International Journal for Numerical Methods in Engineering最新文献

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.

Accurate stiffness and damage identification are the most important parts of structural health monitoring (SHM) for civil engineering structures. Reinforced concrete (r/c) structures are especially challenging due to the numerous cracks dispersed along the length of concrete elements. These cracks can originate from, for example, regular load of a structure, shrinkage or overloading. The usual way to tackle stiffness identification of r/c structures is to obtain the averaged linear stiffness of selected element areas through finite element model-based or response-based methods. In this paper, a variation of a weighted residual penalty-based local smoothing technique for direct stiffness identification was developed and compared to the state-of-the-art methods. The method is based on direct measurement of the axis rotations and rotational natural modes using novel MEMS rotation rate sensors. The rotational modes can be later smoothed without additional traditional translational acceleration measurements to calculate the curvature and stiffness of the beam. However, as shown in the paper, rotational modes can also be used directly for stiffness identification. The experimental analysis shows that the application of rotational measurements facilitates response-based stiffness identification of the r/c elements, providing more accurate damage identification.

This article presents a comparative study of the computational characteristics of Finite Element Analysis (FEA) and Isogeometric Analysis (IGA) in studying large elastic deformations and large-amplitude vibrations of shell-type structures. A geometrically nonlinear seven-parameter shell model is employed in a Lagrangian description in which the shell deformation is represented in mid-surface. Using a curvilinear coordinate system suitable for various geometries, the kinematic and kinetic of the problem are established, and Hamilton's principle is applied to derive the governing equations. The strain–displacement relationships and consequently, the remaining variational formulations are expressed in a matrix-vector form, allowing for direct implementation in both FEA and IGA. This efficient formulation enables a fair and consistent comparison between the two methods. Several numerical examples are examined, including the well-known static benchmark problems and their corresponding forced vibration analyses. The primary contribution of this article is the demonstration of the computational efficiency of isogeometric analysis in challenging case studies of geometrically nonlinear shells. Additional novel contributions include deriving a unified formulation for seven-parameter FEA and IGA shell models as well as analyzing the large-amplitude free and forced vibrations of shells.