I hope this finds you in good health.

Now that I have self-isolated myself due to the COVID-19 situation, I decided to make the best use of my time and learn ELMER!

I would like to use ELMER for a part of my research in which I need to model a torsional and a translational spring at a point (node).

While I found the forum very helpful, I noticed that most of the posts concerning spring boundary condition have been left unanswered.

I would like to use the “spring” keyword in ELMER in a systematic way so that it makes it clearer for everyone and myself how to introduce a translational/rotational spring to a boundary or a node.

My goal is to obtain large-amplitude deflections of a cantilevered beam subjected to a distributed load, using different ways to model the clamped end:

1) Setting u(i=1,2,3)=0 at the clamped boundary

2) Introducing a spring with a large stiffness to the clamped boundary

3) Setting u(i=1,2,3)=0 at every nodes on the clamped boundary

4) Introducing springs with a large stiffness at every point (node) on the clamped boundary

As expected, (1), (2), and (3) yield almost identical results. However, once I define the following Bc, the solution does not converge.

!!!! Type 4: Spring at Nodes

Boundary Condition 4

Target nodes (12) = Integer 1 4 5 6 805 806 807 808 809 810 811 812 !nodes on one end of the beam

Name = "ClampedNodes"

Displacement 1 = 0 !logitudinal

Spring 2 = Real 1.0e3 !transverse

Displacement 3 = 0 !spanwise

End

It seems that the solver skips "Spring 2 = Real 1.0e3", and considers no constraint in direction 2.

Could someone have a look at the following .sif content and let me know if I'm doing something wrong especially with the "Type 4: Spring at Nodes" defined as "Boundary Condition 4"?

Thanks in advance,

Best wishes

Mo

Header

CHECK KEYWORDS Warn

Mesh DB "." "."

Include Path ""

Results Directory ""

End

Simulation

Max Output Level = 5

Coordinate System = Cartesian

Coordinate Mapping (3) = 1 2 3

Simulation Type = Steady state

Steady State Max Iterations = 1

Output Intervals = 1

Timestepping Method = BDF

BDF Order = 1

Solver Input File = case.sif

Post File = case.vtu

End

Constants

Gravity(4) = 0 -1 0 9.82

Stefan Boltzmann = 5.67e-08

Permittivity of Vacuum = 8.8542e-12

Boltzmann Constant = 1.3807e-23

Unit Charge = 1.602e-19

End

Body 1

Target Bodies(1) = 1

Name = "Body 1"

Equation = 1

Material = 1

End

Solver 1

Equation = Nonlinear elasticity

Variable = -dofs 3 Displacement

Procedure = "ElasticSolve" "ElasticSolver"

Exec Solver = Always

Stabilize = True

Bubbles = False

Lumped Mass Matrix = False

Optimize Bandwidth = True

Steady State Convergence Tolerance = 1.0e-5

Nonlinear System Convergence Tolerance = 1.0e-7

Nonlinear System Max Iterations = 100

Nonlinear System Newton After Iterations = 3

Nonlinear System Newton After Tolerance = 1.0e-3

Nonlinear System Relaxation Factor = 1

Linear System Solver = Direct

Linear System Direct Method = Umfpack

element=p:2

End

Equation 1

Name = "Nonlinear"

Active Solvers(1) = 1

End

Material 1

Name = "Plastic"

Poisson ratio = 0.3

Youngs modulus = 120

End

**!!!! Type 1: Clamped BC**

!Boundary Condition 1

!Target Boundaries (1) = 2

!Name = "Clamped"

!Displacement 3 = 0

!Displacement 2 = 0

!Displacement 1 = 0

!End

**!!!! Type 2: Introducing a Spring with large stiffness**

!Boundary Condition 2

!Target Boundaries(1) = 2

!Name = "SpringBC"

!Spring 2 = Real 1.0e3

!Displacement 3 = 0

!Displacement 1 = 0

!End

**!!!! Type 3: Zero-deflection at Nodes**

!Boundary Condition 3

!Target nodes (12) = Integer 1 4 5 6 805 806 807 808 809 810 811 812

!Name = "ClampedNodes"

!Displacement 1 = 0

!Displacement 2 = 0

!Displacement 3 = 0

!End

**!!!! Type 4: Spring at Nodes**

Boundary Condition 4

Target nodes (12) = Integer 1 4 5 6 805 806 807 808 809 810 811 812

Name = "ClampedNodes"

Displacement 1 = 0

Spring 2 = Real 1.0e3

Displacement 3 = 0

End

! Distributed load along the length of the beam

Boundary Condition 5

Target Boundaries (1) = 3

Name = "Load"

Force 2 = -1e-5

End