Typically, you would either use something like "surf" in Matlab to plot scalar values in a plane or "quiver" to display a vector field. Using surf, you may plot the components u and v and/or the absolute displacement in different figures. Quiver lets you plot both components as vectors in the same figure.

@Elsheikh.. Thanks for ur response but Plotting two different plots doesnt give the effect of compression and expansion state of the plate. also as i have mentioned that every point on the plate has a displacement in x and y direction and both these equations are functions of x,y. So the final plot needs to look like a compression and expansion state of plate rather than a displacement in z direction.

@Gravenkamp.. Thanks for the response.. i have tried quiver, but it only gives the velocity vector. What i am looking is a grid which is compressed at some point and is expanded at an other point. Also u and v are instantaneous displacements of a point on the plate and the resultant displacement of the point shoud also lie on the x-y plane.

In that case, maybe you can use "mesh" to plot a distorted grid.

x=linspace(0,1,40);

y=linspace(0,1,40);

[x,y]=meshgrid(x,y);

u0=zeros(size(x));

u=-0.2*sin(x*pi);

v=-0.1*cos(x*pi);

mesh(x+u,y+v,zeros(size(x)),zeros(size(x))+0.5,'facecolor','none')

colormap gray

axis equal

view(2)

grid off

Thanks Hauke

The code given again gives a top view representation of dispalcement in z direction hence the grid looks distorted. I have tried mesh, surf etc. all give the displacement in 3D grid ie result in z direction. The required grid distortion in x,y plane is the resultant of each grid point displacements in x,y direction. Thanks again

The code I provided plots the distorted mesh within the xy-plane. Note that the z-displacement is 0 everywhere. Isn't that what you need?

I'll post it again in a slightly simplified and commented version to clarify.

% coordinates of undistorted grid

x=linspace(0,1,40);

y=linspace(0,1,40);

[x,y]=meshgrid(x,y);

z=zeros(size(x));

% arbitrary displacement in x direction

u=-0.2*sin(x*pi);

% displacement in y direction

v=-0.1*cos(x*pi);

% coordinates of distorted mesh

xd=x+u;

yd=y+v;

% plot distorted mesh

mesh(xd,yd,z)

% change to top view

view(2)

Dear Hauke

Thanks for being so patient.

I think the function you have taken is dependant on single variable x that is why you are getting a clean distorted grid.

try this function

u=-0.2*sin(x*pi).*sin(y*pi)+-0.2*cos(x*pi).*cos(y*pi);

v=-0.1*cos(x*pi).*sin(y*pi)+-0.2*cos(x*pi).*cos(y*pi);

You see if you remove view(2) and plot and see the plot mesh(xd,yd) it will show you a 3D plot with z direction displacement. now when u add z to mesh command it only flattens the z direnction deflection in x-y plane taking a relative orientation.

my problem is that every point in the grid is moving in x-y plane and the resultant of their x,y deflection is again in x-y plane. there is no flattening of z direction deflection.

For ur benefit i am giving you my equations of u and v

u=(3981215166341783.*cos(pi.*x))/19807040628566084398385987584 + (7476391693783937.*cos(2.*pi.*x))/36028797018963968 - (3981215166341783.*cos(3.*pi.*x))/19807040628566084398385987584 + (1217393838885743.*cos(4.*pi.*x))/18014398509481984 + (5387515050969975.*cos(pi.*y))/316912650057057350374175801344 + (7450591007501763.*cos(2.*pi.*y))/36028797018963968 - (8715097876569077.*cos(3.*pi.*y))/79228162514264337593543950336 + (4914651561812227.*cos(4.*pi.*y))/72057594037927936 + cos(12.566370614359172953850573533118.*y).*(0.1591549430917164570771380084936.*sin(4.7123889803846898576939650749193.*x) + 0.1591549430917164570771380084936.*sin(1.5707963267948966192313216916398.*x)) - 1.0.*cos(12.566370614359172953850573533118.*x).*(0.04007099550498452414220220842391.*sin(4.7123889803846898576939650749193.*y) + 0.04007099550498452414220220842391.*sin(1.5707963267948966192313216916398.*y)) - 1.0.*cos(12.566370614359172953850573533118.*y).*(0.040674021125264185906218690908304.*sin(4.7123889803846898576939650749193.*x) + 0.040674021125264185906218690908304.*sin(1.5707963267948966192313216916398.*x)) - 1.0.*cos(12.566370614359172953850573533118.*y).*(0.0000000026368214830571228632649151113529.*sin(4.7123889803846898576939650749193.*x) + 0.0000000026368214830571228632649151113529.*sin(1.5707963267948966192313216916398.*x)) + cos(12.566370614359172953850573533118.*y).*(0.0000000026739014016986726007153054398839.*sin(4.7123889803846898576939650749193.*x) + 0.0000000026739014016986726007153054398839.*sin(1.5707963267948966192313216916398.*x)) - 1.0.*cos(12.566370614359172953850573533118.*x).*(0.093919502001088501094899541965771.*sin(4.7123889803846898576939650749193.*y) + 0.093919502001088501094899541965771.*sin(1.5707963267948966192313216916398.*y)) - 1.0.*cos(12.566370614359172953850573533118.*x).*(0.000000003214428353230603467428765597368.*sin(4.7123889803846898576939650749193.*y) + 0.000000003214428353230603467428765597368.*sin(1.5707963267948966192313216916398.*y)) - cos(12.566370614359172953850573533118.*y).*(0.00000000263694323658858800636734410511.*cos(4.7123889803846898576939650749193.*x) - 0.00000000263694323658858800636734410511.*cos(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*y).*(0.0000000026739123833897457559450882062151.*cos(4.7123889803846898576939650749193.*x) - 0.0000000026739123833897457559450882062151.*cos(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*y).*(0.040674021126315880486015178638235.*cos(4.7123889803846898576939650749193.*x) - 0.040674021126315880486015178638235.*cos(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*y).*(0.11767076280164372648005965176331.*cos(4.7123889803846898576939650749193.*x) - 0.11767076280164372648005965176331.*cos(1.5707963267948966192313216916398.*x)) - cos(12.566370614359172953850573533118.*y).*(0.15915494309189534560822210096376.*cos(4.7123889803846898576939650749193.*x) - 0.15915494309189534560822210096376.*cos(1.5707963267948966192313216916398.*x)) + cos(12.566370614359172953850573533118.*x).*(0.0000000032525119029432904531688368915188.*sin(4.7123889803846898576939650749193.*y) + 0.0000000032525119029432904531688368915188.*sin(1.5707963267948966192313216916398.*y)) - cos(12.566370614359172953850573533118.*x).*(0.0000000032146269785995822769382737665986.*cos(4.7123889803846898576939650749193.*y) - 0.0000000032146269785995822769382737665986.*cos(1.5707963267948966192313216916398.*y)) + 1.0.*cos(12.566370614359172953850573533118.*x).*(0.0000000032527100508474403613897689546551.*cos(4.7123889803846898576939650749193.*y) - 0.0000000032527100508474403613897689546551.*cos(1.5707963267948966192313216916398.*y)) + 1.0.*cos(12.566370614359172953850573533118.*x).*(0.040070995504490663514037960844416.*cos(4.7123889803846898576939650749193.*y) - 0.040070995504490663514037960844416.*cos(1.5707963267948966192313216916398.*y)) + 1.0.*cos(12.566370614359172953850573533118.*x).*(0.093919502001777320890163387951975.*cos(4.7123889803846898576939650749193.*y) - 0.093919502001777320890163387951975.*cos(1.5707963267948966192313216916398.*y)) - cos(12.566370614359172953850573533118.*x).*(0.13484081426698314889062101726334.*cos(4.7123889803846898576939650749193.*y) - 0.13484081426698314889062101726334.*cos(1.5707963267948966192313216916398.*y)) - 1.0.*cos(12.566370614359172953850573533118.*y).*(0.11767076280251795494350459042922.*sin(4.7123889803846898576939650749193.*x) + 0.11767076280251795494350459042922.*sin(1.5707963267948966192313216916398.*x)) - (8083830663489267.*cos(pi.*x).*cos(pi.*y))/4835703278458516698824704 + (8715097876569077.*cos(pi.*x).*cos(2.*pi.*y))/158456325028528675187087900672 - (6417481163655411.*cos(2.*pi.*x).*cos(pi.*y))/39614081257132168796771975168 + (7979505200959803.*cos(pi.*x).*cos(3.*pi.*y))/4835703278458516698824704 + (7985815793738191.*cos(3.*pi.*x).*cos(pi.*y))/4835703278458516698824704 - (78918677504443.*cos(pi.*x).*cos(4.*pi.*y))/309485009821345068724781056 - (2749672779483597.*cos(2.*pi.*x).*cos(2.*pi.*y))/18014398509481984 + (5030988319655785.*cos(4.*pi.*x).*cos(pi.*y))/39614081257132168796771975168 + (2307520233227949.*cos(2.*pi.*x).*cos(3.*pi.*y))/9903520314283042199192993792 - (2139160387885137.*cos(3.*pi.*x).*cos(2.*pi.*y))/39614081257132168796771975168 - (7764052441832851.*cos(2.*pi.*x).*cos(4.*pi.*y))/144115188075855872 - (7923183764875597.*cos(3.*pi.*x).*cos(3.*pi.*y))/4835703278458516698824704 - (7670344728523405.*cos(4.*pi.*x).*cos(2.*pi.*y))/144115188075855872 + (78918677504443.*cos(3.*pi.*x).*cos(4.*pi.*y))/309485009821345068724781056 - (4555619344570199.*cos(4.*pi.*x).*cos(3.*pi.*y))/39614081257132168796771975168 - (8195634174835529.*cos(4.*pi.*x).*cos(4.*pi.*y))/576460752303423488 + cos(12.566370614359172953850573533118.*x).*(0.13484081426683878704757903430391.*sin(4.7123889803846898576939650749193.*y) + 0.13484081426683878704757903430391.*sin(1.5707963267948966192313216916398.*y)) - 4977318915857159/18014398509481984;

v=(2099546306628005.*cos(pi.*x))/39614081257132168796771975168 + (2885792671847677.*cos(2.*pi.*x))/302231454903657293676544 - (4991374238398653.*cos(3.*pi.*x))/79228162514264337593543950336 + (1903543767956795.*cos(4.*pi.*x))/604462909807314587353088 - (3961408125713217.*cos(pi.*y))/19807040628566084398385987584 + (5791552566995019.*cos(2.*pi.*y))/604462909807314587353088 + (2119353347256571.*cos(3.*pi.*y))/9903520314283042199192993792 + (3772225742053363.*cos(4.*pi.*y))/1208925819614629174706176 - 1.0.*cos(12.566370614359172953850573533118.*x).*(0.0000000054330875712025683480228207342711.*sin(4.7123889803846898576939650749193.*y) + 0.0000000054330875712025683480228207342711.*sin(1.5707963267948966192313216916398.*y)) + cos(12.566370614359172953850573533118.*y).*(0.0000000062259156920456416428288318154763.*sin(4.7123889803846898576939650749193.*x) + 0.0000000062259156920456416428288318154763.*sin(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*y).*(0.0000000018502639078169270511710509526541.*cos(4.7123889803846898576939650749193.*x) - 0.0000000018502639078169270511710509526541.*cos(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*y).*(0.0000000043364901189315227774624297692051.*cos(4.7123889803846898576939650749193.*x) - 0.0000000043364901189315227774624297692051.*cos(1.5707963267948966192313216916398.*x)) - cos(12.566370614359172953850573533118.*y).*(0.000000006226013890645529575777530625358.*cos(4.7123889803846898576939650749193.*x) - 0.000000006226013890645529575777530625358.*cos(1.5707963267948966192313216916398.*x)) - cos(12.566370614359172953850573533118.*y).*(0.069620575311776352012468735829156.*cos(4.7123889803846898576939650749193.*x) - 0.069620575311776352012468735829156.*cos(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*y).*(0.070445461517096390621429255005703.*cos(4.7123889803846898576939650749193.*x) - 0.070445461517096390621429255005703.*cos(1.5707963267948966192313216916398.*x)) + 1.0.*cos(12.566370614359172953850573533118.*x).*(0.0000000018779374510118595653504266248662.*cos(4.7123889803846898576939650749193.*y) - 0.0000000018779374510118595653504266248662.*cos(1.5707963267948966192313216916398.*y)) + 1.0.*cos(12.566370614359172953850573533118.*x).*(0.0000000054331324528965198247181705525547.*cos(4.7123889803846898576939650749193.*y) - 0.0000000054331324528965198247181705525547.*cos(1.5707963267948966192313216916398.*y)) - cos(12.566370614359172953850573533118.*x).*(0.0000000073484897775083733043490098599751.*cos(4.7123889803846898576939650749193.*y) - 0.0000000073484897775083733043490098599751.*cos(1.5707963267948966192313216916398.*y)) - cos(12.566370614359172953850573533118.*x).*(0.057109518471780276267768346904325.*cos(4.7123889803846898576939650749193.*y) - 0.057109518471780276267768346904325.*cos(1.5707963267948966192313216916398.*y)) + 1.0.*cos(12.566370614359172953850573533118.*x).*(0.057911561709125137704639702756251.*cos(4.7123889803846898576939650749193.*y) - 0.057911561709125137704639702756251.*cos(1.5707963267948966192313216916398.*y)) - 1.0.*cos(12.566370614359172953850573533118.*x).*(0.057109518471773906323531304694182.*sin(4.7123889803846898576939650749193.*y) + 0.057109518471773906323531304694182.*sin(1.5707963267948966192313216916398.*y)) + cos(12.566370614359172953850573533118.*x).*(0.057911561709130712510206379087181.*sin(4.7123889803846898576939650749193.*y) + 0.057911561709130712510206379087181.*sin(1.5707963267948966192313216916398.*y)) + cos(12.566370614359172953850573533118.*x).*(0.0000000073485672859656600678731014744728.*sin(4.7123889803846898576939650749193.*y) + 0.0000000073485672859656600678731014744728.*sin(1.5707963267948966192313216916398.*y)) - 1.0.*cos(12.566370614359172953850573533118.*y).*(0.0000000018501228965373477058095097169887.*sin(4.7123889803846898576939650749193.*x) + 0.0000000018501228965373477058095097169887.*sin(1.5707963267948966192313216916398.*x)) - (5217797223241427.*cos(pi.*x).*cos(pi.*y))/144115188075855872 - (2535301200456459.*cos(pi.*x).*cos(2.*pi.*y))/1267650600228229401496703205376 + (289677969192779.*cos(2.*pi.*x).*cos(pi.*y))/2475880078570760549798248448 + (5154524131820937.*cos(pi.*x).*cos(3.*pi.*y))/144115188075855872 + (2575221740324783.*cos(3.*pi.*x).*cos(pi.*y))/72057594037927936 - (2139160387885137.*cos(pi.*x).*cos(4.*pi.*y))/39614081257132168796771975168 - (8520094515087779.*cos(2.*pi.*x).*cos(2.*pi.*y))/1208925819614629174706176 + (1663791412799551.*cos(4.*pi.*x).*cos(pi.*y))/19807040628566084398385987584 - (2535301200456459.*cos(2.*pi.*x).*cos(3.*pi.*y))/19807040628566084398385987584 + (713053462628379.*cos(3.*pi.*x).*cos(2.*pi.*y))/79228162514264337593543950336 - (1485463369611107.*cos(2.*pi.*x).*cos(4.*pi.*y))/604462909807314587353088 - (5114089204835959.*cos(3.*pi.*x).*cos(3.*pi.*y))/144115188075855872 - (3007167917442621.*cos(4.*pi.*x).*cos(2.*pi.*y))/1208925819614629174706176 + (8715097876569077.*cos(3.*pi.*x).*cos(4.*pi.*y))/158456325028528675187087900672 - (6813621976226733.*cos(4.*pi.*x).*cos(3.*pi.*y))/79228162514264337593543950336 - (396795445902643.*cos(4.*pi.*x).*cos(4.*pi.*y))/604462909807314587353088 - 1.0.*cos(12.566370614359172953850573533118.*x).*(0.000000001878062228487243628511581764082.*sin(4.7123889803846898576939650749193.*y) + 0.000000001878062228487243628511581764082.*sin(1.5707963267948966192313216916398.*y)) - 1.0.*cos(12.566370614359172953850573533118.*y).*(0.069620575311971160986708376236459.*sin(4.7123889803846898576939650749193.*x) + 0.069620575311971160986708376236459.*sin(1.5707963267948966192313216916398.*x)) + cos(12.566370614359172953850573533118.*y).*(0.070445461517273688875172615717438.*sin(4.7123889803846898576939650749193.*x) + 0.070445461517273688875172615717438.*sin(1.5707963267948966192313216916398.*x)) - 1.0.*cos(12.566370614359172953850573533118.*y).*(0.0000000043365252921739462399629551584359.*sin(4.7123889803846898576939650749193.*x) + 0.0000000043365252921739462399629551584359.*sin(1.5707963267948966192313216916398.*x)) - 3855666708817529/302231454903657293676544;

Reg

Kavikant

Dear Kavikant,

I think it's working fine. I plotted your equations with my code posted above, I will attach the figures. The deformations u and v are added to the coordinates x and y, hence the distortion is only within a plane. All z-coordinates are set to zero. Unless I completely misunderstand your task, this is what you are looking for

Note that, if you remove the third argument of 'mesh' as you did in your response, the functionality will be completely different.

mesh(xd,yd) uses the values in xd as the z-coordinates and yd as the colors. These values are then plotted over a regular grid. That's why you obtain a plot with nonzero z-values.

Dear Hauke thanks again. But my plot looks different with the same code.