International Journal for Numerical Methods in Engineering最新文献

During structural design, the geometry of the structure is frequently modified. Each configuration requires numerical simulations to determine the associated physical fields, which are both computationally demanding and labor-intensive. This study presents a geometry-adaptive peridynamics (GAPD) method to enhance simulation efficiency under varying geometries. In our method, a grid trimming technique is introduced to avoid the need for geometric reconstruction with each new configuration. New configurations are generated through the trimming of a parent configuration. Specifically, the bonds in the parent configuration that intersect with the boundary of the new configuration are broken. While this trimming operation facilitates grid generation, it also introduces certain limitations, such as the inability to perform grid refinement. Then, high-dimensional equations of the new configuration are projected onto a low-dimensional system with fewer degrees of freedom (DOFs) using a set of geometry-adaptive basis vectors, which are extracted from the flexibility matrix of the parent configuration. The number of DOFs in the problem is effectively reduced, thereby enhancing the simulation efficiency. Numerical examples are conducted using GAPD to investigate the thermal and mechanical behaviors of laboratory specimens, demonstrating the promising applicability of GAPD even under significant geometric changes. In addition, two practical engineering problems are studied: first, the rapid structural design optimization of aircraft seats; second, the fast assessment of the thermal performance of different turbine rotors during their structural design process. The results show that GAPD significantly enhances computational efficiency while maintaining numerical accuracy.

Discovering equations from data, particularly high-dimensional data, is challenging in various fields of science and engineering and has the potential to revolutionize science and technology. This paper presents a new non-intrusive reduced-order modelling (NIROM) method to discover a lower-dimensional version of the equations of fluids from the data. Unlike Navier–Stokes, these equations have a lower dimensional size and are easy to solve. This method provides a different perspective for understanding fluid dynamics, particularly turbulent flows. In this method, the autoencoder deep neural network is used to project the high-dimensional space into a lower-dimensional nonlinear manifold space to find the latent dynamics. The Proper Orthogonal Decomposition (POD) is then used to stabilise the nonlinear manifold space in order to guarantee a stable manifold space for pattern or equation discovery for highly nonlinear problems such as turbulent flows. Sparse regression is then used to discover the low-dimensional equations of fluid dynamics in the latent nonlinear manifold space. What distinguishes this approach is its ability to discover low-dimensional equations of fluid dynamics in the nonlinear manifold space. We demonstrate this method in several high-dimensional complex fluid dynamic systems, such as lock exchange and two cylinders. The results demonstrate that the resulting method is capable of discovering lower-dimensional equations that researchers in this community took many decades to resolve. In addition, this model discovers dynamics in a lower-dimensional manifold space, thus leading to great computational efficiency, model complexity, and avoiding overfitting. It also provides new insight into our understanding of sciences such as turbulent flows.

In this work, we investigate a nonconforming finite element (FE) approximation of phase-field parameterized topology optimization governed by the Stokes flow. The phase field, the velocity field and the pressure field are approximated by conforming linear FEs, nonconforming linear FEs (Crouzeix-Raviart elements) and piecewise constants, respectively. When compared with the standard conforming counterpart, the nonconforming FEM can provide an approximation with fewer degrees of freedom, leading to improved computational efficiency. We establish the convergence of the resulting numerical scheme in the sense that the sequences of phase-field functions and discrete velocity fields contain subsequences that converge to a minimizing pair of the continuous problem in the $��{�H�}^{�1�}�$-norm and a mesh-dependent norm, respectively. We present extensive numerical results to illustrate the performance of the approach, including a comparison with the popular Taylor-Hood elements.

The classic finite element (FE) method suffers from low computational efficiency when dealing with wave propagation in unbounded domains, as a sufficient number of elements are required per wavelength. This issue becomes particularly pronounced in soil dynamics problems involving semi-infinite ground. In this paper, we develop a 2.5D finite-length thin layer (FTL) method to efficiently calculate ground vibrations. Based on the well-established thin layer method, the ground is first discretized in the vertical direction, producing a series of thin layer elements. Through the quadratic eigenvalue analysis, the mode shapes of the thin layer elements are obtained. By superimposing the left- and right-propagating mode shapes, the stiffness matrix of the 2.5D FTL element is constructed. Since the mode shapes are derived analytically, the length of the 2.5D FTL element is not restricted by the analyzing frequency or corresponding ground wavelength, significantly reducing the degrees of freedom (DOFs) of the ground model. The ground responses computed by the 2.5D FTL method are compared with those obtained using the classic dynamic flexibility method and the 2.5D FE method, demonstrating the high accuracy of the 2.5D FTL method. The 2.5D FTL element is subsequently incorporated into the 2.5D finite element, with the perfectly matched layer (PML) serving as an absorbing boundary. Numerical results exhibit good compatibility between the 2.5D finite element and the 2.5D FTL element. Additionally, a case study of ground vibrations from an underground tunnel is conducted, illustrating the capability of the proposed method in analyzing dynamic interactions between complex engineering structures and soils.

Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to efficiently search for the global minimum of a black-box computational model. Gaussian processes have limited applicability in engineering design problems, which usually have many design variables but typically a low intrinsic dimensionality. Their scalability can be significantly improved by identifying a low-dimensional space of latent variables that serve as inputs to the Gaussian process. In this paper, we introduce a multi-view learning strategy that considers both the input design variables and output data representing the objective or constraint functions, to identify a low-dimensional latent subspace. Adopting a fully probabilistic viewpoint, we use probabilistic partial least squares (PPLS) to learn an orthogonal mapping from the design variables to the latent variables using training data consisting of inputs and outputs of the black-box computational model. The latent variables and posterior probability densities of the PPLS and Gaussian process models are determined sequentially and iteratively, with retraining occurring at each adaptive sampling iteration. We compare the proposed probabilistic partial least squares Bayesian optimisation (PPLS-BO) strategy with its deterministic counterpart, partial least squares Bayesian optimisation (PLS-BO), and classical Bayesian optimisation, demonstrating significant improvements in convergence to the global minimum.