1. Joël Cugnoni, LMAF/EPFL, 2012

2.  How can we model more complex cases ? ◦ It is possible to define interactions between different regions of a model by the means of additional equations that relate the degrees of freedoms of multiple nodes.  Bilateral constraints to “glue” separate parts: ◦ Node to node interaction : Equation constraint ◦ Node to surface interaction : Kinematic coupling ◦ Surface to surface interation: Tie constraint  Unilateral constraints: ◦ Contact: no penetration between two faces, friction & sliding => non linear behaviour, not in course

3.  Available in Interaction->Constraints->Equation  one linear equation between several DOFs a1 Node1.DOF1 + a2 Node2.DOF2 + … = constant Antisymmetry 1 * Node17.U1 + 1 * Node23.U1 = 0 1723 x y Mechanism (Pulley) 1 * Node12.U2 - 1 * Node21.U1 = 0 14 21

4.  Available in Interaction->Constraints->Coupling->Kinematic coupling  Multiple equations to keep relative position constant including rotations  Tranfers the displacements / rotation of the Master node to slave surface  Usually used with reference points to link parts or apply moments / rotation to one face x y Master Node : reference point with 6 DOFS Slave Nodes : 3 DOFS Kinematic coupling

5.  Available in Interaction->Constraints->Tie  Multiple kinematic equations to keep relative position constant between each point of the master surface and their corresponding projection on the slave surface  Usually used to link two parts of an assembly to ensure continuity of the displacements (approximation) x y Master surface Slave surface Projection lines Small distance (projection tolerance)

6.  Three methods: ◦ Continuous CAD model: Merge all parts in CAD -> export STP model -> import in Abaqus -> partition to differentiate the materials ◦ Merged geometry: model as an assembly in CAD -> export as STP -> import in Abaqus -> create assembly and position parts -> Merge geometry + keep internal interfaces ◦ Tie / coupling constraints: model as an assembly in CAD -> export as STP -> import in Abaqus -> create assembly and position parts -> Create Tie / coupling to model the interactions between parts

7.  See assembly1.cae  Procedure: ◦ open assembly1-input.cae ◦ create instance for piston and axe1 ◦ align axe1 with coaxial + face to face (-13mm offset) ◦ merge and keep interfaces ◦ add instance for biele1 ◦ align with coaxial +face2face +4mm offset ◦ assign properties to all parts / regions and then create step ◦ create 1st constraint: tie for axis to biele surfaces ◦ create datum point in the middle of lower biele axis ◦ create reference point ◦ create constraint: kinematic coupling btw RP and lower axis of biele ◦ boundary condition: pressure 0.1MPa on top of cylinder, all displacement & rotation constrained on RP ◦ mesh fused part with tets quad 2.8mm ◦ mesh biele with hexa sweep or wedges (partition by extending faces) ◦ run job ◦ show results with several cutting plane to show  1) mesh continuity between the merged parts  2) displacement continuity but mesh discontinuity where tie is used