International Journal for Numerical Methods in Engineering最新文献

We establish a surrogate model for computational homogenization of composite materials consisting of multiple viscoelastic constituents. A surrogate macroscopic material is identified by performing interpolation using radial basis functions (RBFs) and cubic spline functions on a constitutive database generated by a series of microscopic analyses or, equivalently, numerical material tests (NMTs) on a unit cell to represent anisotropic stress relaxation behavior as well as its dependence on strain rate and temperature. After briefly reviewing the two-scale boundary value problem derived based on homogenization theory, an RBF interpolation with a normalized kernel is formulated for a discrete dataset, and an optimization algorithm is applied to determine the three hyperparameters so as to achieve proper interpolation. Then, we formulate the surrogate homogenization model (SHM) using the interpolants to substitute for the macroscopic viscoelastic response. To show the specific procedure of the proposed surrogate modeling and demonstrate the performance of the created SHM, a representative numerical example is presented in the offline and online stages. In the offline stage, NMTs are carried out in the space of training data, including the temperature, to generate a dataset as long as the macroscopic stresses can be learned exhaustively, and then optimization is performed to determine the set of hyperparameters. Then, to validate the created SHM, its responses to unseen loading and temperature histories are compared with the corresponding NMT results. In the online stage, the created SHM is used to carry out a macroscopic analysis of a simple structure under specific loading and temperature conditions, and subsequently, the obtained macroscopic stresses are compared with those obtained from the localization analysis results. The results are also compared with those obtained from the single-scale direct numerical analyses.

Finite periodic layout for multicomponent systems signifies a compelling design strategy for constructing complex larger structures through assembling repeating representative unit-cells with various orientations. In addition to better transportability, handleability and replaceability, design with structural segmentation has been considered particularly valuable for additive manufacturing of large workpiece due to limited printing dimension of machine. However, existing design optimization of periodic structures has been largely restricted to simple translational placements of unit-cells, sophisticated tessellation with differently oriented topological unit-cells remains underexplored. This paper presents an efficient and adaptable topology optimization framework for concurrently optimizing periodic structures comprised of repeating topological unit-cells and their tailored orientations. By introducing a weighting factor associated with different orientation states of unit-cells, a dominant orientation for each unit-cell can gradually emerge in the course of optimization process. The proposed procedure combines the solid isotropic material with penalization (SIMP) model for topology optimization of unit-cell and the discrete material optimization (DMO) technique for the optimization of its orientation. The optimization objective is to minimize structural compliance subject to volume fraction constraint. Through sensitivity analysis, optimality criteria can be applied to simultaneously optimize a representative unit-cell (RUC) topology and the orientation weighting factors in the periodic macrostructure. Several 2D and 3D examples are investigated to demonstrate significant enhancement in compliance reduction of up to 34% compared to conventional periodic design without orientation optimization. This represents a notable improvement in finite periodic structural optimization, particularly leveraging the topology optimization to tailor unit-cell orientation rather than relying on brute-force search approaches. Our methodology paves a new avenue for designing more efficient and readily manufacturable lightweight structures with enhanced performance metrics.

In this study, we developed a method of estimating the correction terms that makes the Hamiltonian used in phase-field analysis by quantum annealing correspond to the free energy functional of the conventional phase-field analysis using the finite difference method. For the estimation of the correction terms, we employed a factorization machine. The inputs to the factorization machine were the phase-field variables in domain-wall encoding and the differences between the Gibbs free energy and Hamiltonian. We obtained the difference value in quadratic unconstrained binary optimization (QUBO) form as the output of learning using the factorization machine. The QUBO form difference was subjected to the original Hamiltonian as the correction term. The performance of this correction term was evaluated by calculating the energy for a equilibrium state of diblock copolymer. In phase-field analysis, the time evolution equation is formulated so that the total free energy decreases; hence, a lower the free energy means a more accurate result close to that of a conventional method. When we performed annealing with correction terms, the microstructure showed a Gibbs free energy that was lower than that obtained without the correction terms.

Phase field modeling of fracture has gained attention as a relatively simple and fundamental approach to predict crack propagation. However, the significant computational demands still pose challenges, particularly in dynamic simulations. To mitigate these challenges, we present a newly devised asynchronous variational integrator (AVI) for phase field modeling of dynamic fracture, implemented within the framework of the finite element library FEniCS. The AVI allows each spatial mesh element to progress independently with its own characteristic time step. In the new approach, displacement updates occur as usual at each time step, while the phase field is globally solved after the displacement update of the largest spatial mesh element rather than after each time step. Benchmark problems are investigated to assess the performance and reliability of the new method, revealing notable computational savings while effectively capturing intricate dynamic fracture behavior.

Slender structures, such as rods, often exhibit large deformations even under moderate external forces (e.g., gravity). This characteristic results in a rich variety of morphological changes, making them appealing for engineering design and applications, such as soft robots, submarine cables, decorative knots, and more. Prior studies have demonstrated that the natural shape of a rod significantly influences its deformed geometry. Consequently, the natural shape of the rod should be considered when manufacturing and designing rod-like structures. Here, we focus on an inverse problem: Can we determine the natural shape of a suspended 2D planar rod so that it deforms into a desired target shape under the specified loading? We begin by formulating a theoretical framework based on the statics of planar rod equilibrium that can compute the natural shape of a planar rod given its target shape. Furthermore, we analyze the impact of uncertainties (e.g., noise in the data) on the accuracy of the theoretical framework. The results reveal the shortcomings of the theoretical framework in handling uncertainties in the inverse problem, a fact often overlooked in previous works. To mitigate the influence of the uncertainties, we combine the statics of the planar rod with the adjoint method for parameter sensitivity analysis, constructing a learning framework that can efficiently explore the natural shape of the designed rod with enhanced robustness. This framework is validated numerically for its accuracy and robustness, offering valuable insights into the inverse design of soft structures for various applications, including soft robotics and animation of morphing structures.

In this contribution we present an adaptive model order reduction technique for non-linear finite element computations of micro-heterogeneous materials. The presented projection-based method performs updates of the reduced basis during the iterative process and at the end of each load step. Convergence is achieved in all stages of the simulation and the best choice of basis vectors is assured. A novel technique for the choice of basis, the recursive Proper Orthogonal Decomposition, is introduced and compared to an existing technique, the comparative Proper Orthogonal Decomposition, in an academic two-dimensional unit cell example. Numerical examples of real two- and three-dimensional microstructures unveil the performance of the adaptive technique for industrial applications.

This study proposes a novel framework for solving large-scale unsteady flow topology optimization problems. While most previous studies on fluid topology optimization assume steady-state flows, an increasing number of recent studies deal with unsteady flows, which are more general in engineering. However, unsteady flow topology optimization involves solving the governing and adjoint equations of a time-evolving system, which requires a significant computational cost for topology optimization with a fine mesh. Therefore, we propose a large-scale unsteady flow topology optimization based on the building-cube method (BCM), which is one of the hierarchical Cartesian mesh methods. Although the BCM has been confirmed to have excellent scalability and is suitable for massively parallel computing, there are no studies that have applied it to unsteady flow topology optimization. In the proposed method, the governing and adjoint equations are discretized by a cell-centered finite volume method based on the BCM, which can achieve high parallel efficiency even with a fine mesh. The effectiveness of the proposed method for large-scale computing is discussed through several examples of optimization and verification of computational efficiency by weak scaling.

This work introduces a combined model that integrates a linear state-space model with a Koopman-type machine-learning model to efficiently predict the dynamics of nonlinear, high-dimensional, and field-circuit coupled systems, as encountered in areas such as electromagnetic compatibility, power electronics, and electric machines. Using an extended nonintrusive model combination algorithm, the proposed model achieves high accuracy with an error of approximately 1%, outperforming baselines: a state-space model and a purely data-driven model. Moreover, it delivers a computational speed-up of three orders of magnitude compared with the traditional time-stepping volume integral method on the same mesh in the online prediction stage, at the cost of a one-time training effort and previously mentioned error, making it highly effective for real-time and repeated predictions.