Displaying Results in Solids

Every day, thousands of structural engineers design structural components using design check formulas that include the critical buckling load. But where do these old formulas come from, that Leonard Euler established over 200 years ago and that form the basis of all three structural steel design concepts?

This paper is focused on the specific aspects of designing membrane structures that have specific requirements, such as form-finding and cutting pattern generation. An integral part of the design of these structures is the process of finding suitable prestressed shapes and generating cutting patterns. The text briefly describes two basic processes in the design of membrane structures. The physical principles are explained and the individual theses illustrated by examples.

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.

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

The form-finding process gives you a structural model with active forces in the "prestress load case" This load case shows the displacement from the initial input position to the form-found geometry in the deformation results. In the force or stress-based results (member and surface internal forces, solid stresses, gas pressures, and so on), it clarifies the state for maintaining the found form. For the analysis of the shape geometry, the program offers you a two-dimensional contour line plot with the output of the absolute height and an inclination plot for the visualization of the slope situation.

Now, a further calculation and structural analysis of the entire model is performed. For this purpose, the program transfers the form-found geometry including the element-wise strains into a universally applicable initial state. You can now use it in the load cases and load combinations.

The "Orthotropic | Fabric | Nonlinear Elastic (Surfaces)" material model allows you to define prestressed fabric membranes using the representative microstructure-solid element model – RVE.

By considering the fabric geometry in the microstructure model, the corresponding transversal strain effect can now be considered for all force conditions in the membrane.