Current Projects

Efficient calculation of shell structures from highly complex CAD models

Abstract Over the past decades, a divergence between design and computation has developed in the field of engineering. While the design in computer-aided design (CAD) programs is mostly based on Non-Uniform Rational B-splines (NURBS), and thus the majority of the geometries used can be represented exactly, the finite element method (FEM) with linear Lagrange basis functions dominates in the field of computation. The use of the latter method for computation leads to a faceted approximation of the geometry, and thus requires model conversion, which is often time-consuming and costly. This problem is the main motivation for isogeometric analysis (IGA), which has been researched worldwide since the mid-2000s, and is increasingly finding its way into computational practice as well. Numerous research papers have already proposed successful adaptations of elements and methods to isogeometric analysis, and found highly efficient formulations. One area that continues to require a great deal of research is the efficient and robust computation of highly complex CAD models, which can consist of thousands of individual domains. Although there are already a large number of publications on this topic, no satisfactory solution has yet been found.

In the project Efficient Computation of Shell Structures from Highly Complex CAD Models, which is funded by the German Research Foundation (DFG), this problem is to be researched and solved. For this purpose, a combination of the approach functions of the spectral element method with a NURBS geometry description is developed in order to completely avoid the problem of very small carrier areas in trimmed structures. Since the sub-area structure given in the NURBS geometry model is maintained and the individual sub-areas are meshed independently, the meshing procedure is trivial and requires very few resources. The individual sub-areas are connected using the Mortar method, which enforces equality of deformations along common edges in the weak form.

Author 
Dr. Nima Azizi

Funding Institution
DFG, Project number: 503246947

Keywords
spectral element method, trimmed NURBS, area coupling; shell formulation.

Determination of elastic-plastic stresses with the simplified yield zone theory under consideration of effects according to theory II. Order

Brief description
The simplified yield zone theory (VFZT) is used for the simplified estimation of state variables of elastically-plastically loaded structures, especially under cyclic loading. These are usually obtained using incremental elastic-plastic analyses for a finite element model of the structure over many loading cycles. The VFZT, on the other hand, allows the approximate determination of the structure behavior in the single-cycle condition in a simplified way. With only a few linear elastic analyses, an estimate of the accumulated strain, the strain amplitude, the deformation state, etc. can be obtained.

So far, however, the VFZT is only available for calculations according to I. order theory, in which the deformations must be so small that it is sufficient to formulate the equilibrium conditions on the undeformed system. However, it is obvious that for structures that can develop a ratcheting mechanism, second-order geometric effects also occur as a result of the progressive deformation, which make it necessary to formulate the equilibrium conditions on the deformed system (second-order theory). Within the framework of the project, a VFZT of the second order is therefore to be developed.

As an example, a pipe bend under in-plane bending is mentioned (in the adjacent figure simplified modelled as a half torus shell), in which downward forces ensure that the maximum stress arises through circumferential bending near the crown. If an internal pressure exists at the same time, its stiffening effect ensures a reduction of the bending stresses according to theory of the second order.

Author
Maximilian Zobel, M. Sc.
Prof. Dr.-Ing. Hartwig Hübel

Funding Institution
DFG, Project HU 1734/5-1

Keywords
fatigue, ratcheting, simplified elastic-plastic analysis