Underpressure Dome

Cable and tensile membrane structures are regarded as very slender and aesthetic building structures. The partly very complex double-curved shapes can be found using suitable form-finding algorithms. One possible solution is to search for the form via the equilibrium between the surface stress (provided prestress and an additional load such as self-weight, pressure, and so on) and the given boundary conditions.

Compliance with building codes, such as Eurocode, is essential to ensure the safety, structural integrity, and sustainability of buildings and structures. Computational Fluid Dynamics (CFD) plays a vital role in this process by simulating fluid behavior, optimizing designs, and helping architects and engineers meet Eurocode requirements related to wind load analysis, natural ventilation, fire safety, and energy efficiency. By integrating CFD into the design process, professionals can create safer, more efficient, and compliant buildings that meet the highest standards of construction and design in Europe.

In computational fluid dynamics (CFD), complex surfaces that are not completely solid can be modeled using porous or permeability media. In the actual world, examples of such things include windbreak fabric structures, wire meshes, perforated facades and claddings, louvers, tube banks (stacks of horizontal cylinders), and so on.

Compared to the RF-FORM-FINDING add-on module (RFEM 5), the following new features have been added to the Form-Finding add-on for RFEM 6:

• Specification of all form-finding load boundary conditions in one load case
• Storage of form-finding results as initial state for further model analysis
• Automatic assignment of the form-finding initial state via combination wizards to all load situations of a design situation
• Additional form-finding geometry boundary conditions for members (unstressed length, maximum vertical sag, low-point vertical sag)
• Additional form-finding load boundary conditions for members (maximum force in member, minimum force in member, horizontal tension component, tension at i-end, tension at j-end, minimum tension at i-end, minimum tension at j-end)
• Material types "Fabric" and "Foil" in material library
• Parallel form-findings in one model
• Simulation of sequentially building form-finding states in connection with the Construction Stages Analysis (CSA) add-on

Once you activate the Form-Finding add-on in the Base Data, a form-finding effect is assigned to the load cases with the load case category "Prestress" in conjunction with the form-finding loads from the member, surface, and solid load catalog. This is a prestress load case. It thus mutates into a form-finding analysis for the entire model with all member, surface, and solid elements defined in it. You reach the form-finding of the relevant member and membrane elements amid the overall model by using special form-finding loads and regular load definitions. These form-finding loads describe the expected state of deformation or force after the form-finding in the elements. The regular loads describe the external loading of the entire system.

Do you know exactly how the form-finding is performed? First, the form-finding process of the load cases with the load case category "Prestress" shifts the initial mesh geometry to an optimally balanced position by means of iterative calculation loops. For this task, the program uses the Updated Reference Strategy (URS) method by Prof. Bletzinger and Prof. Ramm. This technology is characterized by equilibrium shapes that, after the calculation, comply almost exactly with the initially specified form-finding boundary conditions (sag, force, and prestress).

In addition to the pure description of the expected forces or sags on the elements to be formed, the integral approach of the URS also enables a consideration of regular forces. In the overall process, this allows, for example, for a description of the self-weight or a pneumatic pressure by means of corresponding element loads.

All these options give the calculation kernel the potential to calculate anticlastic and synclastic forms that are in an equilibrium of forces for planar or rotationally symmetric geometries. In order to be able to realistically implement both types individually or together in one environment, the calculation provide you with two ways to describe the form-finding force vectors:

• Tension method - description of the form-finding force vectors in space for planar geometries
• Projection method - description of the form-finding force vectors on a projection plane with fixation of the horizontal position for conical geometries