Documents published in Scipedia

• Modeling of an oblique incident P-wave within a water saturated soil with the wave based method

  M. Lainer, G. Müller

  WCCM2024.

  
  

  Abstract

  In this contribution, a coupling approach between the Wave Based Method and an oblique incident P1-wave is presented. The approach is used to model a poroelastic halfspace with an empty canyon by applying Biot’s theory for low frequencies. The system’s response is compared with a reference solution from literature. Moreover, a second coupling approach is introduced to permit the modeling of a filled canyon. In the special case of a canyon filled with the material of the surrounding soil, the simulation results are compared with the underlying analytical solution

  Abstract
  In this contribution, a coupling approach between the Wave Based Method and an oblique incident P1-wave is presented. The approach is used to model a poroelastic halfspace [...]

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• Stochastic FE-BE method for homogenization analysis of 2D diffusion problems considering uncertainties of inclusion shape

  K. Koro

  WCCM2024.

  
  

  Abstract

  The stochastic method for homogenization analysis of diffusion problems considering uncertainties of inclusion shape is developed using a microscopic spectral stochastic BEM and a macroscopic FEM. The spatial variation of inclusion shape is modeled using KarhunenLoeve expansion with exponential-type covariance kernels. The characteristic function on a 2-D unit cell and the homogenized diffusion tensor are calculated using the spectral stochastic BEM. The macroscale diffusion problems are solved using the stochastic FEM with the polynomial chaos (PC) expansion. Through numerical tests, the expected value and the standard deviation of the concentration in macroscale problems and their distribution are investigated.

  Abstract
  The stochastic method for homogenization analysis of diffusion problems considering uncertainties of inclusion shape is developed using a microscopic spectral stochastic BEM [...]

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• Optimal design of graphene-reinforced composites using shunted piezoelectric systems for optimal vibration attenuation

  M. Daraki, G. Drosopoulos, G. Foutsitzi, G. Stavroulakis

  WCCM2024.

  
  

  Abstract

  . Smart structures exploit the synergy between several coupled physical phenomena to produce materials and structures with enhanced properties. Such structures incorporate integrated sensors and actuators, mechanical and electronic components and control. The design of smart structures is a multidisciplinary challenge, which is of high importance for viability and resilience of industry. Usage of piezocomposites with integrated nonlinear shunted circuits for vibration suppression improves effectiveness and accuracy of many high-value products. The finite element method is widely used to simulate the mechanical response of composite materials and multi-physics problems. In this work a numerical investigation is conducted on small scale beams aiming to improve their vibration response by applying piezoelectric shunted circuits. Finite element models are developed in MATLAB, simulating graphene-reinforced nanocomposite piezoelectric beams with shunted circuits under vibration excitations. Piezoelectric materials are applied to the beams to allow for the interaction between electric charge and mechanical deformation. In addition, shunted circuits, which are paired with piezoelectric elements, are used to provide damping (vibration suppression) of one or more critical eigenfrequencies. To derive the optimal vibration response, a particle swarm optimization (PSO) algorithm is adopted. Optimization is then aimed to minimize the vibration amplitude as well as optimize the mechanical and electrical parameters of the investigated system.

  Abstract
  . Smart structures exploit the synergy between several coupled physical phenomena to produce materials and structures with enhanced properties. Such structures incorporate [...]

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• Nonlinear interaction in composites using physics informed neural networks

  G. Stavroulakis, A. Mouratidou, G. Drosopoulos

  WCCM2024.

  
  

  Abstract

  Modelling of composites requires the consideration of various components that work together and interact in a linear and nonlinear way. Linear and nonlinear modelling in view of demanding needs, like representative volume element calculations within numerical homogenization and the advent of new tools, like physics informed neural networks, are reviewed in this article. In particular, a concept is proposed towards the implementation of a unilateral contact mechanics law within physics-informed neural networks. The theoretical framework and related applications are presented. Results indicate that the proposed deep learning approach can further be applied towards solving contact mechanics problems, considering the mechanical interactions between the constituents of composites.

  Abstract
  Modelling of composites requires the consideration of various components that work together and interact in a linear and nonlinear way. Linear and nonlinear modelling in view [...]

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• 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 INTERPRET, VERIFY, AND DECOUPLE MULTI-PHYSICS SYSTEMS

  T. Price-Broncucia, S. Amorese, R. Baptista, 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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