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It is important to steadily refine lightweight designs with regard to saving resources and energy in common with good economic efficiency.
Thin structured sheet metals offer significantly improved component stiffnesses in addition to an upgraded buckling behavior compared to flat, unstructured sheet metals.
By using a distortion energy based homogenization method it is possible to develop a mechanical surrogate model which describes effective mean properties. The accurate selection of symmetric and periodic boundaries enables to determine the required parameters. The conditions are contemplated on elementary cells whose structural mechanical behavior is representative for the elastic behavior of large structures. By doing this, the amount of elements can be reduced and thus the calculating time of large components can considerably be saved.
For an efficient surrogate model it is required to analyze and compare numerical with experimental investigations. Some different versions of optimization will be tested to get better approximation of the data.
In this paper a successful topology optimization of a centrifugally loaded aero-engine part is presented. For the topology optimization, which is a nonlinear problem due to several contact regions, a self-developed topology optimization algorithm in combination with a commercial FE-solver is used. The goal of the optimization was the reduction of stresses in the structure.
©2014 Rolls-Royce Deutschland Ltd & Co. KG. Published by Elsevier Masson SAS. All rights reserved.
The impact performance of structural components made of fibre-reinforced plastic is often one of the limiting properties during the design process. To improve the damage resistance regarding transverse low-velocity impact loading, a rubber layer (KRAIBON®) is integrated into the composite laminate of tubular carbon/epoxy specimens. Numerous impact tests, using two different rubber compounds and three different layups, are carried out. The specimens are impacted using a modified Charpy pendulum. Force–time histories have been used to determine the damage threshold load. To visualise damage such as delaminations and inter-fibre failures, the impacted samples have been examined using microsectioning.
It is shown that a significant improvement in impact damage resistance can be achieved by integrating a rubber layer into a carbon/epoxy laminate.
Due to the demand of more and more detailed FEM simulation results of whole aero-engine models, the number of DOF of such models (Fig. 1) increases dramatically. Although the available computational power for the solution of such highly nonlinear, dynamic boundary value problems also increased during the last years, the overall computational time of these high-fidelity models for the simulation of a few milliseconds of the running engine is in the order of several weeks even on high performance clusters with thousands of CPU cores. Typically, for such highly dynamic FEM computations explicit time integration schemes are used in order to solve the equations of motion. To keep such a numerical integration stable, the time step size may not exceed a certain critical
time step size. Unfortunately, the critical time step size of an explicit time integration algorithm for the engine models under consideration is in the order of 10-8. This means that the simulation of a running engine over a time span of a few seconds results in a computational time of several years with clusters, which are available nowadays. Therefore, implicit time integration schemes, which are unconditionally stable and allow much bigger time steps, have to be used. Since in an implicit integration, in contrast to an explicit one, an equilibrium iteration is always necessary, the computational costs for an implicit time step are much higher than for an explicit time step.
Almost all commercial FE codes use the classical Newmark implicit time integration scheme. It will be shown that this algorithm fails especially for the simulation of fast rotating structures if bigger time steps are used. This is demonstrated at the example of academic examples as well as for more realistic rotor models. To overcome the problems of the Newmark integration, a 3-Point-Newmark-
Euler-Backward integration scheme [1,2] has been selected, which consists of alternating Newmark and 3-Point-Euler-Backward steps. The additional interpolation information for the Euler-step is provided by the previous Newmark step. This integration procedure has been implemented and successfully applied to the FEM simulation of fast rotating structures, which will be also demonstrated during the presentation.
Instabilities occurring during the implicit time-integration are still handicapping a time-efficient solution of large FEM systems of equations. Especially the simulation of flexible rotating structures is barely mastered by implicit FEM codes. For this, the Newmark algorithm and related algorithms are used for many years. Here, we derive the reasons for the mentioned inevitable numerical issues and present concepts that lead to an efficient and stable solution.
This paper presents a new FE-based stress-related topology optimization approach for finding bending governed flexible designs. Thereby, the knowledge about an output displacement or force as well as the detailed mounting position is not necessary for the application. The newly developed objective function makes use of the varying stress distribution in the cross section of flexible structures. Hence, each element of the design space must be evaluated with respect to its stress state. Therefore, the method prefers elements experiencing a bending or shear load over elements which are mainly subjected to membrane stresses. In order to determine the stress state of the elements, we use the principal stresses at the Gauss points. For demonstrating the feasibility of the new topology optimization approach, three academic examples are presented and discussed. As a result, the developed sensitivity-based algorithm is able to find usable flexible design concepts with a nearly discrete 0 − 1 density distribution for these examples.
Considerations About the Necessary Mesh Density of Bearings in Detailed Finite Element Models
(2014)
In order to predict properly the behavior of very complex mechanical models, much focus needs to be done on the level of model details as well as the techniques used to predict component movements based on mechanical and thermal loads. In particular bearings and joints play a significant role in big model assemblies such as aero-engines where most of the structures are modeled by solid elements rather than using traditional shell or beam elements. This approach is very complex and expensive in terms of computational effort however can lead to increased simulation accuracy when done properly.
This publication will answer questions related to the modeling techniques required for detailed bearings (not only rotor bearings) and joints of an aero-engine application where these components are not idealized or simplified, i.e. the ball in a ball joint is meshed by solid elements. The investigation will discuss the question about the number of elements needed to mesh a ball joint in such a way that a correct rotation is possible. If the mesh is too coarse, a rotation would be impossible due to the faceting of the rotating parts. It will be shown that a proper rotation depends on a correct relation between the radius of the inner ball, the gap size of the bearing and the number of nodes in the circumferential direction. For this relation an analytical formula has been derived and successfully tested at some examples. Furthermore, some finite element codes offer the possibility of smoothed contact surfaces. These options improve the situation but they might cause issues too. For this reason these smoothed contact options are also considered under the aspects mentioned above.
Copyright © 2014 by Rolls-Royce Deutschland Ltd & Co KG
Creating very detailed finite element models of aero-engines is a very time-consuming process especially if structured meshes have to be generated for thousands of parts. Isogeometric analysis offers the possibility of an accelerated model creation process while achieving higher accuracy by using the non-uniform rational B-spline functions used for the geometry description also as basis functions for the finite element analysis. In this case, no meshing is necessary anymore. Here, we demonstrate this process by applying a self-developed tool which creates a geometry description and a computational model of a part at the same time. By the help of this tool we build up a simplified mechanical aero-engine model, which is used for transient implicit computations simulating the acceleration process of the rotor. We discuss the results as well as the computational time of isogeometric models in comparison to classical finite element models.
Especially for rotating structures like bearings non-smooth contact surfaces, as they appear in classical finite element modeling, lead to various problems during the analysis involving mesh interlocking and spurious oscillations in contact forces. In order to eliminate these issues, very fine meshes and additional smoothing strategies are employed in case of the finite element method (FEM).
But also Non-Uniform Rational B-splines (NURBS) based isogeometric analysis (IGA) can be very useful for the contact analysis due to the inherent higher order continuity of NURBS basis functions. In this contribution, the contact behavior using classical FEA and IGA approaches is studied by means of an example of a pendulum under gravitational load. In addition, a more practical example of a coupled IGA–FEM problem with a cylindrical roller bearing is also reported in this paper. This research study of contact analysis has been carried out for the above mentioned examples using LS-DYNA and illustrates that contact surfaces of coarsely meshed geometry lock the rotation of the parts in case of classical FEM. On the contrary, when the contact surface is represented by NURBS elements it allows the rotation of
the parts and effectively alleviates the contact force oscillation.
Comparative Evaluation of Isogeometric Analysis and Classical FEM with Regard to Contact Anaylsis
(2019)
Isogeometric analysis represents a newly developed technique that offers the application of Computer Aided Designs (CAD) concept of Non-uniform Rational B-Splines (NURBS) tool to describe the geometry of the computational domain. The simplified transition of CAD models into the computational domain eliminates the problems arising from the geometrical discontinuities induced by the faceted approximation of the mesh. Moreover, numerical analysis directly on NURBS objects significantly reduces the design-to-analysis time compared to traditional FEA approach. In the field of contact mechanics, when finite elements are applied to geometry with curved surfaces, the result is a non-smooth geometrical representation of interface surfaces which may lead to mesh interlocking, high jumps and spurious oscillations in contact forces. To eliminate these issues, various surface smoothening strategies are to be employed in case of FEM. Isogeometric based analysis alleviates these issues without employing any additional smoothening strategy due to inherent higher order continuity of NURBS basis functions and much more accurate results are obtained compared to conventional FE approach. In the current study, LS-DYNA is used to demonstrate the capabilities and advantage of an isogeometric analysis though an example of pendulum under gravitational load. The numerical simulation results are analytically validated and the comparison of NURBS surfaces with faceted surfaces is carried out to investigate the accuracy.