%
%?GBMM1D?-?ONE?DIMENSIONAL?Galerkin-based?MESHLESS?PROGRAM?FOR?SOLVING?A?1D?BAR?OF?UNIT?LENGTH
%??????????SUBJECTED?TO?A?LINEAR?BODY?FORCE?OF?MAGNITUDE?X?WHOSE?EXACT?SOLUTION?IS?GIVEN?BY
%??????????u?=?（x/2?-?x^3/6）/E
%
%??????????BACKGROUND?CELL?QUADRATURE?IS?EMPLOYED?TO?EVALUATE?INTEGRALS
%??????????????-?CELLS?ARE?COINCIDE?WITH?THE?INTERVALS?BETWEEN?THE?NODES
%??????????????-?ONE?POINT?GAUSS?QUADRATURE
%
%??????????LAGRANGIAN?MULTIPLIER?METHOD?IS?EMPLOYER?TO?IMPOSE?THE?ESSENTIAL?BOUNDARY?CONDITIONS
%

clear?all

%?SET?UP?NODAL?COORDINATES?ALONG?BAR?DETERMINE?NUMBER?OF?CELLS
dx?=?0.1;????????????????%?Distance?between?adjacent?nodes
xi?=?[0.0?:?dx?:?1.0];???%?Nodal?coordinates
nnodes?=?length（xi）;
ncells?=?nnodes-1;

%?SET?MATERIAL?PROPERITES
E?=?1.0;?????%?Elastic?modulus
area?=?1.0;??%?Area?of?cross?section

%?DETERMINE?RADIUS?OF?SUPPORTS?FOR?EACH?NODE
scale?=?3.0;
dm?=?scale*dx*ones（1nnodes）;

%SET?UP?GAUSS?POINTS?WEIGHTS?AND?JACOBIAN?FOR?EACH?CELL
gg?=?zeros（1ncells）;??%?Coordinates?of?Gauss?points
jac?=?dx/2;????????????%?Jacobian?for?each?cell
weight?=?2;????????????%?weight?for?each?Gauss?points
gg?=?dx/2?:?dx?:?1.0-dx/2;

%?INITIALIZE?MATRICES
K?=?zeros（nnodes）;
P?=?zeros（nnodes1）;
G?=?zeros（nnodes1）;

%?LOOP?OVER?GAUSS?POINTS
for?j?=?1:length（gg）
????xg?=?gg（j）;

????%?EVALUATE?SHAPE?FUNCTIONS?AND?THEIR?DERIVATIVES?AT?GAUSS?POINT?xg
????[PHI?DPHI?DDPHI]?=?MLS1DShape（2?nnodes?xi?1?xg?dm?‘SPLIN‘?0.0）;

????%?ASSEMBLE?DISCRETE?EQUATIONS
????K?=?K?+?（weight*E*area*jac）*（DPHI‘*DPHI）;

????fbody?=?area*xg;
????P?=?P?+?（weight*fbody*jac）*PHI‘;
end

%?ENFORCE?BOUNDARY?CONDITION?USING?LAGRANGE?MULTIPLIERS

xg?=?0.0;??%?Prescribed?displacement?boundary
[PHI?DPHI?DDPHI]?=?MLS1DShape（2?nnodes?xi?1?xg?dm?‘SPLIN‘?0.0）;

G（1:31）?=?-PHI（1:3）‘;
Q?=?[0];
M?=?[K?G;?G‘?zeros（1）];

%?SOLVE?FOR?NODAL?PARAMETERS
d??=?M\[P‘?Q]‘;

uh?=?zeros（nnodes1）;??%?Nodal?displacements
sh?=?zeros（nnodes1）;??%?Nodal?stress

for?j=1:nnodes
???[PHI?DPHI?DDPHI]?=?MLS1DShape（2?nnodes?xi?1?xi（j）?dm?‘SPLIN‘?0.0）;
???uh（j）?=?PHI?*?d（1:nnodes）;
???sh（j）?=?E?*?DPHI?*?d（1:nnodes）;
end

%?EVALUATE?RELATIVE?ERROR?NORMS
ue?=?（xi/2.0?-?xi.*xi.*xi/6.0）/E;??%?Exact?solution
se?=?（1?-?xi.*xi）/2.0;

erru?=?norm（ue‘-uh）/norm（ue）*100
errs?=?norm（se‘-sh）/norm（se）*100

%?PLOT?RESULTS
figure
subplot（121）;??plot（xi?ue?xi?uh）;
subplot（122）;??plot（xi?se?xi?sh）;

%?Output?nodal?displacements?and?stresses
fid1?=?fopen（‘G1DBarDis.dat‘‘w‘）;
fid2?=?fopen（‘G1DBarStr.dat‘‘w‘）;

fprintf（fid1‘%10s%10s%10s\n‘?‘x‘?‘ue‘‘uh‘）;
fprintf（fid2‘%10s%10s%10s\n‘?‘x‘?‘se‘‘sh‘）;

for?j?=?1?:?nnodes
???fprintf（fid1‘%10.4f%10.4f%10.4f\n‘?xi（j）?ue（j）?uh（j））;
???fprintf（fid2‘%10.4f%10.4f%10.4f\n‘?xi（j）?se（j）?sh（j））;
end
???
fclose（fid1）;
fclose（fid2）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????6594??2009-09-09?18:01??《無網格法》書籍代碼\FORTRAN程序庫\DFCONSOL.LIB

?????文件?????780796??2009-09-09?18:01??《無網格法》書籍代碼\FORTRAN程序庫\DFOR.LIB

?????文件?????104648??2009-09-09?18:01??《無網格法》書籍代碼\FORTRAN程序庫\DFPORT.LIB

?????文件???????2112??2009-09-09?18:05??《無網格法》書籍代碼\readme.txt

?????文件????1621059??2009-09-09?18:03??《無網格法》書籍代碼\第七章程序：面向對象的二維無網格法程序OMLL\EOMLL.rar

?????文件?????925070??2009-09-09?18:00??《無網格法》書籍代碼\第七章程序：面向對象的二維無網格法程序OMLL\omll-3d.rar

?????文件?????847585??2009-09-09?17:59??《無網格法》書籍代碼\第七章程序：面向對象的二維無網格法程序OMLL\OMLL.rar

?????文件?????893712??2009-09-09?18:02??《無網格法》書籍代碼\第七章程序：面向對象的二維無網格法程序OMLL\Omll2D.rar

?????文件?????126025??2009-09-09?18:00??《無網格法》書籍代碼\第七章程序：面向對象的二維無網格法程序OMLL\plate.rar

?????文件???????6581??2009-09-09?17:58??《無網格法》書籍代碼\第三章程序：一維伽遼金型無網格法MATLAB程序\EFG1D.rar

?????文件???????2890??2009-09-09?17:56??《無網格法》書籍代碼\第三章程序：一維伽遼金型無網格法MATLAB程序\GBMM1D.m

?????文件???????2952??2009-09-09?17:54??《無網格法》書籍代碼\第二章程序：一維移動最小二乘近似的MATLAB程序\MLS1D.m

?????文件???????3014??2009-09-09?17:54??《無網格法》書籍代碼\第二章程序：一維移動最小二乘近似的MATLAB程序\MLS1DShape.m

?????文件???????2190??2009-09-09?17:55??《無網格法》書籍代碼\第二章程序：一維移動最小二乘近似的MATLAB程序\Weight.m

?????文件???????5208??2009-09-09?17:57??《無網格法》書籍代碼\第五章程序：一維MLPG法MATLAB程序\MLPG1D.m

?????文件???????3429??2009-09-09?17:59??《無網格法》書籍代碼\第六章程序：一維最小二乘無網格法MATLAB程序\MWLS1D.m

?????文件???????2012??2009-09-09?17:56??《無網格法》書籍代碼\第四章程序：一維配點型無網格法MATLAB程序\CBMM1D.m

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\FORTRAN程序庫

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\第七章程序：面向對象的二維無網格法程序OMLL

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\第三章程序：一維伽遼金型無網格法MATLAB程序

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\第二章程序：一維移動最小二乘近似的MATLAB程序

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\第五章程序：一維MLPG法MATLAB程序

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\第六章程序：一維最小二乘無網格法MATLAB程序

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼\第四章程序：一維配點型無網格法MATLAB程序

?????目錄??????????0??2009-09-12?14:29??《無網格法》書籍代碼

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??????????????5335877????????????????????25