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Optimize deformation
Posted May 25, 2016, 8:19 a.m. EDT Optimization, Structural Mechanics 4 Replies
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Hi
I have a static simulation where I deform a 3D structure. I would like to use the optimization module to find out how much I need to pull in the edge of the structure so that a certain point inside has a certain displacement.
Simplified lets say I clamp a rubber band in one end, draw a dot somewhere on it and pull in the other end. Then I would like to know how much I should pull so that the point displaces fx 20 mm.
In the long run I want to find out how to displace and rotate one of the boundaries of my structure so that a grid of points gets as close to a reference grid as possible.
My problem is I don't know how to set up the objective function. I can import the reference grid with Cut Point 3D and get the displacement field for all the points, but I dont know how to use it in the optimization.
Br Rasmus
I have a static simulation where I deform a 3D structure. I would like to use the optimization module to find out how much I need to pull in the edge of the structure so that a certain point inside has a certain displacement.
Simplified lets say I clamp a rubber band in one end, draw a dot somewhere on it and pull in the other end. Then I would like to know how much I should pull so that the point displaces fx 20 mm.
In the long run I want to find out how to displace and rotate one of the boundaries of my structure so that a grid of points gets as close to a reference grid as possible.
My problem is I don't know how to set up the objective function. I can import the reference grid with Cut Point 3D and get the displacement field for all the points, but I dont know how to use it in the optimization.
Br Rasmus
4 Replies Last Post May 26, 2016, 8:53 a.m. EDT
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Posted:
9 years ago
Hi
for such a simple case you do not need to use the optimization module, you can get around by a simpler way by adding a global equation to your current model:
1) define the force as "my_F" as a boundary condition (ideally, as a point load will make a singularity), then
2) define an average operator "aveop1()" to get the average displacement of your reference measurement boundary (or integrate a single point to get the point displacement). Then
3) add a global equation to define the variable "my_F" and write as equation "(aveop1(u)-Udesired)" Where "Udesired" is a parameter with the desired displacement along U (or adapt to your vector direction)
4) then solve
COMSOL will add a new dependent variable "my_F" to the equation set and solve as a mean-square search for the optimum "my_F" to get "(aveop1(u)-Udesired)=0".
You may even define a Parametric Sweep (or stationary continuation) with the parameter "Udesired" to plot the evolution as Udesired changes
There are a few examples in the Application Library, this is typically how one would apply a moment load to a structure (the equations are somewhat longer to write out but it works beautifully :)
If you have several variables to optimize simultaneously, then the optimization module is of great help
--
Good luck
Ivar
for such a simple case you do not need to use the optimization module, you can get around by a simpler way by adding a global equation to your current model:
1) define the force as "my_F" as a boundary condition (ideally, as a point load will make a singularity), then
2) define an average operator "aveop1()" to get the average displacement of your reference measurement boundary (or integrate a single point to get the point displacement). Then
3) add a global equation to define the variable "my_F" and write as equation "(aveop1(u)-Udesired)" Where "Udesired" is a parameter with the desired displacement along U (or adapt to your vector direction)
4) then solve
COMSOL will add a new dependent variable "my_F" to the equation set and solve as a mean-square search for the optimum "my_F" to get "(aveop1(u)-Udesired)=0".
You may even define a Parametric Sweep (or stationary continuation) with the parameter "Udesired" to plot the evolution as Udesired changes
There are a few examples in the Application Library, this is typically how one would apply a moment load to a structure (the equations are somewhat longer to write out but it works beautifully :)
If you have several variables to optimize simultaneously, then the optimization module is of great help
--
Good luck
Ivar
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Posted:
9 years ago
The example which Ivar is referring to here is:
www.comsol.com/model/loaded-spring-using-global-equations-to-satisfy-constraints-9999
www.comsol.com/model/loaded-spring-using-global-equations-to-satisfy-constraints-9999
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Posted:
9 years ago
Hi Ivar
Thanks for the answer. The rubber band example was just to give an example. I really need to use the optimization module because i want to be able to change the rotation and displacement (6 variables) of the boundary and optimize the displacement of a grid of points (~ 30 points) so i dont see how to get around that with your solution.
Br Rasmus
Thanks for the answer. The rubber band example was just to give an example. I really need to use the optimization module because i want to be able to change the rotation and displacement (6 variables) of the boundary and optimize the displacement of a grid of points (~ 30 points) so i dont see how to get around that with your solution.
Br Rasmus
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Posted:
9 years ago
Hello Rasmus,
Does your license include the Optimization Module? You can check on that under File > Licensed and Used Products. If it does, you could define as your objective function (to be minimized) the sum of the square of the differences between experimental and simulated displacements.
Best,
Jeff
PS1: Since you have both displacements and rotations, you may need to pick some form of scaling between the two in your objective function, i.e. the C coefficient in Objective_Function=Sum (u_model-u_exp)^2 + C*Sum (theta_model-theta_exp)^2
PS2: If instead of a few discrete point values you had a continuous field of experimental data for your displacements, you would minimize the integral of the square of the difference, i.e. the L^2 norm of the "error".
Does your license include the Optimization Module? You can check on that under File > Licensed and Used Products. If it does, you could define as your objective function (to be minimized) the sum of the square of the differences between experimental and simulated displacements.
Best,
Jeff
PS1: Since you have both displacements and rotations, you may need to pick some form of scaling between the two in your objective function, i.e. the C coefficient in Objective_Function=Sum (u_model-u_exp)^2 + C*Sum (theta_model-theta_exp)^2
PS2: If instead of a few discrete point values you had a continuous field of experimental data for your displacements, you would minimize the integral of the square of the difference, i.e. the L^2 norm of the "error".