1,720,966 research outputs found
POD-DEIM model order reduction for strain softening viscoplasticity
Full text linkWe demonstrate a Model Order Reduction technique for a system of nonlinear equations arising from the Finite Element Method (FEM) discretization of the three-dimensional quasistatic equilibrium equation equipped with a Perzyna viscoplasticity constitutive model. The procedure employs the Proper Orthogonal Decomposition-Galerkin (POD-G) in conjunction with the Discrete Empirical Interpolation Method (DEIM). For this purpose, we collect samples from a standard full order FEM analysis in the offline phase and cluster them using a novel kk-means clustering algorithm. The POD and the DEIM algorithms are then employed to construct a corresponding reduced order model. In the online phase, a sample from the current state of the system is passed, at each time step, to a nearest neighbor classifier in which the cluster that best describes it is identified. The force vector and its derivative with respect to the displacement vector are approximated using DEIM, and the system of nonlinear equations is projected onto a lower dimensional subspace using the POD-G. The constructed reduced order model is applied to two typical solid mechanics problems showing strain-localization (a tensile bar and a wall under compression) and a three-dimensional square-footing problem
Sensitivity analysis of nonlinear frequency response of defected structures
Full text linkThe computation of the steady-stateresponse of large finite element discretized systems subject to periodic excitations is unfeasible because of excessive run time and memory requirements. One could in principle resort to reduced order models stemming from the high fidelity counterparts, which typically require a solution time orders of magnitude smaller. However, when many simulations are required, as in the case of parametric studies, the overall effort could be still significant and the analysis process could be severely hindered. In this work, we propose a sensitivity approach to assess the influence of model parameters on the nonlinear dynamic response. As opposed to the costly evaluation of reduced order solutions over a range of excitation frequencies and model parameters, the sensitivities of a nominal response allow one to approximate the dynamic response by a simple evaluation of an expansion in the directions spanning the parameter space. Special care must be taken on the closure equation that needs to be appended to the system of equations stemming from the harmonic balance method. We discuss the limitations of the current constant frequency approach and propose an improvement. We demonstrate the merits of the proposed approach on a micro-electro-mechanical system affected by parameterized manufacturing defects. Leveraging from a previous contribution, the nonlinear response and the sensitivities are obtained from a reduced order model which is analytical in the defect parameters. Our procedure is able to deliver accurate probability density functions of quantities of interest (e.g. nonlinear resonance peaks, triple solution bandwidth, etc) against statistical distributions of manufacturing defects at negligible computational cost
A nonlinear reduced order model with parametrized shape defects
Full text linkWe propose a formulation to derive a reduced order model for geometric nonlinearities which is shown to be valid for a set of parametrized defects. The latter are imposed in terms of the superposition of precomputed perturbations of the nominal structure's 3D-mesh, and parametrized by their amplitudes. A reduced order model is then built once and for all using these defect shapes and the nominal model information only. A suitable reduced order basis is introduced as well in order to effectively represent the influence of the defects on the dynamics of the structure. In contrast to many nonlinear parametric reduced order models, the one we propose does not need any previous training of the model in the parameter space. In this way, prohibitively expensive full order simulations can be avoided and offline times are greatly reduced. Numerical tests are performed on a MEMS resonator and a silicon micro-beam to study the effect of shape imperfections on the dynamic response of the system
A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion
Full text linkWe present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy
Finite element based reduction methods for static and dynamic analysis of thin-walled structures
No full textAbstract not availableAerospace Engineerin
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Accuracy of Calculation Procedures for Offshore Wind Turbine Support Structures
No full textThe demand for energy will continue to increase in the coming years and offshore wind energy shows great potential to become a key player in Europe’s renewable energy future. The wind flow offshore is more stable and the average wind velocity is higher than onshore. Moreover, no size restriction exists for offshore wind turbines. However, the levelized cost of electricity for offshore wind energy should be decreased in order to ensure that the transition to offshore wind energy is economically feasible. One way to realize this cost reduction is by optimizing the structural design of the offshore wind turbine. As the support structure is one of the main cost items of the offshore wind turbine, structural optimization of this structure should be investigated. In the current support structure design procedure, the turbine designer (TD) is responsible for the design of the tower, whereas the foundation designer (FD) is responsible for the design of the foundation and the transition piece. These designs are driven by the dynamic loads acting on these structures during the lifetime of the offshore wind turbine. Hence, accurate load predictions are a rerequisite to enable design optimization of the support structure. Therefore the TD runs a large number of aero-elastic simulations with the complete offshore wind turbine model to determine the global loads on the offshore wind turbine. From these simulations, loads or displacements at the tower/foundation interface are extracted and provided to the FD. Subsequently, the FD uses these interface responses in a post-processing analysis in order to obtain loads in the foundation structure. However, inaccuracies can arise at two points in the support structure calculation procedure: * In the aero-elastic model if a reduced or simplified foundation model is integrated in order to keep the aero-elastic model compact and to minimize computation costs. * In the post-processing analysis applied by the FD. To retrieve the response of the foundation model the FD can use either interface loads or displacements, applied either in a dynamic or a quasi-static analysis. By combining different model reduction and post-processing methods, various calculation procedures can be defined. In this thesis the accuracy of these different calculation procedures, that eventually determine the design of the offshore support structure, are analyzed. To this end, both a qualitative and a quantitative study are performed. In the first part of this thesis the different calculation procedures are analyzed from a theoretical perspective. Model reduction methods are explained and the impact of the reduction on the accuracy of the results is investigated. Furthermore, the accuracy of the post-processing methods is investigated and the differences between a quasi-static and a dynamic analysis and between a force and a displacement controlled approach will be outlined. The second part of this thesis concerns a case study in which the various calculation procedures will be applied to a representative offshore wind turbine model on both a monopile and jacket type of foundation. Finally, as fatigue is often the main design driver of the support structure, this case study is used to analyze the impact of an error in the response on the fatigue damage result. This study shows that the use of reduced foundation models in the aero-elastic model can decrease the accuracy of the results, as the reduced model is an approximation of the full model. Therefore, in order to obtain accurate results, the offshore wind turbine model with the reduced components should be spectrally and spatially converged within the frequency range of the external load spectrum. With respect to the post-processing methods, it will be shown that a quasi-static analysis provides accurate results only if the first free or fixed interface eigenfrequency of the foundation structure is higher than the highest excitation frequency in the external load for respectively the force or the displacement controlled approach. Moreover, as the first fixed interface eigenfrequency of a structure is higher than its first free interface eigenfrequency, a quasi-static displacement controlled approach will remain accurate up to higher excitation frequencies than a quasi-static force controlled approach. Furthermore, since both a monopile and a jacket based support structure are modeled, it is found that the accuracy of the different calculation procedures strongly depends on the type of foundation structure. This is reflected by the results from the fatigue calculations; as the monopile behaves in a quasi-static manner within the excitation bandwidth the fatigue damage results are relatively accurate for all calculation procedures. However, the jacket shows much more dynamic behavior and subsequently the fatigue damage results of the quasi-static force controlled approach are highly underestimated. Finally, it is shown that when expanding the response of reduced models, the fatigue damage results can be greatly improved through a quasi-static residual load correction. In conclusion, this work gives an overview of the accuracy of different calculation procedures to determine the design of an offshore wind turbine support structure. As the accuracy depends on several aspects (i.e. characteristics of the structure, use of reduced models, post-processing method and external load spectrum), several requirements are formulated for specific calculation procedures in order to make sure the obtained results are accurate. As a result, one can have more confidence in the optimized design of the support structure and over-dimensioning or the application of additional safety factors is unnecessary. In the end, this will lead to a reduction of costs for the support structure which thereby reduces the levelized cost of electricity for offshore wind energy.Precision and Microsystems EngineeringMechanical, Maritime and Materials Engineerin
Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives
No full textNonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associating with NNMs is that the computation for real-size models is expensive, particularly for models with distributed nonlinearities e.g. those of geometric nature. The NNM computation involves repeated direct nonlinear time integration combined with a sensitivity analysis to determine the frequency-energy dependency for the modes of interest. In this thesis, NNMs are computed from reduced order models (ROMs) comprising LNMs and Modal Derivatives (MDs). The MDs have a direct relationship with the vibration modes (VMs), and can therefore be used as natural extension to LNMs to accurately represent the NNMs of interest. Two projection based reduction methods are used, one being the classical Galerkin projection reduction technique, the other is obtained from a quadratic coordinate transformation based on the Taylor series expansion. The NNMs computed from the ROMs are directly compared to those obtained from the full system analysis, which will highlight the importance of MDs in capturing essential nonlinear phenomena. The methodology is demonstrated on a doubly clamped beam, a shallow arch and a Roorda-frame.Engineering MechanicsPrecision and Microsystems EngineeringMechanical, Maritime and Materials Engineerin
Model order reduction of nonlinear magnetic problems
No full textComputational numerical methods are important tools in science and technology today. Numerical simulations of nonlinear problems are usually computationally expensive. Model order reduction is a technique to reduce computation time of mathematical numerical models. Model order reduction of nonlinear problems is still in its developing state. In this thesis, model order reduction techniques are implemented to a special class of nonlinear problems, where the non-linearity is localized in only some parts of the domain. The implementation of model order reduction techniques for this work can be divided into three parts. The first part consists of identification of the part of the domain, that is acting nonlinearly, and then condensing the rest of the domain on this nonlinear part. This method is called nonlinear condensation. The second part consists of finding appropriate reduction basis for the conventional Galerkin projection method. Reduction basis formed using static modes, magnetic modes, modal derivatives and proper orthogonal decomposed snapshots are used. The third part is called hyper reduction and is based on the idea of approximating the nonlinear terms of the analysis, by computing it over a subset of elements rather than the complete domain. To compensate for the energy of the remaining elements, elemental contribution terms from the sampling subset are multiplied by corresponding weights. Hence the name of this method: the Energy-Conserving mesh sampling and weighting (ECSW) hyper reduction method. This thesis concentrates on computational magnetics, but the discussed methods can be applied to any other problem involving localized non-linearities. These methods have been found to yield moderately accurate to very accurate results, while providing a speed-up of an order of magnitude of one to two.Engineering MechanicsPrecision and Microsystems EngineeringMechanical, Maritime and Materials Engineerin
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