Elastic Foundation Model 2 Aereal Damping Normal Force Law of Contact Elements 3 Adhesion Avoidance brPage 11br DLR ECCOMAS Multibody Dynamics 2003 Vehicle System Dynamics tk nk tk nk tk tk tk 4 Regularised Coulombs Friction Tangential For ID: 69531
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DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Motivation Contact Point JumpMulti PointContactConforming ContactWeak points of contact point approach:Extreme simplification of complex physical phenomenaGeometric determination of contact points requires smooth surfacesContact kinematics fails in several arrangements of non strictly convex surfacesWeak points of FEA contact analysis:Efficiency not compatible with MBS simulationExtremely complex in theory and implementationPolygonal Contact Model (PCM):Contact model for complexly shaped bodiesRobust, efficient algorithm for MBS simulation DLRECCOMAS Multibody Dynamics 2003Vehicle System DynamicsBasic Ideas Body surfacesrepresented by polygon meshesAereal discretisation of contact patchesContact elements represent elastic foundation model and regularised Coulombs frictionResulting force vector acts as applied force of the MBS (force element) DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics MeMfMeMfMeMfMeMf Collision DetectionCollision Construction of Intersection Polygons Determination of Active Surface Parts Generation of Contact Elements Determination of Contact Force/Torque F = 0, = 0Algorithm Overview DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Task:Determination of all intersection lines of two polygon meshesBasic operation:Determination of intersection line of two triangles in 3D-space (76-181 FLOPs)Brute force method:Basic operation for all possible polygon pairings ((n²))Efficiency improved by about four orders of magnitude by pre-selection of test pairings by Bounding Volume (BV)hierarchiesBV-HierarchyBrute ForceTr-ChecksBV-ChecksIntsec-Lines 189033633015373535Collision Detection DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Binary tree data structureCalculation once per surface (preprocessing)Elements: Axis-aligned cuboids representing convex hulls of contiguous surface partsSpacial refinement from root (whole surface) to leaves (solitary polygons)Efficient collision test of two BVs (12-36 FLOPs) Collision Detection: Bounding Volume Hierarchy DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Collision detection determines intersection lines in irregular orderConstruction of intersection polygons by distance calculation of end points in pairsCirculation direction results from surface orientationConstruction of Intersection Polygons DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Active surface parts represent the boundaries of the intersection volumeIntersected polygons given by collsion detectionDetermination of inner polygons by searching along active surface parts using Doubly Connected Edge Lists (DCEL)Determination of Active Surface Parts DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Contact elements result from active polygons e of master-surface EDetermination of corresponding polygon f by projection of active slave-polygons to plane of e is located inside of fCalculation of u using normal form of plane of e is reference position of relative velocity calculation and force vector-----------------CeCf---------------------Generation of Contact Elements DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics-------1. Elastic Foundation Model2. Aereal Damping Normal Force Law of Contact Elements ------------------------------------ 3. Adhesion Avoidance 9 DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics---------- 4. Regularised Coulombs Friction Tangential Force Law of Contact Elements DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics -----MfCk5. Contact Element Force6. Resulting Torque7. Total Force at M8. Total Torque ()MBS: Applied Forces Total Resulting Contact Force & Torque DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics 3 bodies18 degrees of freedom6 contact pairingsBubbles: 950 trianglesContainer: 4 trianglesSynthetical parameterisationMultiple and conforming contactsLSODE atol = rtol = 2.0e-4-Mean step-size 0.8 ms-Real-time factor* 276 s / 3 s = 92* Mobile PIII 1133 MHz / SIMPACK 8.6 / Win 2kExample: Bouncing Bubbles DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics 15+1 bodies29 degrees of freedom27 contact pairingsMan: 20452 trianglesCar: 1240 trianglesEstimated parameterisationDOPRI5 atol = rtol = 1.0e-3-Mean step-size 2.0 ms-Real-time factor* 288 s /1,5 s = 192* Mobile PIII 1133 MHz / SIMPACK 8.6 / Win 2kExample: Pedestrian Crash DLRECCOMAS Multibody Dynamics 2003Vehicle System DynamicsValuationAdvantagesEasy providing of contact surfacesComplexly shaped contact surfaces-Multiple contact patches-Multiply bordered contact patches-Conforming contactVery robust algorithmBetter approximation than single point modelsEfficiency fits into MBS simulationOpen source code: www.pcm.hippmann.orgDisadvantagesHigh quality polygon meshes required-Consistent orientation-No cracks-Discretisation results from resolutionNon-practical parametersNot applicable for elastic bodiesNeglecting of adhesive friction and shear stresses in contact patchStiff layers cause stiff ODE DLRECCOMAS Multibody Dynamics 2003Vehicle System Dynamics Gerhard HippmannInstitute of AeroelasticityVehicle System Dynamics GroupDLR OberpfaffenhofenAn Algorithm for Compliant Contact between Complexly Shaped Surfaces in Multibody DynamicsECCOMAS Thematic Conference Multibody 2003,IDMEC/IST, Lisbon, July 1-4, 2003