有限元方法

前言

The major part of this book has been derived by updating the third volume of the fifth edition. However, it now contains three new chapters and also major improvements in the existing ones. Its objective is to separate the fluid dynamics formulations and applications from those of solid mechanics and thus to reach perhaps a different interest group.It is our intention that the present text could be used by investigators familiar with the finite element method in general terms and introduce them to the subject of fluid dynamics. It can thus in many ways stand alone. Although the finite element discretization is briefly covered here, many of the general finite element procedures may not be familiar to a reader introduced to the finite element method through different texts and therefore we advise that this volume be used in conjunction with the text on 'The Finite Element Method: Its Basis and Fundamentals' by Zienkiewicz, Taylor and Zhu to which we make frequent reference.

內(nèi)容概要

這是一套在國際上頗具權(quán)威性的經(jīng)典著作（共三卷）,由有限元法的創(chuàng)始人Zienkiewicz教授和美國加州大學(xué)Taylor教授合作撰寫,初版于1967年,多次修訂再版,深受力學(xué)界和工程界科技人員的歡迎。本套書的特點是理論可靠，內(nèi)容全面，既有基礎(chǔ)理論，又有其具體應(yīng)用。 　　第2卷目次：固體力學(xué)和非線性的一般問題；Galerkin近似方法；非線性代數(shù)方程的解；非彈性和非線性材料；幾何非線性問題—有限變形；有限性變的材料構(gòu)成；約束處理；偽剛性體和剛?cè)嵝泽w；離散元方法；一維結(jié)構(gòu)力學(xué)問題；板彎曲近似：?。↘irchhoff）板和C1連續(xù)性要求；厚Reissner-Mindlin 板—不可簡縮的和混合公式；作為扁平單元的殼；軸對稱殼；作為三維分析的特殊情形的殼—Reissner-Mindlin假定；半解析有限元法—正交函數(shù)的利用和‘有限帶’法；非線性結(jié)構(gòu)問題—大位移和失穩(wěn)；多尺度模型；有限元分析的計算機程序?！　∽x者對象：計算力學(xué)、力學(xué)、土木、水利、機械、航天航空等領(lǐng)域的專家、教授、工程技術(shù)人員和研究生。

作者簡介

作者：(英國)監(jiān)凱維奇 (Zienkiewicz.O.C)

書籍目錄

PrefaceAcknowledgements1  Introduction to the equations of fluid dynamics and the finite element approximation　1.1   General remarks and classification of fluid dynamics problems discussed in this book　1.2   The governing equations of fluid dynamics　1.3   Inviscid, incompressible flow　1.4   Incompressible (or nearly incompressible) flows　1.5   Numerical solutions: weak forms, weighted residual and finite element approximation　1.6   Concluding remarks　References2  Convection dominated problems - finite element approximations to the convection--diffusion-reaction equation　2.1   Introduction　2.2   The steady-state problem in one dimension　2.3   The steady-state problem in two (or three) dimensions　2.4   Steady state - concluding remarks　2.5   Transients - introductory remarks　2.6   Characteristic-based methods　2.7   Taylor-Galerkin procedures for scalar variables　2.8   Steady-state condition　2.9   Non-linear waves and shocks　2.10  Treatment of pure convection　2.11  Boundary conditionsfor convection-diffusion　2.12  Summary and concluding remarks　References3  The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow　3.1   Introduction　3.2   Non-dimensional form of the governing equations　3.3   Characteristic-based split (CBS) algorithm  3.4   Explicit, semi-implicit and nearly implicit forms  3.5   Artificial compressibility and dual time stepping  3.6   'Circumvention' of the Babuska-Brezzi (BB) restrictions  3.7   A single-step version  3.8   Boundary conditions  3.9   The performance of two-step and one-step algorithms on an inviscid problem  3.10  Concluding remarks　References4 Incompressible Newtonian laminar flows  4.1   Introduction and the basic equations  4.2   Use of the CBS algorithm for incompressible flows  4.3   Adaptive mesh refinement  4.4   Adaptive mesh generation for transient problems  4.5   Slow flows - mixed and penalty formulations  4.6   Concluding remarks　References5 Incompressible non-Newtonian flows  5.1   Introduction  5.2   Non-Newtonian flows - metal and polymer forming  5.3   Viscoelastic flows  5.4   Direct displacement approach to transient metal forming  5.5   Concluding remarks　References6 Free surface and buoyancy driven flows  6.1   Introduction  6.2   Free surface flows  6.3   Buoyancy driven flows  6.4   Concluding remarks　References7 Compressible high-speed gas flow  7.1   Introduction  7.2   The governing equations  7.3   Boundary conditions.- subsonic and Suoersonic fl0w  7.4   Numerical approximations and the CBS algorithm  7.5  Shock capture  7.6  Variable smoothing  7.7   Some preliminary examples for the Euler equation  7.8   Adaptive refinement and shock capture in Euler problems  7.9   Three-dimensional inviscid examples in steady state  7.10  Transient two- and three-dimensional problems  7.11  Viscous problems in two dimensions  7.12  Three-dimensional viscous problems……8  Turbulent flows9  Generalized flow through porous media10  Shallow water problems11  Long and medium waves12  Short waves13  Computer implementation of the CBS algorithmAppendixAuthor indexSubject index

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