Viscoelastic Structures covers the four basic problems in the mechanics of viscoelastic solids and structural members: construction of constitutive models for the description of thermoviscoelastic behavior of polymers; mathematical modeling of manufacturing advanced composite materials; optimal-design of structural members and technological processes of their fabrication; and stability analysis for thin-walled structural members driven by time-varying loads.This book familiarizes the reader with state-of-the-art mathematical models for advanced materials and processes, and demonstrates their applications in modeling and simulating specific manufacturing processes. Viscoelastic Structures also demonstrates the effects of material, geometrical, and technological parameters on the characteristic features of viscoelastic structures.* Presents state-of-the-art mathematical models and methods which serve for the analysis of advanced technological processes* Includes numerous examples to demonstrate theory which have not been included in previous literature* Employs one consistent, user-friendly method to study a number of technological processes* Features unique approach to aging materials* Appendices cover background material on tensor calculus, kinematics with finite strains, stochastic differential equations, and evolutionary equations with operator coefficients
Author(s): Drozdov A.D.
Year: 1998
Language: English
Pages: 596
Front Cover......Page 1
Viscoelastic Structures: Mechanics of Growth and Aging......Page 4
Copyright Page......Page 5
Contents......Page 12
1.1 Basic Definitions and Formulas......Page 20
Bibliography......Page 42
2.1 Differential Constitutive Models......Page 44
2.2 Integral Constitutive Models......Page 53
2.3 Creep and Relaxation Kernels......Page 73
2.4 Thermodynamic Potentials and Variational Principles in Linear Viscoelasticity......Page 90
2.5 A Model of Adaptive Links for Aging Viscoelastic Media......Page 99
Bibliography......Page 116
3.1 Nonlinear Differential Models......Page 126
3.2 Nonlinear Integral Models......Page 136
3.3 A Model for Crosslinked Polymers......Page 149
3.4 A Model for Non-Crosslinked Polymers......Page 164
Bibliography......Page 180
4.1 Differential Constitutive Models......Page 190
4.2 Fractional Differential Models......Page 196
4.3 Integral Constitutive Models......Page 222
4.4 A Model of Adaptive Links......Page 231
4.5 A Constitutive Model in Finite Viscoelasticity......Page 245
Bibliography......Page 274
5.1 Constitutive Models in Thermoviscoelasticity......Page 281
5.2 A Model of Adaptive Links in Thermoviscoelasticity......Page 294
5.3 Constitutive Models for the Nonisothermal Behavior......Page 313
Bibliography......Page 347
6.1 Continuous Accretion of Aging Viscoelastic Media......Page 356
6.2 Winding of a Cylindrical Pressure Vessel......Page 390
6.3 Winding of a Composite Cylinder with Account for Resin Flow......Page 412
6.4 Volumetric Growth of a Viscoelastic Tissue......Page 432
Bibliography......Page 455
7.1 Accretion of a Viscoelastic Conic Pipe......Page 465
7.2 Accretion of a Viscoelastic Spherical Dome......Page 483
7.3 Debonding of Accreted Viscoelastic Beams......Page 499
7.4 Torsion of an Accreted Elastoplastic Cylinder......Page 518
Bibliography......Page 529
8.1 An Optimal Rate of Accretion for Viscoelastic Solids......Page 530
8.2 Optimal Accretion of an Elastic Column......Page 551
8.3 Preload Optimization for a Wound Cylindrical Pressure Vessel......Page 561
8.4 Optimal Design of Growing Beams......Page 573
8.5 Optimal Solidification of a Spherical Pressure Vessel......Page 588
Bibliography......Page 608
Index......Page 612
