http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-53043 Topology Optimization of Structures in Unilateral Contact

optimization of structures in unilateral contac

Basic Analysis and Development of GPS-Trackingsystem for Android

Denna rapport redogör dels för utvecklingen av två applikationer för Android och dels för jämförelsen mellan de två. Dessa applikationer skulle regelbundet samla in och skicka sin position till en server för spårning. Tanken var att en administratör för till exempel ett orienteringsevent skulle kunna följa deltagarna i realtid. I slutet av rapporten återfinns en utvärdering av de två applikationerna som utvecklades som försöker avgöra vilken av de två applikationerna som verkar effektivast med avseende på energikonsumtion och dataöverföringshastighet.   Arbetet utfördes åt Progmera i Linköping som tidigare haft en del kunder inom bl a orienteringsbranchen.This report details both the development of two separate applications for Android and a comparative evaluation between the two. The applications where supposed to regularly collect and transmit the device position to a server for tracking. The applications where meant to be used at orientation events to maintain locations of all participants in real-time. At the end of this report the evaluation tries to determine the most effective solution based on energy consumption and data transfer time.   The project was performed for Progmera in Linköping, Sweden. The company had clients in the orientation business

Finite element treatment of two-dimensional thermoelastic wear problems

International audienceThe present paper concerns the numerical treatment of thermoelastic wear problems. The governing equations of thermoelasticity coupled to Signorini contact, Coulomb's friction and Archard's wear are formulated as a system of discrete equations. This equation system is solved, using a Bouligand differentiable Newton method, for five problems of didactic nature

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-86747 Topology Optimization of Hyperelastic Bodies including Non-Zero Prescribed Displacements

prescribed displacement

Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias

In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach

Sequential simulation of thermal stresses in disc brakes for repeated braking

In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles

Topology optimization of hyperelastic bodies including non-zero prescribed displacements

Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff–St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings

Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by Adopting an Eulerian Approach

In this paper frictional heating of a disc brake is simulated while taking wear into account. By performing thermomechanical finite element analysis, it is studied how the wear history will influence the development of hot bands. The frictional heat analysis is based on an Eulerian formulation of the disc, which requires significantly lower computational time as compared to a standard Lagrangian approach. A real disc-pad system to a heavy truck is considered, where complete three-dimensional geometries of the ventilated disc and pad are used in the simulations. A sequential approach is adopted, where the contact forces are computed at each time step taking the wear and thermal deformations of the mating parts into account. After each brake cycle, the wear profile of the pad is updated and used in subsequent analysis. The results show that when wear is considered, different distributions of the temperature on disc are obtained for each new brake cycle. After a few braking cycles two hot bands appear on the disc surface instead of only one. These results are in agreement with experimental observations

Topology optimization of structures in unilateral contact

Abstract In this paper a general framework for topologyoptimization of structures in unilateral contact isdeveloped. A linear elastic structure that is unilaterallyconstrained by rigid supports is considered. Thesupports are modeled by Signorini’s contact conditionswhich in turn are treated by the augmented Lagrangianapproach as well as by a smooth approximation. Thelatter approximation must not be confused with thewell-known penalty approach. The state of the system,which is defined by the equilibrium equation andthe two different contact formulations, is solved by aNewton method. The design parametrization is obtainedby using the SIMP-model. The minimization ofcompliance for a limited value of volume is considered.The optimization problems are solved by SLP. This isdone by using a nested approach where the state equationsare linearized and sensitivities are calculated bythe adjoint method. In order to avoid mesh-dependencythe sensitivities are filtered by Sigmund’s filter. Thefinal LP-problem is solved by an interior point methodthat is available inMatlab. The implementation is donefor a general design domain in 2D as well as in 3Dby using fully integrated isoparametric elements. Theimplementation seems to be very efficient and robust.The original publication is available at www.springerlink.com:Niclas Strömberg and Anders Klarbring, Topology optimization of structures in unilateral contact, 2010, Structural and multidisciplinary optimization, (41), 1, 57-64.http://dx.doi.org/10.1007/s00158-009-0407-zCopyright: Springer Science Business Mediahttp://www.springerlink.com