Engineering with Computers最新文献

Physics informed neural network (PINN) frameworks have been developed as a powerful technique for solving partial differential equations (PDEs) with potential data integration. However, when applied to advection based PDEs, PINNs confront challenges such as parameter sensitivity in boundary condition enforcement and diminished learning capability due to an ill-conditioned system resulting from the strong advection. In this study, we present a multiscale stabilized PINN formulation with a weakly imposed boundary condition (WBC) method coupled with transfer learning that can robustly model the advection diffusion equation. To address key challenges, we use an advection-flux-decoupling technique to prescribe the Dirichlet boundary conditions, which rectifies the imbalanced training observed in PINN with conventional penalty and strong enforcement methods. A multiscale approach under the least squares functional form of PINN is developed that introduces a controllable stabilization term, which can be regarded as a special form of Sobolev training that augments the learning capacity. The efficacy of the proposed method is demonstrated through the resolution of a series of benchmark problems of forward modeling, and the outcomes affirm the potency of the methodology proposed.

This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need to be performed for a given set of physical or geometrical parameters. This step can be computationally expensive in particular for real world, practical applications. We are interested in geometrical parameters and take advantage of the flexibility of splines in representing complex geometries. In this case, the operators are geometry-dependent and generally depend on the parameters in a non-affine way. Moreover, the solutions obtained from trimmed domains may vary highly with respect to different values of the parameters. Therefore, we employ a local reduced basis method based on clustering techniques and the Discrete Empirical Interpolation Method to construct affine approximations and efficient reduced order models. In addition, we discuss the application of the reduction strategy to parametric shape optimization. Finally, we demonstrate the performance of the proposed framework to parameterized Kirchhoff-Love shells through benchmark tests on trimmed, multi-patch meshes including a complex geometry. The proposed approach is accurate and achieves a significant reduction of the online computational cost in comparison to the standard reduced basis method.

Because the complete set of Trefftz functions for the 3D biharmonic equation is not yet well established, a multiple-direction Trefftz method (MDTM) and an in-plane biharmonic functions method (IPBFM) are deduced in the paper. Inspired by the Trefftz method for the 2D biharmonic equation, a novel MDTM incorporates planar directors into the 2D like Trefftz functions to solve the 3D biharmonic equation. These functions being a series of biharmonic polynomials of different degree, automatically satisfying the 3D biharmonic equation, are taken as the bases to expand the solution. Then, we derive a quite large class solution of the 3D biharmonic equation in terms of 3D harmonic functions, and 2D biharmonic functions in three sub-planes. The 2D biharmonic functions are formulated as the Trefftz functions in terms of the polar coordinates for each sub-plane. Introducing a projective variable, we can obtain the projective type general solution for the 3D Laplace equation, which is used to generate the 3D Trefftz type harmonic functions. Several numerical examples confirm the efficiency and accuracy of the proposed MDTM and IPBFM.

As fusion simulation codes increasingly account for the full geometric complexity of magnetically confined fusion systems, a need arose to provide tailored unstructured mesh technologies to address the specific needs of fusion plasma simulation codes and their coupling to other physics simulation codes. This paper presents a high level overview of a set of unstructured mesh developments that include; methods to effectively employ manufacturing CAD models in the construction of quality analysis model geometries, specialized mesh generation and adaptation tools; an infrastructure to support parallel particle-in-cell calculation on unstructured meshes; and an infrastructure for coupling of massively parallel mesh-based fusion codes.

A novel adaptive refinement method is proposed for ordinary state-based PD in both 2D and 3D simulation. We perform an efficient adaptive refinement by splitting a parent particle into several child particles directly which does not require any information from its adjacent particles. The state variables and neighbor list of the child particles can be obtained directly from their parent particles, so that the proposed adaptive refinement method is very efficient and can be easily applied in both 2D and 3D cases without complex adjacent particle list building. To maintain simulation accuracy, the deformation of the parent particles need to be taken into consideration in the refinement process. Therefore, the accumulated strain of a PD particle is defined to calculate the position vector of its child particles in current configuration. With the consideration of the deformation of the parent particle, the fake damage is avoid. And a new criterion is established based on the particle accumulated strain to efficiently determine the particles need to be refined. The numerical examples studied show that the proposed adaptive refinement correctly captures the complicated crack propagation process and eliminates the fake crack growth with slight extra simulation cost, compared to the coarse discretization.

Current advancements in topology optimization research have extensively explored thermoelastic problems. Yet, notable limitations persist in effectively handling design-dependent fluidic pressure loads, particularly in the realm of coupled thermo-mechanical systems. To bridge this gap, this study proposes a novel and consistent methodology that comprehensively accommodates these challenges. The principal contributions of this research are threefold: (1) presenting an innovative and comprehensive solution for triplet thermo-mechanical-pressure problems, achieved through the establishment of a specific pressure field using Darcy’s law and a drainage term, (2) broadening the scope to incorporate flexible polygonal meshes within generalized Solid Isotropic Material with Penalization (SIMP)-based multi-material systems, and (3) introducing an alternative interpolated model related to independent material properties, specifically the general thermal stress coefficient, to simplify the complexity during sensitivity calculations of thermal-strain load in generalized SIMP-based multi-material problems. Additionally, within the scope of this study, several investigations into penalty parameters in solids, not unified in previous coupled thermo-mechanical multi-material problems, are also conducted. Three additional adjoint vectors are introduced using the adjoint variable technique for sensitivity analysis to enhance computational efficiency in the gradient-based mathematical programming algorithm. The effectiveness and reliability of this method are validated through numerical examples, demonstrating its efficiency, robustness, and practicality.

The utilization of Physics-informed Neural Networks (PINNs) in deciphering inverse problems has gained significant attention in recent years. However, the PINN training process for inverse problems is notably restricted due to gradient failures provoked by magnitudes of partial differential equations (PDEs) parameters or source functions. To address these matters, normalized reduced-order physics-informed neural network (nr-PINN) is developed in this study. The goal of the nr-PINN is to reconfigure the original PDE into a system of normalized lower-order PDEs through two sequential steps. To start with, self-homeomorphisms of the PDEs are implemented via scaling factors determined based on measured data. Afterward, each normalized PDE is transformed into a system of lower-order PDEs by primary and secondary variables. Besides, a technique to exactly impose many types of boundary conditions (BCs) by redefining NNs outputs is developed in the context of reduced-order method. The advantages of the nr-PINN model over the original one regarding solution accuracy and training cost are demonstrated through several inverse problems in solid mechanics with different types of PDEs and BCs.

A stabilized element-free Galerkin (EFG) method is proposed in this paper for numerical analysis of the generalized steady MHD duct flow problems at arbitrary and high Hartmann numbers up to (10^{16}). Computational formulas of the EFG method for MHD duct flows are derived by using Nitsche’s technique to facilitate the implementation of Dirichlet boundary conditions. The reproducing kernel gradient smoothing integration technique is incorporated into the EFG method to accelerate the solution procedure impaired by Gauss quadrature rules. A stabilized Nitsche-type EFG weak formulation of MHD duct flows is devised to enhance the performance damaged by high Hartmann numbers. Several benchmark MHD duct flow problems are solved to testify the stability and the accuracy of the present EFG method. Numerical results show that the range of the Hartmann number Ha in the present EFG method is (1le Hale 10^{16}), which is much larger than that in existing numerical methods.

In this work, we present a novel unfitted mesh boundary strategy in the context of the Particle Finite Flement Method (PFEM) aiming to improve endemic limitations of the PFEM relative to boundary conditions treatment and mass conservation. In this new methodology, which we called Cut-PFEM, the fluid–wall interaction is not performed by adding interface elements, as is done in the standard PFEM boundaries. Instead, we use an implicit representation of (all or some of) the boundaries by introducing the use of a level set function. Such distance function detects the elements trespassing the (virtual) contours of the domain to equip them with opportunely boundary conditions, which are variationally enforced using Nitsche’s method. The proposed Cut-PFEM circumvents important issues associated with the standard PFEM contact detection algorithm, such as the artificial addition of mass to the computational domain and the anticipation of contact time. Furthermore, the Cut-PFEM represents a natural ground for the imposition of alternative wall boundary conditions (e.g., pure slip) which pose significant difficulties in a standard PFEM framework. Several numerical examples, featuring both no-slip and slip boundary conditions, are presented to prove the accuracy and robustness of the method in two-dimensional and three-dimensional scenarios.

The present study aims to develop a sustainable framework employing brain-inspired neural networks for solving boundary value problems in Engineering Mechanics. Spiking neural networks, known as the third generation of artificial neural networks, are proposed for physics-based artificial intelligence. Accompanied by a new pseudo-explicit integration scheme based on spiking recurrent neural networks leading to a spike-based pseudo explicit integration scheme, the underlying differential equations are solved with a physics-informed strategy. We propose additionally a third-generation spike-based Legendre Memory Unit that handles large sequences. These third-generation networks can be implemented on the coming-of-age neuromorphic hardware resulting in less energy and memory consumption. The proposed framework, although implicit, is viewed as a pseudo-explicit scheme since it requires almost no or fewer online training steps to achieve a converged solution even for unseen loading sequences. The proposed framework is deployed in a Finite Element solver for plate structures undergoing cyclic loading and a Xylo-Av2 SynSense neuromorphic chip is used to assess its energy performance. An acceleration of more than 40% when compared to classical Finite Element Method simulations and the capability of online training is observed. We also see a reduction in energy consumption down to the thousandth order.