calfem用户帮助.pdf

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Introduction

General purpose functions

clear

diary

disp

echo

format

help

load

quit

save

type

what

who

whos

Line continuation

Comments

Matrix functions

Special characters

Subscripting

Arithmetic

abs

det

diag

full

inv

length

max

min

ones

red

size

sparse

spy

sqrt

sum

zeros

Material functions

hooke

mises

dmises

Element functions

Spring element

spring1e

spring1s

Bar elements

bar2e

bar2g

bar2s

bar3e

bar3s

Heat flow elements

flw3i8e

flw3i8s

Solid elements

plante

plants

plantf

planqe

planqs

planre

planrs

plantce

plantcs

plani4e

plani4s

plani4f

plani8e

plani8s

plani8f

soli8e

soli8s

soli8f

Beam elements

beam2e

beam2s

beam2t

beam2ts

beam2w

beam2ws

beam2g

beam2gs

beam2d

beam2ds

beam3e

beam3s

Plate elements

platre

platrs

System functions

Static system functions

assem

coordxtr

eigen

extract

insert

solveq

statcon

Dynamic system functions

dyna2

dyna2f

fft

freqresp

gfunc

ifft

ritz

spectra

step1

step2

sweep

Statements and macros

for

while

Scripts

Graphics functions

axis

clf

eldraw2

eldisp2

eldia2

elflux2

eliso2

elprinc2

figure

fill

grid

hold

plot

text

title

xlabel

ylabel

zlabel

User's Manual, examples

Introduction to matlab

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Static analysis

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Dynamic analysis

Example 1

Example 2

Example 3

Example 4

Nonlinear analysis

Example 1

Example 2

R e p o r t T V S M - 9 0 0 1 C A L F E M - I I A F N T E E L E M E N T T O O L B O X T O M A T L A B V e r s i o n 3 . 3 Department of Mechanics and Materials C A L F E M A finite element toolbox to MATLAB Version 3.3 Structural Mechanics & Solid Mechanics

Department of Mechanics and Materials Structural Mechanics ISRN LUTVDG/TVSM--99/9001--SE (1-265) ISSN 0281-6679 C A L F E M A finite element toolbox to MATLAB Version 3.3 Copyright © 1999 by Structural Mechanics, LTH, Sweden. Printed by JABE Offset, Lund, Sweden.

The software described in this document is furnished under a license agreement. The software may be used or copied only under terms in the license agreement. No part of this manual may be photocopied or reproduced in any form without the prior written consent by the Division of Structural Mechanics. CALFEM February 1999 c Copyright 1992–99 by the Division of Structural Mechanics and the Department of Solid Mechanics at Lund University. All rights reserved. CALFEM is the trademark of the Division of Structural Mechanics, Lund University. Matlab is the trademark of The MathWorks, Inc. The Division of Structural Mechanics Lund University PO Box 118 S–221 00 Lund SWEDEN Phone: +46 46 222 0000 Fax: +46 46 222 4420 The Department of Solid Mechanics Lund University PO Box 118 S–221 00 Lund SWEDEN Phone: +46 46 222 0000 Fax: +46 46 222 4620 E-mail addresses: calfem@byggmek.lth.se strucmech@byggmek.lth.se general questions to the departments CALFEM questions and comments Homepage: http://www.byggmek.lth.se/Calfem

Preface CALFEMR is an interactive computer program for teaching the ﬁnite element method (FEM). The name CALFEM is an abbreviation of ”Computer Aided Learning of the Finite Element Method”. The program can be used for diﬀerent types of structural mechanics problems and ﬁeld problems. CALFEM, the program and its built-in philosophy have been developed at the Division of Structural Mechanics starting in the late 70’s. Many coworkers, former and present, have been engaged in the development at diﬀerent stages, of whom we might mention Per-Erik Austrell Jonas Lindemann Kent Persson Matti Ristinmaa H˚akan Carlsson Anders Olsson Anders Peterson G¨oran Sandberg Ola Dahlblom Karl-Gunnar Olsson Hans Petersson The present release of CALFEM, as a toolbox to MATLAB, represents the latest develop- ment of CALFEM. The functions for ﬁnite element applications are all MATLAB functions (M-ﬁles) as described in the MATLAB manual. We believe that this environment increases the versatility and handling of the program and, above all, the ease of teaching the ﬁnite element method. Lund, November 22, 2000 Division of Structural Mechanics and Division of Solid Mechanics

Contents 1 Introduction 2 General purpose functions 3 Matrix functions 4 Material functions 5 Element functions 1 – 1 2 – 1 3 – 1 4 – 1 5.1 – 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 – 1 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 – 1 5.2 Spring element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 – 1 5.3 Bar elements 5.4 Heat ﬂow elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 – 1 5.5 Solid elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 – 1 5.6 Beam elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 – 1 5.7 Plate element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 – 1 6 System functions 6.1 – 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 – 1 6.1 6.2 Static system functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 – 1 6.3 Dynamic system functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 – 1 7 Statements and macros 8 Graphics functions 9 User’s Manual, examples 7 – 1 8 – 1 9.1 – 1 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 – 1 9.2 MATLAB introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 – 1 9.3 Static analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 – 1 9.4 Dynamic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 – 1 9.5 Nonlinear analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 – 1

1 Introduction The computer program CALFEM is a MATLAB toolbox for ﬁnite element applications. This manual concerns mainly the ﬁnite element functions, but it also contains descriptions of some often used MATLAB functions. The ﬁnite element analysis can be carried out either interactively or in a batch oriented fashion. In the interactive mode the functions are evaluated one by one in the MATLAB command window. In the batch oriented mode a sequence of functions are written in a ﬁle named .m-ﬁle, and evaluated by writing the ﬁle name in the command window. The batch oriented mode is a more ﬂexible way of performing ﬁnite element analysis because the .m-ﬁle can be written in an ordinary editor. This way of using CALFEM is recommended because it gives a structured organization of the functions. Changes and reruns are also easily executed in the batch oriented mode. A command line consists typically of functions for vector and matrix operations, calls to functions in the CALFEM ﬁnite element library or commands for workspace operations. An example of a command line for a matrix operation is C = A + B0 where two matrices A and B’ are added together and the result is stored in matrix C . The matrix B’ is the transpose of B. An example of a call to the element library is Ke = bar1e(k) where the two-by-two element stiﬀness matrix Ke is computed for a spring element with spring stiﬀness k, and is stored in the variable Ke. The input argument is given within parentheses ( ) after the name of the function. Some functions have multiple input argu- ments and/or multiple output arguments. For example [lambda, X] = eigen(K, M) computes the eigenvalues and eigenvectors to a pair of matrices K and M. The output variables - the eigenvalues stored in the vector lambda and the corresponding eigenvectors stored in the matrix X - are surrounded by brackets [ ] and separated by commas. The input arguments are given inside the parentheses and also separated by commas. The statement help function provides information about purpose and syntax for the speciﬁed function. 1 – 1 INTRODUCTION

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