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This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff–Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of “small” trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales. In this contribution we focus our effort on the analysis of single-patch geometries, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology.

In this contribution, we validate a physical model based on a transient temperature equation (including latent heat), w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest, width, depth, and length of the melt pool by numerical simulation, and report also on the obtainable numerical results of the cooling rate. We first assume the laser to possess a double-ellipsoidal shape and demonstrate that a well-calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double-ellipsoidal shape), the investigated model returns a deviation of 19.3% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity.

Numerical simulations of a complete laser powder bed fusion (LPBF) additive manufacturing (AM) process are extremely challenging, or even impossible, to achieve without a radical model reduction of the complex physical phenomena occurring during the process. However, even when we adopt a reduced model with simplified physics, the complex geometries of parts usually produced by the LPBF AM processes make this kind of analysis computationally expensive. In fact, small geometrical features—which might be generated when the part is designed following the principle of the so-called design for AM, for instance, by means of topology optimization procedures—often require complex conformal meshes. Immersed boundary methods offer an alternative to deal with this kind of complexity, without requiring complicated meshing strategies. The two-level method lies within this family of numerical methods and presents a flexible tool to deal with multi-scale problems. In this contribution, we apply a modified version of the recently introduced two-level method to part-scale thermal analysis of LPBF manufactured components. We first validate the proposed part-scale model with respect to experimental measurements from the literature. Then, we apply the presented numerical framework to simulate a complete LPBF process of a topologically optimized structure, showing the capability of the method to easily deal with complex geometrical features.

In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them, we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology.

The interest for composites has constantly grown in recent years, especially in the aerospace and automotive industries, as they can be moulded in complex form and geometry, as well as exhibit enhanced engineering properties. Nevertheless, despite the accelerated diffusion of laminated composites, the design of these materials is often restrained by the lack of cost-effective modeling techniques. In fact, the existing numerical strategies allowing for cheap simulations of laminated structures usually fail to directly capture out-of-plane through-the-thickness stresses, which are typically responsible for failure modes such as delamination. In this context, a stress recovery approach based on equilibrium has been recently shown to be an efficient modeling strategy in the framework of isogeometric analysis. Since immersed approaches like the finite cell method have been proven to be a viable alternative to mesh-conforming discretization for dealing with complex/dirty geometries as well as trimmed surfaces, we herein propose to extend the stress recovery approach combining the finite cell method, isogeometric analysis and equilibrium to model the out-of-plane behavior of Kirchhoff laminated plates. Extensive numerical tests showcase the effectiveness of the proposed approach.

A key challenge for Industry 4.0 applications is to develop control systems for automated manufacturing services that are capable of addressing both data integration and semantic interoperability issues, as well as monitoring and decision making tasks. To address such an issue in advanced manufacturing systems, principled knowledge representation approaches based on formal ontologies have been proposed as a foundation to information management and maintenance in presence of heterogeneous data sources. In addition, ontologies provide reasoning and querying capabilities to aid domain experts and end users in the context of constraint validation and decision making. Finally, ontology-based approaches to advanced manufacturing services can support the explainability and interpretability of the behaviour of monitoring, control, and simulation systems that are based on black-box machine learning algorithms. In this work, we provide a novel ontology for the classification of process-induced defects known from the metal additive manufacturing literature. Together with a formal representation of the characterising features and sources of defects, we integrate our knowledge base with state-of-the-art ontologies in the field. Our knowledge base aims at enhancing the modelling capabilities of additive manufacturing ontologies by adding further defect analysis terminology and diagnostic inference features.

The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian optimization is employed to adaptively construct accurate Gaussian process surrogate models using a minimal number of high-fidelity model evaluations, strategically focusing sampling in regions of high predictive uncertainty. The trained surrogate model is then leveraged within a Bayesian inversion scheme to infer optimal parameter values by combining prior knowledge with observed quantities of interest, resulting in posterior distributions that rigorously characterize epistemic uncertainty. The framework is theoretically grounded, computationally efficient, and particularly suited for engineering applications in which high-fidelity models -- whether arising from numerical simulations or physical experiments -- are computationally expensive, analytically intractable, or difficult to replicate, and data availability is limited. Furthermore, the combined use of Bayesian optimization and inversion outperforms their separate application, highlighting the synergistic benefits of unifying the two approaches. The performance of the proposed Bayesian framework is demonstrated on a suite of one- and two-dimensional analytical benchmarks, including the Mixed Gaussian-Periodic, Lévy, Griewank, Forrester, and Rosenbrock functions, which provide a controlled setting to assess surrogate modeling accuracy, parameter inference robustness, and uncertainty quantification. The results demonstrate the framework's effectiveness in efficiently solving inverse problems while providing informative uncertainty quantification and supporting reliable engineering decision-making at reduced computational cost.

We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by communicating with each other in terms of their distance. To this end, we generalize a related result for a Fokker-Planck-type model with a nonlocal discontinuous drift and constant diffusion, recently introduced by three of the authors, of which the steady distribution is explicitly computable. For this new nonlocal Fokker-Planck equation, existence, uniqueness and positivity of a global solution are proven, together with precise equilibration rates of the solution towards its quasi-stationary distribution. Numerical experiments are designed to verify the theoretical findings and explore possible extensions to more complex scenarios.

In this contribution, we validate a physical model based on a transient temperature equation (including latent heat) w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest: width, depth, and length of the melt pool by numerical simulation and report also on the obtainable numerical results of the cooling rate. We first assume the laser to posses a double ellipsoidal shape and demonstrate that a well calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3\\% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double ellipsoidal shape) the investigated model returns a deviation of 19.3\\% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5\\%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity.

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.