## Young modulus optimisation over Geometically non Linear Frame Element (FEM)

## Young modulus optimisation over Geometically non Linear Frame Element (FEM)

(OP)

Hello, this is my first post on this forum. My name is Bruno and i'm an MSc student from Canada doing my research project in Switzerland.

The project consists on develop a non linear compliant hydrofoil for sailing catamarans. To achieve the compliance, some hyper elastic materials will be used, the non compliant (rigid) parts of the foil will be manufactured with traditional composites.

Since the geometry of the structural beam is not defined, im doing an FEM code to determine the optimum young modulus distribution, with a determined maximum strain. The output geometry is not important as for now. The idea behind is to establish the maximum deformation and geometry depending on allowed strain. Once the CFD study is finished, we would be able to play with the deformations.

The loads are constant and orthogonal to the elements, simulating the side and lift forces.

My first approach was to use home made FEM code (frame element) with a high E modulus on the first step and then reducing it and recalculating the equivalent bending moment with the new geometry, reapplying the loads, and calculating the strain value to input into the geometrical stiffness matrix. This is a complex approach since the E modulus over the beam changes on every iteration and the previous strain is not equivalent to the t+1 step.

The second approach was to use SimMechanics simulation tool on MatLab and do a similar approach with lumped parameters and super-elements. Sim Mechanics approach.. This method is convenient but difficult since SimMechanics doesn't allow an update on the spring constant (E modulus) on every iteration, during the simulation.

The 3rd approach is to use Abaqus, this FEM software allows to determine a young modulus distribution, and with some coding it is possible to iterate over different distributions, but not on a particular element at the time.

I have an approximate solution using classical equations and some pre-defined geometries, but I would like to have a more scientific approach to the problem.

Thanks in advance, hope I've been clear on the descriptions.

regards,

Bruno.

The project consists on develop a non linear compliant hydrofoil for sailing catamarans. To achieve the compliance, some hyper elastic materials will be used, the non compliant (rigid) parts of the foil will be manufactured with traditional composites.

Since the geometry of the structural beam is not defined, im doing an FEM code to determine the optimum young modulus distribution, with a determined maximum strain. The output geometry is not important as for now. The idea behind is to establish the maximum deformation and geometry depending on allowed strain. Once the CFD study is finished, we would be able to play with the deformations.

The loads are constant and orthogonal to the elements, simulating the side and lift forces.

My first approach was to use home made FEM code (frame element) with a high E modulus on the first step and then reducing it and recalculating the equivalent bending moment with the new geometry, reapplying the loads, and calculating the strain value to input into the geometrical stiffness matrix. This is a complex approach since the E modulus over the beam changes on every iteration and the previous strain is not equivalent to the t+1 step.

The second approach was to use SimMechanics simulation tool on MatLab and do a similar approach with lumped parameters and super-elements. Sim Mechanics approach.. This method is convenient but difficult since SimMechanics doesn't allow an update on the spring constant (E modulus) on every iteration, during the simulation.

The 3rd approach is to use Abaqus, this FEM software allows to determine a young modulus distribution, and with some coding it is possible to iterate over different distributions, but not on a particular element at the time.

I have an approximate solution using classical equations and some pre-defined geometries, but I would like to have a more scientific approach to the problem.

Thanks in advance, hope I've been clear on the descriptions.

regards,

Bruno.

## RE: Young modulus optimisation over Geometically non Linear Frame Element (FEM)

Regarding your three approaches:

1: Why would you be using the FE method here? If the purpose of this approach is to ensure you have a deep understanding of the underlying numerical method then I would expect that finite differences would be easier to understand an implement. If the purpose is to avoid 'black box' commercial solvers then why not use finite volumes (i.e. foamextend branch of openfoam). I struggle to see what would make the FE method preferable over FD or FV in this scenario.

2: Don't use it, nor a I familiar with the work of people that do, so no idea.

3: Is there a particular reason you would be using ABAQUS? Is it for the python scripting abilities it has? If so, that is a valid reason, but I suspect that you may be better off creating a focused set of pre and post processing programs yourself to do the grunt work on this sort of thing rather than try to create a program that then creates another program (python script) that then creates an FEA model. In this scenario it doesn't really matter what FEA package you use (although I also use ABAQUS for this) as you'd be creating the pre-processor in whatever language you are most comfortable with. However, I don't have to couple my analysis with CFD people. If I did, then I'd probably look to see if both sides could reasonably use openfoam so that there could be constant data exchange and feedback between the fluids and structural people.

If you can provide more info and focus about your project then you might find more helpful and focused responses.

Also, this seems to be a ambitious project with a broad scope that sounds like it depends on other parties (over which you might have no authority) delivering specifics on a certain time frame, i.e. the people doing the CFD to give you a defined external geometry to work within. From a project management point of view, this sounds like a disaster waiting to happen (even by student project standards). I suggest you look at your project and try to find a way to rejig it so that your dependency on anyone/anything not directly within your control is minimised.

## RE: Young modulus optimisation over Geometically non Linear Frame Element (FEM)

Thanks a lot for your detailed answer. I will try to make things a bit more clear :).

The whole idea of this design tool, is to be able to define a material property, with strains varying from 1% to 8%, depending on the section, and then generate the desired geometry while loaded. These materials will vary form Glass, to Carbon to Shape Memory Alloys.

1)The reason why, I used the FEM code on MatLab, is to have a better control on the process and to stay as far as possible from the black boxes.I used linear FEM because I'm more familiar with it and because the whole problem can be simplified to a rectangular box beam, with different E*I distribution over the length. The beam is the structural spar of the foil, the shells dont play a big role in the structural side of things for now.

What would be the advantage to use FVM over FEM?

I'm not familiar with openfoam nor foamextend, I will look at them.

What other method would you suggest on this side?

2)SimMechanics it's nice for dynamic mechanical problems, not really our case. But an approximative solution can be achieved, taking a huge calculation time on the downside.3)The reason why we use Abaqus is because the institute we do our project at has a licence and because it's a good solution for non linear FEA. No preference on that side, but I get your point about doing the pre-post processing in one environment rather than to use multiple.I've researched an approach with Abaqus, but what I found was an option with iterative E*I distributions over the wingspan, which optimizes between the distributions defined as input, using "USDFLD".

Would you suggest a better/more efficient solution?

To clarify our working structure:We are two students, one doing the CFD and one doing the structure. We are both working in MatLab, the CFD student is using a combination of Tornado and XFlow, and from his analysis I get all the forces and moments over the wingspan. The outside geometry is not an issue for the moment as only the foil thickness defines the second moment of area boundaries. The whole idea is to implement two tools to determine the optimal geometry for the hydrofoils and the optimal structure. Then use a commercial FEM software to implement the whole thing.

Thanks a lot and sorry for such long answer.

regards,

Bruno.