Foundations of Classical Laminate Theory

verfasst von: Univ.-Prof. Andreas Öchsner

Verlag: Springer International Publishing

Buchreihe : Advanced Structured Materials

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

This book provides a systematic and thorough introduction to the classical laminate theory based on the theory for plane elasticity elements and classical (shear–rigid) plate elements. It focus on unidirectional lamina which can be described based on orthotropic constitutive equations and their composition to layered laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai–Hill and the Tsai–Wu criteria.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The first chapter introduces the major concept of composite material, i.e., the combination of different components, to obtain in total much better properties than a single component for itself. The focus is on fiber-reinforced composites where a single layer has unidirectionally aligned reinforcing fibers. The second part of this chapter introduces to major idea and the continuum mechanical background to model structural members. It is explained that physical problems are described based on differential equations. In the context of structural mechanics, these differential equations are obtained by combining the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation. Furthermore, some explanations on the simplifications of the chosen theory, i.e., the classical laminate theory, are provided.

Andreas Öchsner

Chapter 2. Macromechanics of a Lamina

Abstract

This chapter covers the mechanical modeling of a single layer with unidirectionally aligned reinforcing fibers embedded in a homogeneous matrix, a so-called lamina. It is shown that a lamina can be treated as a combination of a plane elasticity element and a classical plate element. For both classical structural elements and their combination, the continuum mechanical modeling based on the three basic equations, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation is presented. Combining these three questions results in the description of partial differential equations. The chapter closes with different orthotropic failure criteria, i.e., the maximum stress, the maximum strain, the Tsai–Hill, and the Tsai–Wu criterion.

Andreas Öchsner

Chapter 3. Macromechanics of a Laminate

Abstract

This chapter covers the stacking of single laminae, generally under different angles, to a so-called laminate. Based on the approach of the classical laminate theory, a simplified stress analysis and a subsequent failure analysis are derived, without the solution of the system of coupled differential equations for the unknown displacements in the three coordinate directions. This theory provides the solution of the statically indeterminate system based on generalized stress–strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants.

Andreas Öchsner

Chapter 4. Example Problems

Abstract

This chapter presents the solution of some standard calculation problems based on the classical laminate theory. Each solution is based on a step-by-step approach in order to present all the details of the solution procedure. The presented problems comprise the calculation of stresses and strains in symmetric and asymmetric laminates, the application of failure criteria, and the ply-by-ply failure of laminates. In addition, the characterization of basic properties of unidirectional laminae based on pole diagrams for the elastic properties and failure envelopes is presented.

Andreas Öchsner

Backmatter

Titel: Foundations of Classical Laminate Theory
verfasst von: Univ.-Prof. Andreas Öchsner
Verlag: Springer International Publishing
Electronic ISBN: 978-3-030-82631-4
Print ISBN: 978-3-030-82630-7
DOI: https://doi.org/10.1007/978-3-030-82631-4

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