Documents published in Scipedia

• A nonoverlapping domain decomposition method for extreme learning machines solving elliptic partial differential equations

  C. Lee, Y. Lee, B. Ryoo

  WCCM2024.

  
  

  Abstract

  Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which remain fixed throughout the computation, and uses a linear least squares method for training the parameters of the output layer of the neural network. It is known to be much faster than Physics Informed Neural Networks. However, classical ELM is still computationally expensive when a high level of representation is desired in the solution as this requires solving a large least squares system. In this paper, we propose a nonoverlapping domain decomposition method (DDM) for ELMs that not only reduces the training time of ELMs, but is also suitable for parallel computation. In numerical analysis, DDMs have been widely studied to reduce the time to obtain finite element solutions for elliptic PDEs through parallel computation. Among these approaches, nonoverlapping DDMs are attracting the most attention. Motivated by these methods, we introduce local neural networks, which are valid only at corresponding subdomains, and an auxiliary variable at the interface. We construct a system on the variable and the parameters of local neural networks. A Schur complement system on the interface can be derived by eliminating the parameters of the output layer. The auxiliary variable is then directly obtained by solving the reduced system after which the parameters for each local neural network are solved in parallel. An initialization method suitable for high approximation quality in large systems is also proposed. Numerical results that verify the acceleration performance of the proposed method with respect to the number of subdomains are presented.

  Abstract
  Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias [...]

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• A performance analysis procedure based on corrected displacements to evaluate the seismic response of steel 2D frames

  J. Mendoza, B. Sensale, A. Canelas

  WCCM2024.

  
  

  Abstract

  In the proposed methodology, a load pattern is applied in a non-adaptive fashion to obtain the seismic response of two-dimensional steel moment resisting frames. The proposed methodology is based on the structural dynamics theory and consists of a single run nonlinear analysis. This invariant load pattern is formulated by considering higher mode effects with the use of an effective modal mass contribution factor. Also, part of the proposed procedure, a corrective factor is employed to adjust the displacements obtained from the nonlinear analysis ensuring that the drift values obtained from the corrected displacements are adequate. The procedure allows the analysis of the structural response, i.e, story displacement and story drifts. To evaluate the methodology a nine-story steel moment frame is analyzed. Material and geometric non linearities are considered for all the cases. The results are compared with the ones obtained by the Nonlinear time history analysis.

  Abstract
  In the proposed methodology, a load pattern is applied in a non-adaptive fashion to obtain the seismic response of two-dimensional steel moment resisting frames. The proposed [...]

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• Adaptivity and uncertainty of multi-fidelity surrogate models for shape optimization

  J. Wackers, H. Pehlivan Solak, R. Pellegrini, A. Serani

  WCCM2024.

  
  

  Abstract

  Engineering design optimization based on expensive simulation is increasingly performed with surrogate models [1], i.e. approximate models fitted through a small dataset of simulation results. To build surrogates within the lowest possible computational budget, modern approaches use multi-fidelity data (combinations of cheap low-fidelity and expensive high-fidelity simulation results) and adaptive sampling strategies, which add simulation points one by one where they are most likely to discover the optimum [2]. Uncertainty estimation of the surrogate model is crucial for efficient adaptive sampling, since it guides the choice of new sampling points. Thus, underestimation of the uncertainty may lead to sampling in suboptimal regions, missing the true optimum. Existing surrogate models such as Gaussian process regression [3] and Stochastic Radial Basis Functions (SRBF) [4], provide uncertainty estimations, which are often used. Nevertheless, uncertainty estimation is so important for a successful surrogate model, that a more thorough investigation seems warranted. This is the main objective of this paper. This paper studies three issues with uncertainty estimation, in the context of multifidelity SRBF. First, most existing techniques rely on knowledge about the global behavior of the data, such as spatial correlations. However, the number of training points can be too small to reconstruct this global information from the data. We argue that in this situation, user-provided estimation of the function behavior is a better choice (section 3). Furthermore, the dataset may contain noise, i.e. random errors without spatial correlation (section 4). Surrogate models can filter out this noise, usually by modeling it as belonging to a normal distribution with zero mean, but this introduces two separate uncertainties: the optimum amount of noise filtering is unknown, and for a small dataset the local mean of the noisy data may not correspond to the true simulation response. Finally, in multi-fidelity models, the low-fidelity data are corrected by high-fidelity results, which could reduce the amount of uncertainty they introduce.

  Abstract
  Engineering design optimization based on expensive simulation is increasingly performed with surrogate models [1], i.e. approximate models fitted through a small dataset of [...]

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• A probabilistic graphical model approach to decouple multi-physics systems

  R. Baptista, T. Price-Broncucia, R. Morrison

  WCCM2024.

  
  

  Abstract

  Multi-physics scientific codes, like those used in weather prediction and spacecraft simulation, often involve the coupling of many subdomain models. The resulting models are generally expensive to run. These costs, along with the model’s complexity, make downstream tasks like model calibration and uncertainty quantification especially difficult. In this work, we simplify structure in multi-physics models by learning an undirected graphical model corresponding to the system state variables, where the edges in the learned graph represent conditional dependence between variables. Depending on the application of interest, the resulting graph may (1) reveal the probabilistic structure of the joint distribution; (2) identify the most important coupling variables (those that must be shared between subdomain models), and those which may be safely neglected; (3) identify candidate variables for first-pass verification tasks; or (4) decouple parts of a model, while maintaining accuracy in the model predictions. We illustrate these possibilities through two multi-physics numerical models, the Multiple Prediction Across Scales-Atmosphere (MPAS-A) code base and a fire detection satellite model

  Abstract
  Multi-physics scientific codes, like those used in weather prediction and spacecraft simulation, often involve the coupling of many subdomain models. The resulting models [...]

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• A mesoscopic domain decomposition approach composed with preconditioned conjugate gradient for modeling concrete

  Y. Xu, Z. Lin

  WCCM2024.

  
  

  Abstract

  Concrete structure is widely used in civil engineering. Numerical Simulation in mesoscale could provide a powerful analysis tool, which is based on the Total Finite Element Tearing and Interconnecting (TFETI) method. However, the unneglectable computational resource consumption limited the implementation of the meso-modeling method in engineering. This study investigated an efficient solution for concrete structure simulation, which was programmed using Python. A cantilever beam model with dimensions of 100mm × 50mm was simulated and studied. Then, a comparison with the ABAQUS model was given to demonstrate the accuracy and efficiency of the TFETI. Furthermore, a reliability analysis of a 300mm × 300mm concrete sample under the axial compression was performed. The results showed that the TFETI method achieved the same level of accuracy as ABAQUS. Moreover, the TFETI model solving required less computational source for the same number of elements as the one on the ABAQUS. In the reliability analysis of the axially loaded model, TFETI demonstrated superior solution speed. In conclusion, the TFETI exhibits excellent solution efficiency in finite element analysis of concrete structures, offering valuable insights and references for computational analysis of large-dimension civil engineering structures.

  Abstract
  Concrete structure is widely used in civil engineering. Numerical Simulation in mesoscale could provide a powerful analysis tool, which is based on the Total Finite Element [...]

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• A kinematically-exact reduced-order rod model for elastoplastic failure in thin-walled members

  M. Pires Kassab, E. Campello, A. Ibrahimbegovic

  WCCM2024.

  
  

  Abstract

  This work profits from a weakly coupled multiscale approach to derive a 7-DOF kinematically-exact reduced-order rod model for thin-walled members (starting from [1]) with a plastic hardening constitutive equation (based on [2]-[3]) that emulates the coupling between local buckling effects and hardening plasticity at material level. The model is implemented in an in-house finite element program for flexible thin structures and shall be validated against reference solutions. The novelty as compared to [2]-[3] is the extension to the fully 3D context, including torsion-warping degrees-of-freedom and arbitrary (plastic) failure mode capabilities, allowing for the modelling of complex structural problems involving thin-walled rod members. Although kinematically-exact rod models are able to detect critical loads and represent postcritical configurations in many common scenarios, issues are bound to emerge when local effects (such as buckling of web and/or flanges) are relevant, especially when they are coupled with plastic deformations. For rod models, the combination of those factors can be satisfactorily represented in a phenomenological way by embedding them on a stress-resultant/crosssectional strains hardening plastic model, instead of enriching the model´s kinematics and related material law. One can employ weakly coupled multiscale modelling to generate constitutive relationships among the different strain and stress in a pre-processing stage. Information about plasticity, loss of geometrical stiffness and local buckling are passed to the macro-scale rod model without increasing the amount of global degrees-of-freedom. Incremental steps of the numerical solution are solved with the split operator, whereby local variables are solved in an element-wise fashion and thus not introduced in the global system. Quadratic convergence of the overall solution procedure is achieved. The coupling among geometrical and hardening effects limits the load bearing capacity of the structural members and determinates the failure load.

  Abstract
  This work profits from a weakly coupled multiscale approach to derive a 7-DOF kinematically-exact reduced-order rod model for thin-walled members (starting from [1]) with [...]

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• A finite deformation micropolar peridynamic theory and its application to metamaterials

  . Sajal, P. Roy

  WCCM2024.

  
  

  Abstract

  Metamaterials with engineered microstructures exhibit exceptional properties such as negative Poisson’s ratio, energy absorption, and bandgap. These materials can prevent propagation of elastic waves in certain range of frequency called bandgap. The microstructure of these materials affects the overall response of the structures. Microstructures may undergo significant rotations and their rotary inertia needs to be considered along with deformation. As the metamaterials in the study involve cracks, we develop a finite deformation micropolar peridynamics (PD) theory. The proposed PD micropolar theory is validated by comparing the results obtained from the boundary element solutions of plate with a hole. The response of metamaterials with periodic arrangement of holes and cracks is studied under static and dynamic loads and the results are compared with the nonpolar PD theory.

  Abstract
  Metamaterials with engineered microstructures exhibit exceptional properties such as negative Poisson’s ratio, energy absorption, and bandgap. These materials can prevent [...]

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• Generative model to predict the deformation field of CFRP laminates with geometric deviations in wing assembly

  Y. Liu, Y. Zhao, Q. Lin, W. Pan

  WCCM2024.

  
  

  Abstract

  Thin-walled structure of CFRP laminates is widely utilized in the assembly of aircraft wings. The deformation field generated during the assembly process can impact the assembly performance of the structure, thereby influencing the product quality and operational performance of the wings. The geometric deviations on the critical mating surfaces of the laminate and physical parameters are key factors influencing the deformation fields during the assembly process. Analyzing the mapping relationship between fusion assembly data and deformation field plays a crucial role for assessing the assembly results. The traditional analysis methods only consider the impact of simple directional deviations on assembly results and do not comprehensively account for the multi-source input. This paper proposes a multi-source assembly input -deformation analysis framework for CFRP bolted joints in aircraft wing assembly. Taking the parameters representing the geometric deviations and physical parameters as input and deformation field as output, a conditional generative model is employed to learn the influence pattern of the geometric deviations on the deformation field. The framework establishes a prediction model from the deviation field to the deformation field and introduces specific accuracy metrics. Corresponding simulations demonstrate that the proposed method can predict assembly deformation field more efficiently than traditional numerical methods.

  Abstract
  Thin-walled structure of CFRP laminates is widely utilized in the assembly of aircraft wings. The deformation field generated during the assembly process can impact the assembly [...]

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• A fast prediction method for bearing strength of aircraft composite bolted structures considering initial assembly deviation

  Q. Lin, Y. Zhao, Y. Liu, W. Pan

  WCCM2024.

  
  

  Abstract

  Bearing limitation is a key performance indicator for composite bolted joints. Assembly process parameters such as washer structural parameters, interfacial friction coefficients and tightening process parameters have a significant effect on the bearing limitation. In the actual production process, there are inevitably deviations between the assembly process parameters and their design values. The accumulation of assembly process deviations leads to an obvious dispersion of the bearing limitation, which makes it difficult for composite bolted joints to be reliably in service. In this paper, the dispersion of assembly process parameters is experimentally tested to quantitatively characterize its uncertainty. Then, based on the high fidelity finite element analysis method, a data set of bearing limitation under different assembly process parameters is prepared. A data-driven algorithm is used to establish a fast prediction model for bearing limitation. The fast prediction model is used to realize the uncertainty analysis and the reliability evaluation for the bearing limitation. The established analysis method and the obtained conclusions can provide a reference for the reliability design and analysis of composite bolted joints.

  Abstract
  Bearing limitation is a key performance indicator for composite bolted joints. Assembly process parameters such as washer structural parameters, interfacial friction coefficients [...]

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• Hybrid quantum algorithm for the Lattice-Boltzmann method

  D. Wawrzyniak, J. Winter, S. Schmidt, T. Indinger

  WCCM2024.

  
  

  Abstract

  We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity.

  Abstract
  We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision [...]

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