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In this work, an algorithm for topology optimization of incompressible structures is proposed, in both small and finite strain assumptions and in which the loads come from the interaction with a surrounding fluid. The algorithm considers a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially to simulate the interaction between them. Several stabilized mixed finite element formulations based on the Variational Multi-Scale approach are considered to be capable of tackling the incompressible limit for the numerical approximation of the solid. The fluid is considered as an incompressible Newtonian fluid flow which is combined with an Arbitrary-Lagrangian Eulerian formulation to account for the moving part of the domain. Several numerical examples are presented and discussed to assess the robustness of the proposed algorithm and its applicability to the topology optimization of incompressible elastic solids subjected to Newtonian incompressible fluid loads.

This work introduces a distributed memory machine and octree-based Finite Element (FE) framework for modeling metal Additive Manufacturing (AM) processes. In this sense, an Adaptive Mesh Refinement (AMR) is used to accurately capture the complex geometrical domain and the physical phenomena of AM processes for the part-scale analysis. AMR is used in conjunction with refinement criteria suitable for this problem: (1) a geometric criterion for refining the material deposition path, and (2) an accuracy criterion based on an a-posteriori error-indicator of the displacement field. As a consequence, the geometry and numerical solution are accurately captured whilst the number of FEs is kept controlled along the simulation. Numerical simulations involving growing domains are presented to assess the accuracy and computational efficiency of the framework with different octree-based and structured fixed mesh configurations. The overall performance of the framework is evaluated through a strong scalability analysis to track the evolution of the computational time along the simulation, where all steps composing the AM pipeline are independently analyzed. The strong scalability test consists of a discrete evolving domain with over 15 M active nodes, solved on a High-Performance Computer (HPC) using 2, 048 processors.

This work presents an h-adaptive finite-element (FE) strategy to address the numerical simulation of additive manufacturing (AM) of large-scale parts. The wire-arc additive manufacturing is chosen as the demonstrative technology for its manufacturing capabilities suitable for industrial purposes. The scanning path and processing parameters of the simulation are provided via a RS-274 (GCode) file, being the same as the one delivered to the AM machine. The approach is suitable for industrial applications and can be applied to other AM processes. To identify the location in the FE mesh of the heat affected zone (HAZ), a collision detection algorithm based on the separating axis theorem is used. The mesh is continuously adapted to guarantee the necessary mesh resolution to capture the phenomena inside and outside the HAZ. To do so, a multi-criteria adaptive mesh refinement and coarsening (AMR) strategy is used. The AMR includes a geometrical criterion to guarantee the FE size within the HAZ, and a Zienkiewicz–Zhu-based a-posteriori error estimator to guarantee the solution accuracy elsewhere. Thus, the number of active FEs is controlled and mesh manipulation by the end-user is avoided. Numerical simulations comparing the h-adaptive strategy with the (reference) fixed fine meshes are performed to prove the computational cost efficiency and the solution accuracy.

FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting state-of-the-art supercomputing resources. It is a highly modularized, flexible, and extensible library, that provides a set of modules that can be combined to carry out the different steps of the simulation pipeline. FEMPAR includes a rich set of algorithms for the discretization step, namely (arbitrary-order) grad, div, and curl-conforming finite element methods, discontinuous Galerkin methods, B-splines, and unfitted finite element techniques on cut cells, combined with h-adaptivity. The linear solver module relies on state-of-the-art bulk-asynchronous implementations of multilevel domain decomposition solvers for the different discretization alternatives and block-preconditioning techniques for multiphysics problems. FEMPAR is a framework that provides users with out-of-the-box state-of-the-art discretization techniques and highly scalable solvers for the simulation of complex applications, hiding the dramatic complexity of the underlying algorithms. But it is also a framework for researchers that want to experience with new algorithms and solvers, by providing a highly extensible framework. In this work, the first one in a series of articles about FEMPAR, we provide a detailed introduction to the software abstractions used in the discretization module and the related geometrical module. We also provide some ingredients about the assembly of linear systems arising from finite element discretizations, but the software design of complex scalable multilevel solvers is postponed to a subsequent work.

After conducting a comprehensive historical review of presently established methods for computational modeling of multilayered bending plates, the present work introduces a novel 2D multiscale strategy, termed the 2D+ approach. The proposed approach is based on the computational homogenization formalism and is envisaged to serve as an appealing alternative to current methodologies for modeling multilayered plates in bending-dominated situations. Such structural elements involve modern and relevant materials, such as laminated composites characterized by the heterogeneous distribution of low-aspect-ratio layers showing substantial non-linear mechanical behavior across their thickness. Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE, in turn, is capturing the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate-midplane finite element mesh. The chosen kinematics and discretization at the considered scales are particularly selected to (1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, (2) achieve affordable computational times (computational efficiency), and (3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy). The proposed strategy aligns with the standard, first-order, hierarchical multiscale setting, involving the linearization of the macro-scale displacement field along the thickness. It employs an additional fluctuating displacement field in the RVE to capture higher-order behavior, which is computed through a local 1D finite element solution of a Boundary Value Problem (BVP) at the RVE. A notable feature of the presented 2D+ approach is the application of the Hill–Mandel principle, grounded in the well-established physical assumption imposing mechanical energy equivalence in the macro and meso scales. This links the 2D macroscopic plate and the set of 1D mesoscopic filaments, in a weakly-coupled manner, and yields remarkable computational savings in comparison with standard 3D modeling. Additionally, solving the resulting RVE problem in terms of the fluctuating displacement field allows the enforcement of an additional condition: fulfillment of linear momentum balance (equilibrium equations). This results in a physically meaningful 2D-like computational setting, in the considered structural object (multilayered plates in bending-dominated situations), which provides accurate stress distributions, typical of full 3D models, at the computational cost of 2D models.

We report in this work a numerical analysis of the sloshing of a squared tank partially filled with a domestic vegetable oil. The tank is subject to controlled motions with a shake table. The free-surface evolution is captured using ultrasonic sensors and an image capturing method. Only confirmed data within the error range is reported. Filling depth, imposed amplitude and frequency effects on the sloshing wave pattern are specifically evaluated. The experiments also reveal the nonlinear wave behavior. The numerical model is based on a stabilized finite element method of the variational multi-scale type. The free-surface is captured using a level set technique developed to be used with adaptive meshes in Arbitrary Lagrangian–Eulerian framework. The numerical results are compared with the experiments for different sloshing conditions near the first sloshing mode. The simulations satisfactorily match the experiments, providing a reliable tool for the analysis of this kind of problems.

Powder Bed Fusion–Laser Beam (PBF-LB) is a leading technique in metal additive manufacturing, yet it continues to face challenges related to residual stresses and distortions. The inherent strain method has emerged as a valuable predictive tool, offering early assessments of part behaviour due to its simplicity and manageable computational demands. However, accurately defining the inherent strain tensor, which is critical for these models, remains a challenge. This study provides a comprehensive analysis of the local meso-scale model definition and inherent strain calculation procedure in the PBF-LB process using a multi-scale modelling approach. The primary objective is to guide the definition of local high-fidelity thermo-mechanical models. This research investigates the contributions of thermal, plastic, and activation strains (strains due to Finite Element (FE) activation) to the inherent strain tensor, demonstrating the significant impact of activation strains. A sensitivity analysis identified an optimal control volume size to ensure minimal boundary effects. An optimised local high-fidelity model is proposed to efficiently calculate inherent strain tensor, significantly reducing computational costs without compromising accuracy. The method was validated by applying it to a complex SBA actuator geometry, which showed good agreement between predicted and experimental distortions. The consistency of the proposed method with empirically derived tensors further reinforces its potential to improve predictive capabilities in the PBF-LB process, ultimately enhancing part quality.

Powder bed fusion–laser beam (PBF-LB) additive manufacturing enables the production of intricate, lightweight metal components aligned with Industry 4.0 and sustainable principles. However, residual stresses and distortions challenge the dimensional accuracy and reliability of parts. Inherent strain methods (ISMs) provide a computationally efficient approach to predicting these issues but often overlook transient thermal histories, limiting their accuracy. This paper introduces an enhanced inherent strain method (EISM) for PBF-LB, integrating macro-scale temperature histories into the inherent strain framework. By incorporating temperature-dependent adjustments to the precomputed inherent strain tensor, EISM improves the prediction of residual stresses and distortions, addressing the limitations of the original ISM. Validation was conducted on two Ti-6Al-4V geometries—a non-symmetric bridge and a complex structure (steady blowing actuator)—through comparisons with experimental measurements of temperature, distortion, and residual stress. Results demonstrate improved accuracy, particularly in capturing localized thermal and mechanical effects. Sensitivity analyses emphasize the need for adaptive layer lumping and mesh refinement in regions with abrupt stiffness changes, such as shrink lines. While EISM slightly increases computational cost, it remains feasible for industrial-scale applications. This work bridges the gap between simplified inherent strain models and high-fidelity simulations, offering a robust tool for simulation-driven optimisation.

In this work, we present a new variant of the balancing domain decomposition by constraints preconditioner that is robust for multi-material problems. We start with a well-balanced subdomain partition, and based on an aggregation of elements according to their physical coefficients, we end up with a finer physics-based (PB) subdomain partition. Next, we define corners, edges, and faces for this PB partition, and select some of them to enforce subdomain continuity (primal faces/edges/corners). When the physical coefficient in each PB subdomain is constant and the set of selected primal faces/edges/corners satisfy a mild condition on the existence of acceptable paths, we can show both theoretically and numerically that the condition number does not depend on the contrast of the coefficient across subdomains. An extensive set of numerical experiments for 2D and 3D for the Poisson and linear elasticity problems is provided to support our findings. In particular, we show robustness and weak scalability of the new preconditioner variant up to 8232 cores when applied to 3D multi-material problems with the contrast of the physical coefficient up to 10 8 and more than half a billion degrees of freedom. For the scalability analysis, we have exploited a highly scalable advanced inter-level overlapped implementation of the preconditioner that deals very efficiently with the coarse problem computation. The proposed preconditioner is compared against a state-of-the-art implementation of an adaptive BDDC method in PETSc for thermal and mechanical multi-material problems.

In this paper, we formulate and analyze a perturbed formulation of the balancing domain decomposition by constraints (BDDC) method. We prove that the perturbed BDDC has the same polylogarithmic bound for the condition number as the standard formulation. Two types of properly scaled zero-order perturbations are considered: one uses a mass matrix, and the other uses a Robin-type boundary condition, i.e, a mass matrix on the interface. With perturbation, the well-posedness of the local Neumann problems and the global coarse problem is automatically guaranteed, and coarse degrees of freedom can be defined only for convergence purposes but not well-posedness. This allows a much simpler implementation as no complicated corner selection algorithm is needed. Minimal coarse spaces using only face or edge constraints can also be considered. They are very useful in extreme scale calculations where the coarse problem is usually the bottleneck that can jeopardize scalability. The perturbation also adds extra robustness as the perturbed formulation works even when the constraints fail to eliminate a small number of subdomain rigid body modes from the standard BDDC space. This is extremely important when solving problems on unstructured meshes partitioned by automatic graph partitioners since arbitrary disconnected subdomains are possible. Numerical results are provided to support the theoretical findings.