ASSESSMENT OF A MULTI-THREADED FEAP PERFORMANCE IN COMPOSITE SHELLS COMPUTATIONS

P. Jarzebski (Karlsruher Institut für Technologie), K. Wisniewski (Institute of Fundamental Technological Research Polish Academy of Sciences), W. Wagner (Karlsruher Institut für Technologie)

17:50

Multi-scale models used in computation of composite shells require a significant com-putational power and, therefore, a finite-element code should take advantage of such techniques as: 1) parallel solvers, e.g. PARDISO, MUMPS, PaStiX, (2) parallelization of a loop over elements using, e.g. OpenMP, and (3) domain decomposition and spread-ing tasks over a cluster of computers, usspread-ing e.g. MPI. A significant programmspread-ing effort is needed to convert a large and complicated existing FE code into a parallel one; in this paper, we focus on the first two techniques.

Personal computers have processors with several (2-32) cores, which make them shared memory architectures, for which communication is implicit. An appropriate paralleliza-tion technique for such architectures is a threading parallelism, which may be based on the OpenMP standard, specifying parallelization in terms of compiler directives, library routines and environment variables. OpenMP defines the ’fork-join’ parallelism, because it launches multiple parallel threads (fork) in parallel regions of a code and joins them into a single thread (the master one) for serial processing in non-parallel regions.

We parallelize a loop over elements in the research code FEAP (Taylor, 2014) using OpenMP to enable parallel computations on a multi-core machine with shared memory.

This requires several modifications of the code and a specific method of synchronization for assembling, see (Jarzebski, Wisniewski & Taylor, 2015). Besides, the interface to the parallel sparse solver HSL MA86 (Hogg & Scott 2010) is implemented, which enables the use of various re-ordering methods. The so-parallelized FEAP is designated ‘ompFEAP’

and preliminary tests show its very good performance (Jarzebski, Wisniewski, 2016).

In this presentation, we assess the performance of ompFEAP on the machine with up to 32 cores using several shell benchmarks. Computations are performed on the bwUni-Cluster of the Karlsruhe Institute of Technology, which built of nodes with either two Octa-core Intel Xeon E5-2670 processors or four Octa-core Intel Xeon E5-4640 proces-sors. We show that the applied parallelization implies a significant speedup and reduces the time of computations at the expense of an only small increase in memory usage.

Hogg J., Scott J. (2010). An indefinite sparse direct solver for multicore machines.

Technical Report TRRAL-2010−011.

Jarzebski P., Wisniewski K., Taylor R.L. (2015). On parallelization of the loop over elements in FEAP. Computational Mechanics 56(1), 77–86.

Jarzebski P., Wisniewski K. (2016). Performance of the parallel FEAP in calculations of effective material properties using RVE. Advances in Mechanics: Theoretical, Com-putational and Interdisciplinary Issues, CRC Press/Balkema, 241-244.

Taylor R.L. (2014). FEAP Ver. 8.4.

Topology Optimization for Injection Molding of Short Fiber-Reinforced Plas-tics

F. Ospald (TU Chemnitz), R. Herzog (TU Chemnitz) 18:10

Today there exists a huge demand for technologies which enable and facilitate the mass production of fiber reinforced composites. Injection molding of short fiber reinforced plastics (SFRP) is a quite popular method especially in the automotive industry, pro-viding high stiffness levels on the one hand and complex moldable shapes on the other hand. Due to the high cost of mold production and injection molding machines, nowa-days lots of research is done to improve models and to develop software for the simulation of this process. This allows to detect problems with the mold design and optimization of the part performance and quality at an early stage of the development.

In the case of SFRP injection molding, the mechanical properties of the finished part are mainly influenced by the local fiber orientation, which itself depends on the shape/topology of the part. We investigate an approximate approach for the compliance-based topology optimization for such parts, by replacing the costly filling and fiber orientation simulation by the solution of an eikonal equation which determines the principal fiber orientation.

The problem is formulated as a variational problem and discretized with the finite ele-ment method. The optimization problem is then solved using the classical SIMP method in combination with a transversely isotropic material law. As a second application we consider topology optimized parts for the identification of material parameters in the sense of optimal experimental designs.

S 4 : Structural mechanics

Thursday 14:00 - 16:00 Marienstr. 13, Ground floor, Lecture hall C

Experimental and numerical investigation of a walking soft robot

K. de Payrebrune (TU Freiberg) 14:00

In many industrial and biomedical fields, robots and automata are used to reduce dan-gerous or repeatable tasks people do not wish to perform, to overcome human limitations in strength and speed, or to operate in hostile environments where humans are unable to work [1, 2]. Recently a new kind of “bio-inspired” robots, so called soft robots, has been the object of extensive research. Thereby, the research is motivated by the potential benefits of soft robots in applications to healthcare, cooperative human assistance, ser-vice robots and biomechanically compatible interactions [2, 3, 5]. With the absence of a skeleton-like structure and the use of soft materials, complex locomotion or movements of the soft robot are possible and hence, situation-related adapted behavior feasible.

However new control strategies and mathematical models are required to advance the field of soft robots and to take their special characteristics into account [5, 6].

This work presents a mathematical model based on the nonlinear rod theory of Euler to reproduce the locomotion of a pneumatically actuated rubber based continuous soft robot. Therefore, the complex geometry of the soft robot is reduced to a material curve in space for which the flexural rigidity is identified experimentally. Further, the pneu-matic actuation is converted into a non-constant pressure dependent curvature, which is the driving input parameter in the model. Solving the balance of linear and angular momentum, the deformation of the soft robot can be predicted under consideration of applied forces and given boundary conditions.

To analyze the locomotion of a quadruped soft robot, its geometry is represented by a segmented rod model. The actuation of each robot segment can be controlled separately and an actuation sequence identified such that the robot moves forward. For the sim-plest controllable gait of a caterpillar, the locomotion is studied for different pressures.

Although the rod theory simplifies the geometry of the robot strongly, very good agree-ments between measureagree-ments and simulations are found. This strengthens the idea to use the computational efficient but geometrically simple rod theory to model complex dynamically actions of soft robots.

[1] M. Hägele and K. Wegener. Service-Roboter-Visionen. Hanser Verlag, (2004).

[2] C. Majidi. Soft Robotics SoRo, 1, 5 –11 (2013).

[3] S. Kim, C. Laschi and B. Trimmer, Trends in Biotechnology, 31, 287 –294 (2013).

[4] R. Pfeifer, M. Lungarella, and F. Iida, Commun. ACM, ACM, 55, 76 –87 (2012).

[5] F. Iida and C. Laschi, Procedia Computer Science, 7, 99 –102 (2011).

Thermomechanical measurement of a brake disc

A. Lamjahdy (RWTH Aachen University), B. Markert (RWTH Aachen University)

14:20

The experimental study of the thermomechanical behaviour of disc brakes is reported.

The goal of this study is to better understand and explain the thermomechanical effects of disc brakes by use of an advanced measurement system. Temperature measurements with an infrared camera, pyrometer and thermocouples have been carried out on the rubbing surface of brake discs and brake pads on a flywheel test bench. The mechanical behaviour is determined with a high-speed detecting capacitive sensor. Based on the advanced measurement system, a detailed description of the occurring phenomena is possible. From these experimental researches, a scenario of brake cycles is conducted.

Moreover, the change of the pad stiffness and pad contact length is studied [1], [2].

Finally, a detailed discussion of the observed experimental behaviour and the theoretical approaches [3] is proposed.

[1] Dufrenoy, P., Weichert, D., Experimental Analysis of Hot Spotting in Sliding Systems, Springer Science, vol. 1, pp. 1-12, 2013.

[2] Wicker, P., Influence des garnitures de frein sur les sollicitations thermiques des disques TGV et consequences sur les risques de fissuration, Ph.D. Thesis, Ecole Central de Lille, 2009.

[3] Markert, B., A survey of selected coupled multifield problems in computational me-chanics, Journal of Coupled Systems and Multiscale Dynamics, vol. 1, issue 1, pp.

22 - 48, 2013.

An experimental and numerical study of gas pressure forming under shock-wave loading

N. Shirafkan (RWTH-Aachen University), B. Markert (RWTH Aachen University)

14:40

Explosive forming is an unconventional technique, in which a fluid is used as the pressure transmission medium. In gas pressure forming process, such as explosive forming, a plate is plastically deformed by means of high kinetic energy. Good surface due to reduced friction, reducing the number of processes or tooling and higher formability of some materials in comparison to conventional methods are the principal advantages of this method. To optimize the forming process, the knowledge of material behavior under very high pressures and deformation rates is required.

This study aims to characterize the high strain rate phenomena for different metals by performing shock-wave tube tests and simulating those with ABAQUS. Series of shock-wave tests are performed for circular metal plate specimens to obtain the global displacement curves. The specimen deformation is controlled through selective material removal during sheet preparation using milling machines. For the numerical simulations, the Johnson-Cook model is used to predict the high strain rate phenomena during the tests. Some conclusions about the different material deformations will be presented.

[1] Sandeep P.Patil, Madhur Popli, Vahid Jenkouk, and Bernd Markert: Numerical modelling of gas detonation process of sheet metal forming, Journal of Physics:

Con-ference Series. Springer International Publishing,(2016).

[2] Yasar, M: Gas detonation forming process and modeling for efficient spring-back prediction, Journal of materials processing technology 150, 270 – 279 (2004).

[3] Syn, C., O’Brien, M., Lesuer, D. Sherby, O: An Analysis of Gas Pressure Form-ing of Superplastic AL 5083 Alloy, International Conference on Light Materials for Transportations Systems (2001).

A machine-learning approach to load-monitoring based on guided waves D. Hesser (RWTH Aachen University), B. Markert (RWTH Aachen

University)

15:00

The research field of structural health monitoring (SHM) describes the way to state the structural integrity. The research objectives are broadly diversified, which are all addressing the improvement of SHM technologies. The goal of this paper is to optimise the robustness over the complete lifetime. In this context, it is important to optimise the capability of sensor networks by applying intelligent signal processing models. These intelligent systems predict the health state based on acquired data in a real-time environ-ment. Piezoelectric sensor networks and guided-wave based analyses are combined with machine learning to create an efficient load-monitoring routine. This load-monitoring approach is chosen to track any change in the environmental conditions, which causes most of the problems in a reference signal based damage approach. The operational con-ditions will change continuously over the complete lifetime. Therefore, the output of the load-monitoring method can be used to compensate the acquired signals and to optimise the robustness of SHM systems. In addition to that, the machine learning algorithm is capable to deal with a big database, to evaluate the data in real-time and to solve the inverse problem. The analysed system will consist of multiple piezoelectric elements to apply guided-waves through the structure and to measure the wave response. The wave response will change based on the health state or loading condition. Finally, the proposed method will expose the influence of loading conditions to improve the perfor-mance and robustness of future SHM systems by means of machine learning and smart elements.

[1] Hesser, D.F., Markert, B.:Excitation strategies for vibration based damage detection using piezoelectric transducers and machine learning, PAMM, 16: 141–142, 2016, doi:10.1002/pamm.201610059

[2] Hesser, D.F., Markert, B.:Optimal Frequency selection for vibration based damage detection using pattern recognition, 8th European Workshop on Structural Health Monitoring (EWSHM), Bilbao, Spain, July 2016.

Multi-stage parameter identification of structural models from experimental data of varying assembly levels

B. Greiner (Universität Stuttgart), J. Wagner (Universität Stuttgart) 15:20

Classical applications of the Finite Element Method (FEM) in the aerospace industry include structural models of a high variety. For instance, models are used to predict dynamical properties during all design and integration phases such as qualification and characterization tests as well as in regular operation. During development, test results can be used for the identification and updates of model parameters, which in turn can then be employed to improve the prediction of other, not yet tested or not testable items.

In recent years, the development of structures with electromechanical components, such as actively controlled subsystems or systems with structural health monitoring, has extended the amount of available data suitable for parameter identification in operational conditions even beyond the development phase.

The contribution presents an approach of using measurement data from different stages of assembly levels for the identification and update of model parameters not only of individual part and assembly models but also for the integrated entire structure. The method is applied to a simple trusswork test structure as well as to the Stratospheric Ob-servatory for Infrared Astronomy’s (SOFIA) Telescope Assembly. Experimental modal analyses of subassemblies and the whole telescope assembly as well as vibration mea-surements during operational conditions are used to estimate model parameters for an updated finite element model derived from legacy models created during the observa-tory’s design phase.

While estimating parameters for subassembly models is often more intuitive than a global approach, estimation uncertainties propagating onto higher assembly levels have to be considered when assessing the model accuracy of a composed complete model.

Thermally loaded elastic-plastic shrink fit with FGM-hub T. Apatay (Gazi University), E. Arslan (Inonu University), W. Mack (TU Wien)

15:40

As shrink fits are a simple and cost-effective means of transfer of moment, they frequently are found in mechanical engineering. Some examples are shrunk-on rings, armature bandages, or tires of railway wheels [1]. Since under certain circumstances a partially plastic design for better utilization of the material is admissible [2], not only elastic but also elastic-plastic states have been studied comprehensively (see the application-oriented monograph [3]). In further investigations, special attention was paid on the one hand to the widely-used thermal assembly process (e.g. [5]) and on the other hand to the behaviour under operating conditions like heating and/or rotation (e.g. [5]). Since for given geometry of the shrink fit and friction coefficient at the interface between inclusion and hub the transferable moment depends solely on the interface pressure, the latter should be as large as possible; as mentioned above, this may be achieved by a partially plastic design, for example. Moreover, it becomes increasingly important in engineering practice to minimize the weight of the device while maintaining a good performance of the shrink fit.

Hence, an interesting option is the use of a functionally graded material (FGM), particu-larly for the hub [6]; as is well known, in a machine part of FGM the material properties like modulus of elasticity, density, coefficient of thermal expansion, and yield stress vary continuously and can - to a certain extent - be tailored in an appropriate way. Whereas in [6] a purely elastic shrink fit of this kind (under plane stress conditions, correspond-ing to a thin hub) was considered, the aim of the present study is to investigate the essential features of an elastic-plastic design, taking operation at elevated temperature into account. The material properties are presupposed to vary according to a power law in the radial direction; in particular, the case of radially decreasing density of the hub is considered. The latter property may be realized, e.g., by using a steel/aluminum FGM, which can be produced by a powder-metallurgical process. Specifically, the case of a shrink fit with solid inclusion under plane strain conditions subject to homogeneous heating is considered. It is shown that for a sufficiently large ratio of outer surface radius to interface radius a good performance of the device can be maintained while a substantial saving of weight as compared to a homogeneous hub is possible. All the results are derived by analytical means, and the effect of various degrees of grading is discussed. While numerical examples are given particularly for a hub of steel/aluminum FGM, the general results nevertheless are applicable to any FGM with similar ratios of the material properties of the constituents.

[1] I. Dolezel, V. Kotlan, B. Ulryich. Design of joint between disk and shaft based on induction shrink fit. J. Comput. Appl. Math. 270 (2014), 52–62.

[2] U. Gamer. A concise treatment of the shrink fit with elastic-plastic hub. Int. J. Solids Struct. 29 (1992), 2463-2469.

[3] F.G. Kollmann. Welle-Nabe-Verbindungen. Konstruktionsbücher Bd. 32. (Springer, Berlin, 1984).

[4] M. Lorenzo, J.C. Perez-Cerdan, C. Blanco. Influence of the thermal assembly process on the stress distributions in shrink fit joints. Key Eng. Mater. 572 (2014), 205-208.

[5] W. Mack, M. Plöchl. Transient heating of a rotating elastic-plastic shrink fit. Int. J.

Eng. Sci. 38 (2000), 921-938.

[6] E. Arslan, W. Mack. Shrink fit with solid inclusion and functionally graded hub.

Comp. Struct. 121 (2015), 217-224.

S 4 : Structural mechanics

Thursday 16:30 - 18:30 Marienstr. 13, Ground floor, Lecture hall C

Modelling of shell structures using the scaled boundary finite element method M. Wallner, H. Gravenkamp (University of Duisburg-Essen), C. Birk

(University of Duisburg-Essen)

16:30

In view of recent trends to lightweight structural designs, the numerical modelling of shell structures is a subject of high interest. Here, major challenges are associated with locking effects. The dominating locking effect for shells is membrane locking, a stiffening phenomenon where parasitic membrane stresses occur in pure bending situations.

Several approaches exist to avoid locking when modelling shell structures. These include reduced integration, assumed natural strain approaches, enhanced assumed strain meth-ods, and discrete strain gap formulations, for example.

This contribution presents a first approach to the numerical analysis of shell structures using the scaled boundary finite element method (SBFEM). The SBFEM is a semi-analytical technique which combines the advantages of the finite element method and the boundary element method. As in the boundary element method, only the boundary of the domain is discretized, thus reducing the spatial dimension by one. As a result of the semi-discretization process, a set of ordinary differential equations is obtained, which can be solved analytically to obtain the static stiffness matrix. The SBFEM is applicable to bounded and unbounded domains. Since locking effects are largely affected by the thickness of the structure, it is expected that discretizing only the mid-surface and handling the solution analytically in the through-thickness direction might decrease locking effects. The development of plate elements based on the SBFEM has already demonstrated that the proposed semi-analytical approach completely avoids shear lock-ing, which occurs for thin plates. Thus, the SBFEM seems to be a promising method to model shell structures with reduced locking effects.

First studies such as a simplified plane strain arch formulation to approximate an ax-isymmetric cylindrical shell will be presented. This approximation already shows a high correlation with the membrane theory of shells. Furthermore, first results obtained for 3D shell formulations will illustrate the potential of the proposed approach based on the SBFEM.

Automatic quadtree-based modeling using a coupled SBFEM/SCM approach H. Gravenkamp (University of Duisburg-Essen), S. Duczek

(Otto-von-Guericke-University of Magdeburg), C. Birk (University of Duisburg-Essen)

16:50

The quadtree decomposition is often recognized as a highly efficient way to discretize arbitrary geometries, particularly in the context of automatic image-based simulations.

A typical quadtree discretization consists of square-shaped cells only, while each square can successively be subdivided into four quadrants depending on the inhomogeneities

or gradients that need to be resolved. Unfortunately, this strategy is not applicable to conventional finite element implementations in a straightforward fashion without intro-ducing hanging nodes at the interfaces between elements of different size. It has been demonstrated recently that the scaled boundary finite element method (SBFEM) can directly exploit quadtree meshes since in this method only the boundaries of each cell need to be discretized by an arbitrary number of line elements. The SBFEM offers the

or gradients that need to be resolved. Unfortunately, this strategy is not applicable to conventional finite element implementations in a straightforward fashion without intro-ducing hanging nodes at the interfaces between elements of different size. It has been demonstrated recently that the scaled boundary finite element method (SBFEM) can directly exploit quadtree meshes since in this method only the boundaries of each cell need to be discretized by an arbitrary number of line elements. The SBFEM offers the