Engineering with Computers最新文献

Differential equation-driven evolution strategies are often associated with boundary-driven topology optimization methods, such as the level set method. However, differential equations can also be utilized effectively in density-based approaches. This paper presents a design update scheme formulated using differential equations to evolve elemental densities in topology optimization. The proposed scheme transforms the differential equation into an absolute increment format, closely related to the optimality criteria (OC) method, which is traditionally implemented in a relative increment format in density-based methods. The relative increment format of the OC method typically ensures an efficient and stable optimization process, whereas the absolute increment format tends to enable a more active and responsive optimization process, potentially leading to optimized results with improved performance. Furthermore, the absolute increment format can be converted into a relative one if needed. This study explores compliance minimization problems for both isotropic composite and single-material cases. Detailed MATLAB implementations for these cases are presented and thoroughly explained. Numerical examples demonstrate that the differential equation-driven update scheme effectively addresses density distribution optimization problems, offering an alternative to classical density methods.

Understanding the mechanical behaviour of defective materials is key to predicting failure and enhancing performance. Traditional fracture mechanics often requires assumptions about geometry and loading that are unavailable in experimental systems. We present a MATLAB-based computational toolbox that extracts configurational forces and mixed-mode SIFs directly from experimentally measured displacement or deformation gradient fields, like digital image/volume correlation and high (angular) resolution electron backscatter diffraction. The toolbox implements path-independent energy integrals, including the J- and M-integrals, and introduces a novel mode decomposition formulation that isolates mode I-III SIFs contributions without predefined specimen geometries, applied loads, or boundary conditions. Applications to microcracks, dislocations, and fatigue cracks demonstrate its robust, geometry-independent characterisation, which can enable data-driven analysis of defect behaviour in anisotropic and complex materials. The framework is material-agnostic in principle and operates directly on experimental fields; however, its current implementation assumes small-strain kinematics, making it most applicable to linear and anisotropic elastic and elastoplastic materials such as metals and ceramics.

Supplementary information: The online version contains supplementary material available at 10.1007/s00366-025-02262-5.

Weak imposition of essential boundary conditions (i.e., weak BCs) for the Navier-Stokes equations of incompressible flows allows a certain amount of controlled numerical flow slip on the solid surface. Numerical flow slip mimics the presence of a thin boundary layer that would otherwise need to be captured using a fine mesh resolution. As a result, weak BCs enable the use of coarser meshes near solid walls without sacrificing numerical solution accuracy, which significantly reduces the computational costs, especially for 3D, wall-bounded turbulent flows. However, weak BCs for compressible flows are not as well understood as those for the incompressible-flow case. In particular, numerical instabilities were observed in some cases where the weak BCs were simultaneously imposed for the velocity and temperature fields. In the present effort, to address these stability issues, we develop a methodology for the design of compressible-flow weak BC operators and demonstrate the improved performance of the resulting weak BC formulations using challenging 2D and 3D test cases.

Many engineering challenges involve optimising multiple criteria that often represent conflicting targets, posing significant difficulties for standard methods like gradient-based algorithms. This complexity is especially important in the context of acoustic wave propagation, where noise barriers are designed to attenuate sound pressure level (SPL). Achieving optimal performance requires carefully balancing design factors such as shape and material selection with economic constraints, making the optimisation process both technically demanding and computationally intensive. This paper proposes the development of a noise prediction surrogate model for the multi-objective optimisation of acoustic barriers. This model is developed based on data set generated employing a two-dimensional singular boundary method. The optimisation process is conducted using a multi-objective Bayesian optimisation algorithm, which is applied to the problem of acoustic line source diffraction in the presence of a porous noise barrier. Two distinct barrier configurations are considered: a straight-walled barrier and a T-shaped barrier. With a view to reduce the SPL behind the noise barrier, the set of spanned parameters includes the SPL on the side of the barrier opposite to the source, barrier's height, cap length of T-shaped barrier, porosity, tortuosity, and airflow resistivity of the material, integrating both microstructural and macrostructural aspects into the optimisation. Surface impedance boundary condition is used in the model to represent the dissipation at the surface of the noise barrier. The results demonstrate that the proposed optimisation framework enables efficient exploration of trade-offs to achieve an optimal barrier design that balances acoustic performance, material cost, and shape constraints.

Magnetic Resonance Imaging (MRI) scanners employ superconducting magnets to produce a strong uniform magnetic field over the bore of the scanner as part of the imaging process. Superconductors are preferred, as they can generate the required field strengths without electrical resistance, but, to do this, the materials need to be cooled to very low temperatures, typically around 4.2 K. However, due to imperfections in the windings, cracks and small air gaps in the epoxy resin between the wires, heating can occur leading to a process known as magnet quench. During magnet quench, the magnet temperature rises quickly, and the magnet loses its superconductivity. This work presents an accurate numerical model for predicting magnet quench for axisymmetric MRI scanners by solving the coupled system of thermal, electromagnetic and circuit equations by means of a high order/hp-version finite element method where regions of high gradients are resolved with boundary layer elements. A series of numerical results are included to demonstrate the effectiveness of the approach.

A generic side mirror can be approximated to the combination of a half cylinder topped with a quarter of sphere. The flow structure in the wake of the side mirror is highly transient and the turbulence plays an important role affecting aeroacoustics through pressure fluctuation. Thus, this geometry is one of the test cases object of several numerical studies in recent years to assess the aerodynamic and aeroacoustic capabilities of the turbulence models. In this context, this study presents how the second-generation URANS closure STRUCT-(epsilon ) is able to properly predict the expected stagnation, flow separation and vortex shedding phenomena. Besides, the predictive accuracy for the noise generation mechanism is evaluated by comparing the spectra of the sound pressure level measured at several static pressure sensors with the numerical results obtained with the STRUCT-(epsilon ). The response of this turbulence model has exceeded that from other hybrid methods and is in good agreement with the results from Large-Eddy Simulations or the experiments. To conclude the paper, the applicability of STRUCT-(epsilon ) to construct a Spectral Proper Orthogonal Decomposition method that helps identifying the most energetic modes to appropriately capture the dominant flow structures is also introduced.

Soft materials play an integral part in many aspects of modern life including autonomy, sustainability, and human health, and their accurate modeling is critical to understand their unique properties and functions. Today’s finite element analysis packages come with a set of pre-programmed material models, which may exhibit restricted validity in capturing the intricate mechanical behavior of these materials. Regrettably, incorporating a modified or novel material model in a finite element analysis package requires non-trivial in-depth knowledge of tensor algebra, continuum mechanics, and computer programming, making it a complex task that is prone to human error. Here we design a universal material subroutine, which automates the integration of novel constitutive models of varying complexity in non-linear finite element packages, with no additional analytical derivations and algorithmic implementations. We demonstrate the versatility of our approach to seamlessly integrate innovative constitutive models from the material point to the structural level through a variety of soft matter case studies: a frontal impact to the brain; reconstructive surgery of the scalp; diastolic loading of arteries and the human heart; and the dynamic closing of the tricuspid valve. Our universal material subroutine empowers all users, not solely experts, to conduct reliable engineering analysis of soft matter systems. We envision that this framework will become an indispensable instrument for continued innovation and discovery within the soft matter community at large.

This study proposes a novel framework for learning the underlying physics of phenomena with moving boundaries. The proposed approach combines Ensemble SINDy and Peridynamic Differential Operator (PDDO) and imposes an inductive bias assuming the moving boundary physics evolves in its own corotational coordinate system. The robustness of the approach is demonstrated by considering various levels of noise in the measured data using the 2D Fisher–Stefan model. The confidence intervals of recovered coefficients are listed, and the uncertainties of the moving boundary positions are depicted by obtaining the solutions with the recovered coefficients. Although the main focus of this study is the Fisher–Stefan model, the proposed approach is applicable to any type of moving boundary problem with a smooth moving boundary front without an intermediate zone of two states. The code and data for this framework is available at: https://github.com/alicanbekar/MB_PDDO-SINDy.

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we extend the application of this algorithm to address systems of differential-algebraic equations (DAEs) in general form. Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness.

Structural reliability analysis poses significant challenges in engineering practices, leading to the development of various state-of-the-art approximation methods. Active learning methods, known for their superior performance, have been extensively investigated to estimate the failure probability. This paper aims to develop an efficient and accurate adaptive Kriging-based method for structural reliability analysis by proposing a novel learning function allocation scheme and a hybrid convergence criterion. Specifically, the novel learning function allocation scheme is introduced to address the challenge of no single learning function universally outperforms others across various engineering contexts. Six learning functions, including EFF, H, REIF, LIF, FNEIF, and KO, constitute a portfolio of alternatives in the learning function allocation scheme. The hybrid convergence criterion, combining the error-based stopping criterion with a stabilization convergence criterion, is proposed to terminate the active learning process at an appropriate stage. Moreover, an importance sampling algorithm is leveraged to enable the proposed method with the capability to deal with rare failure events. The efficiency and accuracy of the proposed method are demonstrated through four numerical examples and one engineering case.