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  • Answer

    The cause of such an effect could be free edges, which can deform almost infinitely during Form-Finding. A state of equilibrium is difficult to achieve.

    As a basis for Form-Finding, there should be no free edges on the membrane surface. Ropes must be arranged on the free edges of the membrane whose stiffness can be based, for example, on the folded or reinforced edge strips of the membrane.
  • Answer

    The geometrically nonlinear flattening process takes over the real mesh geometry of the planar, buckling, single curved or double curved surface components from the selected cutting patterns and planarizes these planar components by minimizing the distortion energy assuming a defined material behavior.

    The iterative calculation used for this is controlled by the parameters in the menu "Calculation Parameters"/"Cutting Patterns" tab.

    The "Max Number of Iterations" parameter is limiting the scope of the calculation and stops the process when the set maximum iteration is reached. Provided the convergence criterion does not depend on the "Tolerance for Convergence Criterion" parameter in the Convergence range when the maximum iteration has been reached, the program displays error message 10154.

    If no error message is output by the program, it is reasonable to assume a proper convergence.

    The error can usually be solved by adjusting the flattening geometry or increasing the maximum number of iterations.

  • Answer

    Generally, the form-finding process in RFEM always considers all model data. In the form-finding, the elastic supporting elements on the membrane react with deformations in the direction of the acting membrane tension stress. The integral process passes the prestressed model for the subsequent calculation if the forces of all deformed elements are in equilibrium with the membrane geometry below the specified prestress.

    Figure 01 - Form-finding with deformed supporting structure

    However, the support structure's non-linearity "Only form-finding -Condition" (also called form-finding support) at the membrane edges can be suppressed for pure form-finding.

    In this case, the form-finding process results in a shape whose prestress is in equilibrium with the set form-finding support forces and remaining boundary reactions.

    For the structural analysis of all other load cases and combinations, the form-finding supports are deactivated and the form-finding support forces are applied as external loads to maintain the global equilibrium on the entire model.

    Due to the removal of supports, the membrane responds in the subsequent analyzes (LC and CO) with the semi-rigid supporting structure. Without additional loading, this reaction is similar to relaxation with a concomitant reduction in prestress

  • Answer

    The form-finding warps the surfaces into each other because the defined prestress on the boundary line between the two membranes does not coincide at the same angle and consequently the affected FE nodes are not in equilibrium with the boundary reactions. In this case, the FE nodes of the membrane surfaces move in the direction of the remaining resultant until the form-finding process finds a solution within the tolerance limit value. Since this solution is usually only achievable with a large displacement of the FE nodes in space, the surfaces assigned to the FE nodes seem to "swim" into each other.

    This behavior results in an unfavorable FE mesh arrangement in conjunction with a singular membrane force distribution. In this case, the prestress must be adjusted to reach a balanced position or an element must be arranged at the limit situation to transfer forces from the imbalance.

  • Answer

    The perimeter of membrane cuttings is described by boundary lines. These boundary lines can be as follows:

    1. globally defined boundary lines of the assigned membrane surfaces or
    2. retroactively introduced cutting lines for dividing the cuttings on the membrane surfaces
    The cuttings can only consist of a global line definition or retroactively imported cutting lines, or of mixtures of both types.

    Figure 01 - Border Lines of Cuttings

    The global boundary lines are untouchable due to their fixed geometry description (arc, circle, spline, etc.) and are thus also implemented in the design of the plane cuttings.

    On the other hand, subsequently introduced cutting lines are based on the FE Mesh of the surfaces assigned in the cutting line specification and have no influence on the mesh itself.

    The cutting units encircled by boundary lines and cutting lines take over the FE Mesh of the assigned surfaces for flattening. Since the cutting lines run over the FE elements themselves, independently of the global mesh in the boundary zone, the edges of the original FE elements can not be used to describe the cutting edge definition. In this case, the affected FE elements within the cutting line area are divided by the cutting lines.

    Depending on the orientation of the cutting line, the FE elements are split in the middle or almost on the edge. Since the FE elements on the edge can cause some problems with geometry, a certain tolerance limit has been entered for the decision. This checkbox controls the critical length ratio between the FE edge length specified by the cutting line and the original edge length of the FE. If the ratio is smaller than the given restrictive value, the cutting line refers to the original FE node.

    Figure 03 - Smoothing

    This fact may lead to an "Irritation" of the cutting line when the cutting lines are passing close to the FE element edges. This situation can be optimized by reducing the given limit of tolerance.

  • Answer

    The form-finding with prestress can be activated in the surface properties using the function "Edit Surface Stiffness" in the "Form-Finding" tab.

    The "Form-Finding" tab only becomes visible in the program when you activate the RF-FORM-FINDING module in the General Data for the surfaces with these types of stiffness:

    1. Default,
    2. Orthotropic,
    3. Membrane and
    4. Membrane - Orthotropic
    Generally, the program activates form-finding with a default prestress for surfaces with the stiffness type Membrane and Membrane - Orthotropic automatically.

  • Answer

    Singular reactions are induced by inappropriate form-finding data on membrane edges and an unfavorable FE mesh.

    1. If a cable with unfavorable form-finding settings (extreme sag or insufficient force) is applied to a membrane edge, the membrane surface is unusual in the form-finding process and results in a non-optimally arranged FE mesh with corresponding singular force reactions.

      Figure 01 - Unfavorable Form-finding Setting

      In this case, you have to adjust the form-finding settings of the membrane and the boundary element to each other.

    2. The form-finding process starts with the initial FE mesh design. If this arrangement is already unfavorable in advance and does not correspond to the necessary shape parameters, the force corresponding to the found shape is also negatively affected.

      Figure 02 - Wrong Mesh Design

      In this case, adjust the base geometry so that the initial mesh corresponds to all shape parameters.
    The graphical display of the mesh quality before and after form-finding can be activated in the Display Navigator.

    Mesh Quality

  • Answer

    The integral flattening procedure in RF-CUTTING-PATH does not flat each cutting individually, but rather the complete model geometry in one step. The line type of the respective cutting units also has an effect on the adjacent cuttings.

    In the case of a welding line between two cuttings, the program ensures a line uniformity in the connecting zone. The geometry of the cuttings is determined so that the relevant edge lengths of the cuttings are identical.

    The line type "Boundary line" allows for an independent view of the subsequent cutting units. The length of the boundary lines in the adjacent area may be different.

    Basically, the cutting units meet the following conditions:

    1. Surface compensation,
    2. Boundary line compensation and
    3. Type of the boundary line 
    These requirements are numerically precisely represented in the integral calculation. Especially for cuttings in the boundary area, the process can usually not determine a universally applicable cutting form due to too many boundary conditions.

    In this case, the program is approaching an optimal solution. The affected cuttings are particularly noticeable due to their curvature in relation to the uncompensated solution. Due to the greater degree of modification, these cuttings also differ slightly from the defined compensation specifications, but are in equilibrium with all other cuttings due to the overall calculation.

    Deformation Process

  • Answer

    The program does not define any fixed length for distribution of the boundary line compensation. Rather, the compensation is defined at the boundary line nodes and reacts in connection with the integral flattening depending on the geometry and stiffness.

    In the calculation, the integral flattening considers all compensatory strains on the surface and on the edges with the strains of flattening itself.

    Deformation Procedure

  • Answer

    The flattening procedure in the RF-CUTTING-PATTERN module is an iterative process that is flattening the respective areas of cutting pattern by minimizing the distortion energy assuming an assigned material behavior.

    Simplified, the method is bearing together the initial geometry in a press assuming a friction-free contact until the stresses from the flattening are in equilibrium with each other.

    → See Video

    As this process covers the complete mechanical system of the curved structural component, you can additionally consider the compensation directly as a applied expansion load.

    Figure 01 - Compensation

    Since the expansions from the compensation specification interact with the expansions from the flattening in the RF-CUTTING-PATTERN Algorithm, this type of considering compensation cannot be compared with the usual, flat scaling of uncompensated cuttings. The consideration of the complete "Cutting Mechanism" with all expansion terms could provide a very high-quality geometry.

    Before the flattening itself, the integral flattening procedure defines a coordinate system (warp and weft direction) from the mean orientation of the FE elements and uses the initially defined coordinate system to describe expansion of the compensation and stiffness, independently of the respective position of the FE elements in the coordinate system orientation. Thus, the comparison shown in the video is only valid for an isotropic linear elastic membrane model.

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