A Simplified Approach to the Classical Laminate Theory of Composite Materials: Application of Bar and Beam Elements
暫譯: 複合材料經典層合板理論的簡化方法：桿件與樑元素的應用

Öchsner, Andreas

A Simplified Approach to the Classical Laminate Theory of Composite Materials: Application of Bar and Beam Elements

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商品描述

This book provides a systematic introduction to composite materials, which are obtained by a layer-wise stacking of one-dimensional bar/beam elements. Each layer may have different mechanical properties, but each single layer is considered as isotropic. The major idea is to provide a simplified theory to easily understand the classical two-dimensional laminate theory for composites based on laminae with unidirectional fibers. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria.

Partial differential equations lay the foundation to mathematically describe the mechanical behavior of any classical structural member known in engineering mechanics, including composite materials. The so-called classical laminate theory provides a simplified stress analysis, and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements. The procedure provides the solution of a statically indeterminate system based on a generalized stress-strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants. This laminate theory is typically provided for two-dimensional plane problems, where the basic structural element is a simple superposition of a classical plane elasticity element with a thin plate element under the consideration of an orthotropic constitutive law.

This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory, has been developed. The idea is to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understanding this simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case.

商品描述(中文翻譯)

本書系統性地介紹複合材料。這類材料是透過逐層堆疊一維桿件／梁元素所形成的。每一層可能具有不同的機械性質，但各個單層皆視為等向性材料。全書的主要概念，是提供一套簡化理論，以便讀者輕鬆理解以單向纖維層板（laminae）為基礎的複合材料經典二維層板理論（classical laminate theory）。除了彈性行為之外，本書也根據最大應力、最大應變、Tsai-Hill 與 Tsai-Wu 準則探討破壞行為。

偏微分方程式是以數學方式描述工程力學中任何經典結構構件（包括複合材料）機械行為的基礎。所謂經典層板理論（classical laminate theory）可在無須求解未知位移所構成的耦合微分方程組的情況下，提供簡化的應力分析以及後續的破壞分析。此程序會在考慮構成關係（constitutive relationship）以及所謂應力合力（stress resultants）的定義下，根據廣義應力–應變關係，求解靜不定系統。這套層板理論通常用於二維平面問題，其中基本結構元素是在考慮正交異向性構成律（orthotropic constitutive law）的情況下，將經典平面彈性元素與薄板元素簡單疊加而成。

對某些學生而言，這種二維方法及其背後所依據的進階連續體力學建模可能相當具挑戰性，尤其是在科技大學等實務導向的高等教育機構中。因此，本書發展出一種簡化方法，即所謂簡化經典層板理論（simplified classical laminate theory）。其概念是僅使用等向性的一維元素，也就是桿件與梁元素的疊加，來介紹經典層板理論的主要計算步驟。理解這套簡化理論容易得多，而最後一步則是說明進一步推廣至一般二維情況時所產生的差異。

作者簡介

Andreas Öchsner is a full professor of Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. After completing his Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), he served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003 while pursuing his Doctor of Engineering Sciences (Dr.-Ing.) degree. From 2003 to 2006, he was an assistant professor at the Department of Mechanical Engineering and the head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007-2013) as a full professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also the head of the Advanced Materials and Structure Lab. From 2014 to 2017, he was a full professor at the School of Engineering, Griffith University, Australia.

作者簡介(中文翻譯)

Andreas Öchsner 是德國 Esslingen University of Applied Sciences 輕量化設計與結構模擬領域的正教授。1997 年，他在 University of Stuttgart 完成航空工程 Dipl.-Ing. 學位後，於 1997 至 2003 年期間在 University of Erlangen-Nuremberg 擔任研究與教學助理，同時攻讀工程科學博士（Dr.-Ing.）學位。2003 至 2006 年間，他擔任 Department of Mechanical Engineering 的助理教授，並兼任隸屬於 University of Aveiro（葡萄牙）的 Cellular Metals Group 主任。2007 至 2013 年，他在 Technical University of Malaysia 的 Department of Applied Mechanics 擔任正教授，並兼任 Advanced Materials and Structure Lab 主任。2014 至 2017 年間，他擔任 Griffith University School of Engineering 的正教授。

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