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C++面向对象的有限元程序设计

于 2020-12-08 发布
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C++面向对象的有限元程序设计,空间8结点等参元的分析计算第二章有限元分析计算的理论基础(空间8结点等参元)有限元法进行的前提是满足四个假定:连续性假定、完全弹性假定、均匀与各向同性假定、小变形和小位移假定。有限元法是建立在弹性力学的基础之上的。它是以平衡微分方程(数学上)、变形协调方程(几何方程)、本构方程(物理方程)作为基本的理论方程,同时又有圣维南原理、基于能量形式的虚位移原理作为解决问题的手段。有限元法是依照弹性力学的基本解法进行求解的,不论有限元法的哪种单元类型,在求解的过程和步骤上都是一样的,只不过求解的具体方法和细节处理有所不同。本文就以空间8结点等参元的求解的过程为例来进行编程,别的单元类型可以自己开发。而且,有了面向对象的于段,许多单元类型可以用继承的方式加以实现。2.1自然坐标系与位移模式自然坐标系与直角坐标系,如图(-1,-1,1)58(-1,1,1)X(1,-1,1)67(1,1,14(-1s3(1.1,1)局部自然坐标系与整体直角坐标系之间的关系(2-1)其屮N是关于三个自然坐标系变量;.,t的矩阵,x,y1,21,x2,…,zs是六面体的八个顶点(结点)在直角坐标系下的位置坐标,它们是已知的,xy,z与;s,t就有了对应的关系。N被称为形函数矩阵,N100N0N=0N100NNI小(22)其中N1=N(r,s,t)=(+m)1+.+t11≤i≤8(2-3)整体直角坐标与局部自然坐标的关系又可以表达成:x∑Ny∑N偎定结点间的位移变化是线性的,则位移模式可以表达为:(2-5)其中1,V1,w1,u2,…,ws是八个顶点(结点)的位移。2.2应变与位移间的关系根据变形协调方程,有:OulozAEou Ov(2-6)6×16×24vOw cu其中[B=[B1BB(2-7)ONON0aNB1≤i

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The SAR data was provided by Radarsat Intenational THinterferogram was generated and provided by Vexcel Corporation, Boulder, Coloradop00This text is printed on acid-free paper.Copyright o 1998 by John Wiley Sons, Inc. All rights reservedNo part of this publicationreproduced, stored in a retrievalsystem or transmitted in any form or by any means, elechanical photocopying, recording, scanning or otherwise,xcept as permitted under Sections 107 or 1O% of the 1976of the Publisher or authorization through payment of theontates Copyright Act, without cither theppropriate per-copy fee to the Copyright Clearance Center, 222750-4744. Requests to the Publisher for permission show(978)ood Drive, Danvers, MA 01923, (978)750-8400, faxnc.. 605 Third A venue. New York, NY 10158-0012(212)850-6011fax(212)850-6008,E-Mail:PERMREQ@WILEY.COMTwo-dimensional phase unwrapping: theory, algorithms, andsoftware/Dennis C Ghiglia and Mark D Pritt.SBN0-471-24935-1(cloth: alk. paper)1. Synthetic aperture radar. 2. 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