ixcube 4-10 Brief introduction for membrane and cable systems.

Transcription

1 ixcube 4-10 Brief introduction for membrane and cable systems. ixcube is the evolution of 20 years of R&D in the field of membrane structures so it takes a while to understand the basic features. You must consider that 3 built in Form-Finding methods are available so input differs in function of the type of modelling and strategy used.

2 Force Density Method (FDM) This method models the membrane as a net of links and nodes. The links between nodes will be flagged as membrane elements and will have a property that indicates if the link is a warp or a weft fiber. A Membrane model will be made out of 2 layered groups a Tenso-Group and a Mesh Group. The Tenso-Group will keep the link elements and we will treat them as normal fem2 elements ( we assign C value, material and any other property) while the mesh group will be used to calculate area, apply wind and snow loads on the model and at the end make final patterns for production. Pre-Stress of the membrane will be controlled by the C values assigned for the membrane links and boundary cables. Prestress can be plotted in Plot -> Response Fig 1

3 Fig 2 Fig 3 - Pre-stress plot after form finding with the FDM method

4 NFDM and URS Method When using the NFDM method or the URS method we always use Tenso-Groups to model our membrane shape but the FDM net is not used anymore. The solver will find the final shape using the Triangle mesh elements and this means only the mesh sub-group is filled with a triangle mesh. The NFDM and the URS methods are conceptually more easy to use since we use real units (pre-stress and cable pre-tension are force/length and a force ). The quality of the mesh of course will drive the quality of the final solution like any FEA analysis. Fig 4 - Example of stress plot for a model using the NFDM method

5 GENERAL CONCEPTS The fem model needs to be created inside Fem Groups: There are 3 types of Fem Groups: 1) Tenso-Group : Tenso-Groups are special groups to keep membrane mesh elements. The Tenso-Group will create automatically a sub-group named Mesh when we add Tri-mesh elements. Membrane loads are applied to the mesh and also this is the only group enabled in the patterning module. 2) Fem2 : Fem2 is a group for 2 node elements. We can add cable,truss and beam elements inside a Fem2 group. Fem2 groups have the facility to group simple elements in chains ( a list of connected fem2 elements) Chain elements will compare under the Fem2 group in the browser tree and we can select, change their property or delete them in a simple and direct way enabling a simplified editing for list s of connected elements. 3) Shell-Plate group : This group will hold Plate-shell elements. These elements have a bending, shear and in plane stiffness. Fem2 Main Properties : When we select a fem2 object we see a list of properties

6 Fig 5 Fig 6 C Value (FDM only. Valid for all elements flagged as FF-Deformable) If we are using the FDM ( Force Density Method ) the pre-stress for the membrane and the pre-tension for the cable elements is controlled by the C value. The C value is the ratio between F/L where f is the final Force in the Element and L is the final length, so the C value has the dimension of a force over a length, if you change units remember to check C values of the membrane and cable elements. Type This is the type of fem element, available types are : Membrane : this is a special element used ONLY in FDM method Cable : Tension only element Beam : Timoshenko beam element Truss : Tension-Compression only element Gap : compression only element Spring : Spring element

7 Rigid-Link : infinite stiff element Notes: The membrane type element is a special element for membrane models used in the FDM method. With this element we model the Membrane-Net in the Force Density method and the software will calculate automatically are influence. The stress is controlled with FDM C value. Behavior Only for Beam elements. We generally set beam elements to have a linear behavior, this means small deformations and rotations while the non-linear beam will undergo large rotations. Use non-linear for all other elements ( cables, truss, ) Deformability (This is a very important Flag) This property controls if the element geometry will be a result of the Form-Find process OR it will stay in a fixed position while form-finding and after that become a part of the stiff model. For example we are making a model made out of a membrane connected to a stiff ring on a pole. While Form-Finding we do not want to deform the ring or the pole but only the membrane, after form-finding a global equilibrium must be implied between the membrane stress state and the supporting pole-ring element. For this reason after the FF step a global stiffness matrix analysis will find the final equilibrated solution where the only loads applied in the model are the pre-stress of membrane and cables.

8 Seed This is the common property for fem elements, it collects a material where E modulus, Poisson and other material related properties are set plus a geometry cross section with Inertia, Area ect. Please look at the Data-Base Explore to see available materials and sections. Angle (Only Beam elements) This is the angle of rotation around the local X axis ( axial axis ) of the stiffness plane (Y-Z or plane 2-3). The beam elements have a local reference frame called (X-Y-Z) the colors of these axis on screen are always the 3 main RGB (Red, Green, Blue) so it s easy to remind which color is the 1 2 or 3 local beam axis. Plot of the local axis can be activated in Plot->Options->Labels Object Axis (see figure 7) Fig 7

9 End Restraint A - End Restraint B (Only Beam elements) Only for Beam elements. Beam elements are by default fixed to the 2 end nodes with all DOFS (degrees of freedom) We can locally unfix one or more degree of freedom by setting the relative check box to false The check boxes are : Dx = movement in local X direction ( direction 1 ) Dy = movement in local Y direction ( direction 2 ) Dz = movement in local Z direction ( direction 3 ) Rx = rotation around local X direction ( direction 1 ) Ry = rotation around local Y direction ( direction 2 ) Rz = rotation around local Z direction ( direction 3 ) A value of True = Fixed False = Free Weft Flag (FDM only - Only Membrane Elements ) This flag tells which direction this fiber belongs too (Warp or Weft ). When using the FDM method the membrane model is made out of a spatial grid of membrane elements. Since membrane material has generally different properties in warp and weft we need a method to specify which elements are warp and which elements are weft. Pretension (NFDM,URS and FDM method) This is the pre-tension for elements flagged as FF-Deformable when we are using the NFDM method or URS method. (if we are using the FDM method the C value controls pre-tension for elements flagged as FF-Deformable).

10 For elements flagged as Stiff-Deformable we can also assign a pretension in this field. After Form-Finding the system will start a non-linear Newton Raphson matrix analysis. In this analysis the elements flagged as Stiff-Deformable will have initial pretension equal to the value input in this field. (Elements flagged as FF-Deformable will have a pretension computed in the FF process). NOTE: If we are using the FDM method and we want to assign a pre-tension to elements flagged as stiff-deformable we NEED to activate the check box keep pretension (see fig 6 ) Properties for Membrane Mesh Elements Fig 8 When using the NFDM or the URS method we will see after selecting mesh elements the properties: (fig 8 )

11 N Layers: Number of membrane layers (Not used in the stiffness analysis for the current release) Warp Stress Pre-stress in the warp direction as F/L ( force over length ) Weft Stress Pre-stress in the weft direction in F/L ( force over length ) Seed Material to use for this membrane mesh Be aware that the direction of the warp-weft fibers must be assigned. Please look at the video tutorials on how to assign warp-weft direction to a mesh Group.

12 Shell elements In the current version shell-plate elements can be used only as stiff-deformable. This means they will never enter the FF process. This will change in future releases. When we select a plate-shell element we can see the properties : Thickness Thickness of the plate shell element Deformability Use stiff-deformable for current version Seed Material to use for the plate-shell element

13 Layers and Groups Like any CAD program the system has the concept of layers to group common entities. FEM Groups ( Tenso-Groups, Fem2 and Shell-Plate Groups ) will be placed under the current layer when they are created. You can drag and drop a group to a new layer to put order in your model. Layers not empty cannot be deleted. Fem elements ALWAYS belong to a FEM group. A FEM group is in effect a container for FEM entities. A FEM Group behaves like any CAD entity (line,circle,solid,surface). When we issue a transformation tool like Copy, Rotate, Mirror, Polar Array, Scale the ENTIRE group and not the specific sub-entities will be transformed (copied). Only the DELETE command will be applied on sub-entities ( FEM elements). To delete a FEM Group there is a specific command on the browser. Example : We create a Tenso-Group and fill it with a triangle mesh using one of the modeling tools available.

14 If we select one triangle from the mesh and issue a copy the entire Mesh Plus its parent Group (Tenso-Group ) will be copied. Note: CAD commands will operate on FEM groups ONLY with a PRESELECTION. This means : A) Select one or more fem elements B) Recall a CAD transform command C) At the prompt to select elements click the Enter key to accept current selection D) Input other parameters to run the command If we recall a CAD transform command without selecting any FEM element these will NOT BE selectable at the command prompt. This behavior lets us control in a accurate way what we are moving copying ect. Form-Finding When the Form-Finder is run the following steps are performed in sequence : 1) The restraints of the model are checked. Nodes attached to elements that do not have rotational stiffness are automatically fixed for the rotation. 2) The system checks the model to detect part flagged as FF-Deformable and the part flagged as Stiff-Deformable (if any exists). 3) The objects flagged as Stiff-Deformable will fix the restraints of connected nodes to Fully-Fixed and the relaxation procedure starts. 4) After relaxing the model with the current FF-Solver (FDM,NFDM or URS method ) the nodes fixed as step 2 assume their original restraint (user restraint or restraint set at step 1 ) 5) If a Stiff-Deformable part exists a Newton-Raphson stiffness analysis is performed where the global model will have only pre-stress computed at step 3.

15 6) At the end of the Stiffness analysis elements are updated and final node positions, element stresses and forces are stored as part of the Initial state. Stiffness analysis The fem solver is based on a classical FEA analysis matrix solver with a nonlinear Newton Raphson method. For the stiffness analysis we must set : Number of increments = in how many steps the loads are applied on the model Number of iterations = within each step the solver will iterate at maximum n of iterations to converge to assigned tolerances. For the tolerance we assign a threshold value for : Energy Et : if for 2 consecutive iterations i and i+1 Ei+1 Ei > Et the solver will stop with a convergence not reached error Displacements Dt : if for 2 consecutive iterations i and i+1 Di+1 Di > Dt the solver will stop with a convergence not reached error. Residual Forces Ft : if for 2 consecutive iterations i and i+1 Fi+1 Fi > Ft the solver will stop with a convergence not reached error.