This book presents recent works on lattice type structure. Its aim is to give continuous simple models for thin reticulated structures which may have a very complex pattern. For this reason, the authors treat partial differential equations depending on several small parameters, and give the asymptotic behavior with respect to these parameters. Attention has been paid to mathematical rigor, convergence results and error estimates. Chapter 1 gives an introduction to homogenization methods in perforated domains. Chapter 2 offers the main ideas to study thin reticulated structures. Chapters 3and 4…mehr
This book presents recent works on lattice type structure. Its aim is to give continuous simple models for thin reticulated structures which may have a very complex pattern. For this reason, the authors treat partial differential equations depending on several small parameters, and give the asymptotic behavior with respect to these parameters. Attention has been paid to mathematical rigor, convergence results and error estimates. Chapter 1 gives an introduction to homogenization methods in perforated domains. Chapter 2 offers the main ideas to study thin reticulated structures. Chapters 3and 4 are dedicated to the study of networks in thermal and elasticity problems. Chapter 5 and 6 treat similar problems to those in Chapter 3 and 4, but in this instance, the structure is thin and tall, tower-like.
Chapter 1 Homogenization in Perforated Media Chapter 2 Lattice Type Structures Chapter 3 Thermal Problem for Networks Chapter 4 Elasticity Problem for Networks Chapter 5 Thermal Problem for Tall Structures Chapter 6 Elasticity Problem for Tall Structures
1 Homogenization in Perforated Media.- 1. The General Method of Homogenization.- 2. The Homogeneous Neumann Problem.- 3. Other Boundary Value Problems.- 2 Lattice-Type Structures.- 1. The Two-Dimensional Case.- 2. The Three-Dimensional Case.- 3. Complex Structures and Loss of Ellipticity.- 4. Other Boundary Conditions.- 3 Thermal Problems for Gridworks.- 1. Statement of the Problem.- 2. Case e = k?.- 3. Case ? ? e.- 4. Case e ? ?.- 4 Elasticity Problems for Gridworks.- 1. Statement of the Problem.- 2. Limit Plate Behavior.- 3. Homogenization Result.- 4. Final Explicit Result and Loss of Ellipticity.- 5. Case ? ? e.- 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 = ??.- 3. Case ? ? e.- 4. Case e ? ?.- 5. Comparison of Limit Systems and Solutions.- 6. Numerical Results for a Two-Dimensional Case.- 7. Generalization for a Three-Dimensional Structure.- 6 Elasticity Problems for Thin Tall Structures.- 1. Statement of the Problem.- 2. Limit for e ? 0.- 3. Limit for e ? 0: Homogenization.- 4. Limit for ? ? 0.- 5. Applications to Other Structures.- Final Comments.- References.
Chapter 1 Homogenization in Perforated Media Chapter 2 Lattice Type Structures Chapter 3 Thermal Problem for Networks Chapter 4 Elasticity Problem for Networks Chapter 5 Thermal Problem for Tall Structures Chapter 6 Elasticity Problem for Tall Structures
1 Homogenization in Perforated Media.- 1. The General Method of Homogenization.- 2. The Homogeneous Neumann Problem.- 3. Other Boundary Value Problems.- 2 Lattice-Type Structures.- 1. The Two-Dimensional Case.- 2. The Three-Dimensional Case.- 3. Complex Structures and Loss of Ellipticity.- 4. Other Boundary Conditions.- 3 Thermal Problems for Gridworks.- 1. Statement of the Problem.- 2. Case e = k?.- 3. Case ? ? e.- 4. Case e ? ?.- 4 Elasticity Problems for Gridworks.- 1. Statement of the Problem.- 2. Limit Plate Behavior.- 3. Homogenization Result.- 4. Final Explicit Result and Loss of Ellipticity.- 5. Case ? ? e.- 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 = ??.- 3. Case ? ? e.- 4. Case e ? ?.- 5. Comparison of Limit Systems and Solutions.- 6. Numerical Results for a Two-Dimensional Case.- 7. Generalization for a Three-Dimensional Structure.- 6 Elasticity Problems for Thin Tall Structures.- 1. Statement of the Problem.- 2. Limit for e ? 0.- 3. Limit for e ? 0: Homogenization.- 4. Limit for ? ? 0.- 5. Applications to Other Structures.- Final Comments.- References.
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