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Irreducible and Isotropic Cartesian Tensors
In this chapter we summarize definitions and properties of cartesian, anisotropic, irreducible and isotropic tensors and related tensor operators. In...
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A Boundary-Layer Solution Verified by Buckling of a Rectangular Plate
The so called edge-zone or boundary-layer solutions are widely used in large dediection problems of thin elastic plates [20,35,36] and shells...
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Inclined Girders with End Constraint Subjected to Normal Loads
A two-bar truss subjected to lateral normal distributed loads as shown in Fig. 9.1 represents a double leaf miter-type gate used in navigation locks...
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Chain Model for Dilute Solutions
Various experimental observations reveal an important aspect of the behavior of polymer solutions which is not captured by FENE dumbbell models. When...
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Chain Models for Transient and Semiflexible Structures
In order to be prepared for the analysis of the flexible FENE-C (FENE model which allows for scission/recombination), FENE-B (which allows for...
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6 Dynamic Analysis
A general dynamical system subjected to an external force vector $\vec{f}(t)$...
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10 Equivalent Statistical Linearization
The solution of non-linear vibration problems in terms of probabilistic characteristics of the response is a complex task, since no general methods...
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12 Stability Analysis of Cylindrical Shells with Random Imperfections
As an example of imperfection sensitive structures, the axially compressed cylindrical shell is analyzed in the subsequent sections. Despite of its...
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2 Outline
The monograph is structured as follows: Part I including Chapts. 3–6 reviews briefly the theoretical background of the deterministic methods and...
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The Tensile Strength of Polymer Fibres
A theory of the tensile strength of oriented polymer fibres is presented. From an analysis of the observed fracture envelope it is shown that the...
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Primitive Path Models
Having discussed the range of applicability for various FENE chain models mostly listed in the upper part of Table 14.1 one may expect that we also...
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Simple Simulation Algorithms and Sample Applications
This section offers basic recipes and sample applications which allow the reader to immediately start his/her own simulation project on topics we...
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Elongated Particle Models
In [292] we provided a statistical interpretation of the director theory of Ericksen and Leslie (EL) [293–295] for nematic liquid crystals. Starting...
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Simple Models for Polymeric and Anisotropic Liquids
We hope that the complexity of the world is neither in contrast with the simplicity of the basic laws of physics [1] nor with the simple physical...
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Chain Model for Concentrated Solutions and Melts
A dense collection of repulsive FENE chains serves as a suitable microscopic model for both entangled and unentangled polymer melts. We will consider...
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Concluding Remarks
The development of constitutive relationships which connect strain or strain rate with stress and material behavior is at the heart of a successful...
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Two Methods for Analysis of Continuum Mechanics of Elastic Structures
There are two basic methods to analyze the continuum elastic structural mechanics: One is by applying Newton’s law of motion to a free body element...
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Vibrations of Inclined Bars with End Constraint
Considered are the vibrations of inclined bars with the bottom end flxed in space and the top end having a constraint which requires that this end...
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Effect of Rotatory Inertia and Shear Deformation on Vibration of Inclined Bars with End Constraint
The effect of rotatory inertia and shear deformation on the vibration of the inclined bar with the end constraint studied in Chap. 2 is examined...