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# What is 'soft spring'3

## What is 'soft spring'

(OP)

Greetings all

In the context of FEA, what is 'soft spring'?

When is it switched on and what sort of values are used

Many thanks

Regards

Ed Clymer
Resinfab & Associates
England

### RE: What is 'soft spring'

I can only guess, since you didn't identify the software. My guess is that the spring constrains only in normal and/or tangential direction, that is no torsion constraint. All the refs on the Internet for various FEA software have identified the 'soft spring' as a method for constraining rigid body modes. The idea here is that the FE model is in force and moment equilibrium, and all you are doing is constraining the FE stiffness matrix so that this matrix, which is singular before you apply the boundary constraints, becomes non singular and therefore can be inverted. The net result is no additional stress or strain on the structure you are modeling due to this rigid body constraint. For instance, say you are in 2D plane stress or plane strain--you can think of the matrix equation Ku=f as a system of N degrees of freedom (DOFs) or equations (that is, the matrix 'K' has dimensions NxN, the displacement vector 'u' is Nx1 and forcing vector 'f' is Nx1). There are N-3 independent equations, meaning you need to eliminate or constrain at least 3 DOFs in order to solve for solution vector 'u' given 'K' and 'f'. The 'soft spring' then allows you to eliminate those 3 DOFs or equations while possibly not overconstraining the model, which you could do by eliminating torsional DOFs that should not have been eliminated.

Other than that, is it possible that they are describing a very compliant spring as opposed to a very stiff spring (the compliant spring having a very low stiffness constant 'k', the very stiff spring having a very high stiffness constant 'k')? Perhaps all they are describing is a pillow foundation rather than a hard concrete foundation?

### RE: What is 'soft spring'

Hello,

http://comp.uark.edu/~jjrencis/femur/Learning-Modules/The-Basic-Finite-Element-Equation/sdof2.html

Soft Spring
For such a spring the incremental force f required to produce additional incremental deformation u decreases as spring deformation increases.

Hard Spring
The incremental force required to produce a given displacement becomes increaseingly greater as the spring is deformed.

Regards

Torpen

### RE: What is 'soft spring'

I'm not saying you are wrong, but those are kown as softening springs and hardening springs, where I have heard them discussed.

Either way, not applicable to linear FEA

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

### RE: What is 'soft spring'

In the context of removing rigid body motions from a model which has fully balanced loadings applied (i.e. force in any direction and moments taken about any direction are in equilibrium). The best approach to use is the 3-2-1 method of minimal supports in 3D (which reduces to 2-1 in 2D models). Done correctly the supports react virtually zero loads and do not interfere with the results. The problem with soft springs is that you run the risk of ill-conditioning the model stiffness matrix (i.e. almost singular) and getting the associated numerical problems. Stiffening the soft spring then begins to have an affect on the results. The 3-2-1 method is numerically perfect for the stiffness matrix and delivers excellent results, so long as you apply a balanced set of loads.

### RE: What is 'soft spring'

Prost,

The 3-2-1 method:-

This involves choosing three reasonably well separated points that define a plane (i.e. not three points in a straight line!) Any convenient plane will do, but for the sake of argument let’s use the XY plane. The first point is restrained in all three translational directions.

Now any single object has six degrees of freedom, three in translation and three in rotation, commonly known as rigid body motions since no internal strain energy is involved. What this first point of restraint does is reduce the number of remaining degrees of freedom to the three rotations. The second point is carefully chosen at a Y offset from the first and thus shares the same X and Z coordinates. The second point is restrained in the X and Z directions only. There now remains just a single unrestrained freedom, rotation about the Y axis. The third point is restrained in the Z direction only and thus knocks out this final freedom.

Of course there are many variations that can be used instead, a similar approach can be applied to any of the global planes, or if there is no convenient global plane available then a local axes system will suffice.

However it is achieved the number of supports in a 3D model must equal six for a minimal support condition, any less and the structure is under supported and is insoluble, any more and the structure is over constrained.

When used correctly, the supports prevent rigid body motion without applying any restriction to the deformation of the part and thus will not react any load so long as a fully balanced set of loads and moments has been applied.

This approach allows the FE analyst to mimic a stress engineers free body diagram where all the applied loads have been sketched in. Assuming all loads are applied as realistic pressure distributions, then a very clean set of results is obtained, completely free of artificial stress concentrations.

Limitation - static linear analysis only.

### RE: What is 'soft spring'

If you restrain a point in the model in three traslational directions (your point 1 in the 3-2-1 method), and that point is a part of the mesh, how does that not restrict the deformation of the model?

### RE: What is 'soft spring'

The model is free to deform relative to point 1

### RE: What is 'soft spring'

For what it's worth, often I find the boundary constraints the most difficult to implement. In a 3D finite element model, 6 degrees of freedom (minimum) must be constrained: displacements (u,v,w) and rotations (theta-x,theta-y,theta-z). A symmetry constraint on a plane/face restricts the displacement perpendicular to plane, and two rotations, one each in the directions tangential to the plane. Say you are looking at a long rectangular plate with a centered hole, loaded in tension parallel to the two long edges, that is, a y-direction tension stress. That's two symmetry planes, so you can use one-quarter model to simulate. Say the plate is short in x direction, long in y-direction, thickness in the z-direction. Center of hole is (x,y,z)=(0,0,0). Symmetry plane at y=0 constrains y displacement 'v', AND two rotations, theta-x and theta-z. Symmetry plane at x=0 restrains x-displacement 'u' and two rotations, theta-y and theta-z. Now you have one left, z-displacement 'w'. Since there is no load in the z-direction, you can constrain ANY node you want from moving in the z-direction. Because there is equilibrium in the z-direction (no force, therefore sum of forces is zero!), this causes you no problems with singularities being introduced at that node as there would be if you constrained a y-displacement at a node not on the y=0 plane.

If the thing you are modeling isn't symmetric, then it is usually much more difficult to figure out the boundary constraints. Symmetric or not, you still have to restrict those 6 degrees of freedom.

### RE: What is 'soft spring'

That's exactly what 3-2-1 does !

3 + 2 + 1 = 6

The minimum set of supports necessary to prevent all rigid body motions, but in a way that allows for full unrestricted deformation of the model.

The simplest test of these supports is to let the model expand with a uniform temperature applied throughout, the FE solver will report back to give displacements with zero stress.

Of course if planes of symmetry exist, then it is best practice to make use of them, otherwise the 3-2-1 approach is quite simple to apply.

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