1 Honeycomb Structures.- 2.2 Reinforced Structures.- 3. Complex Structures and Loss of Ellipticity.- 3.1 A General Method for Diagonal Bars.- 3.2 Linearized Elasticity and Loss of Ellipticity.- 3.3 Examples.- 4. Other Boundary Conditions.- 4.1 The Dirichlet Problem.- 4.2 Fourier Conditions.- 4.3 Eigenvalue Problem.- 3 Thermal Problems for Gridworks.- 1. Statement of the Problem.- 2. Case e = k?.- 2.1 Change of Scale.- 2.2 Limit for ? ? 0.- 2.3 Limit for ? ? 0.- 3. Case ? ? e.- 3.1 The Multiple-Scale Method.- 3.2 The Variational Method.- 3.3 Limit for e ? 0.- 3.4 Limit for ? ? 0.- 4. Case e ? ?.- 4.1 Limit for e ? 0.- 4.2 Limit for ? ? 0.- 4.3 Limit for ? ? 0.- 4.4 Comparison of the Different Limits.- 4 Elasticity Problems for Gridworks.- 1. Statement of the Problem.- 2. Limit Plate Behavior.- 2.1 Main Result.- 2.2 A Priori Estimates and Limits of Displacements.- 2.3 Limits of Stresses and Moments and Limit Equations.- 3. Homogenization Result.- 4. Final Explicit Result and Loss of Ellipticity.- 5. Case ? ? e.- 5.1 Limit for ? ? 0.- 5.2 Limit for e ? 0.- 5.3 Limit for ? ? 0.- 5.4 Loss of Ellipticity.- 6. Plates Without Loss of Ellipticity.- 7. Time-Dependent Plates Models: An Experimental Result.- 5 Thermal Problems for Thin Tall Structures.- 1. Statement of the Problem.- 2. Case e = ??.- 2.1 Limit for ? ? 0.- 2.2 Limit for ? ? 0.- 3. Case ? ? e.- 3.1 Limit for ? ? 0.- 3.2 Limit for e ? 0, Then for ? ? 0.- 3.3 Limit for ? ? 0.- 3.4 Limit for e ? 0.- 4. Case e ? ?.- 5. Comparison of Limit Systems and Solutions.- 6. Numerical Results for a Two-Dimensional Case.- 6.1 Limit for ? ? 0.- 6.2 Limit for e ? 0.- 6.3 Numerical Computation of the Homogenized Solution.- 6.4 Limit for ? ? 0.- 6.5 Numerical Computation of the Solution V?.- 7. Generalization for a Three-Dimensional Structure.- 7.1 Case e = ??.- 7.2 Case ? ? e.- 7.3 Case e ? ?.- 6 Elasticity Problems for Thin Tall Structures.- 1. Statement of the Problem.- 1.1 Geometric Assumptions.- 1.2 Variational Formulation.- 2. Limit for e ? 0.- 2.1 Change of Scale.- 2.2 Assumptions on the Data.- 2.3 Limit for e ? 0: Beam Behaviour.- 3. Limit for e ? 0: Homogenization.- 4. Limit for ? ? 0.- 5. Applications to Other Structures.- 5.1 Towers.- 5.2 Tall Structures with Oblique Bars.- Final Comments.- References.
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