International Journal for Numerical Methods in Engineering最新文献

In this work, we propose a new four-node shell element (called BKWH24) with six degrees of freedom per node based on the first-order shell theory of Reissner–Naghdi. The element is valid for thin to thick shells, taking into account membrane, bending, and transverse shear effects with strain components explicitly linear in the thickness coordinate. The BKWH24 shell element is based on the generalisation of the plate-bending BKWA element regarding the approximations of displacements, rotations, and shear strains. The paper presents results for several classical benchmarks for shells and proposes new benchmarks to demonstrate the influence of transverse shear effects in thick shells.

Although the quasi-bond method (QBM) provides a promising numerical tool for handling continuous-discontinuous problems in solid mechanics, it faces inherent limitations including fixed Poisson's ratios and inadequate modeling of mixed-mode fracture in quasi-brittle materials due to neglected shear-softening effects. To overcome these shortcomings, this study proposes an extended quasi-bond method (EQBM) that integrates bond rotation-induced shear deformation as an independent kinematic mechanism and introduces a novel dual-mechanism fracture criterion: (1) a tensile-shear coupling formulation for brittle materials via an elliptical failure envelope and (2) the explicit shear softening coupled with cohesive zone models at the bond level for quasi-brittle materials. Computational efficiency is further enhanced through a hybrid FEM/EQBM coupling strategy. Validation across diverse benchmarks confirms EQBM's accuracy in predicting elastic deformation and complex fracture behavior, including mixed-mode fracture and snap-back behavior. The results demonstrate the effectiveness of the dual-mechanism fracture criterion and EQBM's improvements over conventional approaches.

This paper presents the numerical dispersion analysis of a recently developed local-domain-enriched finite element (LEFE) for wave propagation problems. LEFE enriches standard finite element interpolations with trigonometric functions defined in the element domain, which satisfy the partition of unity and vanish at the nodes. A formulation is developed to determine numerical dispersion errors from spatial and temporal discretizations, with explicit expressions derived for the characteristic equation linking numerical phase velocity to the non-dimensional wavenumber and Courant-Friedrichs-Lewy (CFL) number. Based on this, a sampling theorem is established to estimate optimal element size and time step for accurate analysis. Results show that LEFE with one and two enrichment terms requires 9- and 18-times fewer elements per wavelength than the conventional finite element method (FEM) and significantly outperforms the other existing enriched elements. Unlike the latter elements, LEFE exhibits a monotonic reduction in combined dispersion error with decreasing CFL number. Further, it produces a unique relation between the total-to-spatial dispersion ratio and the product of element size, wavenumber, and CFL number, enabling a generalized time-step criterion. LEFE achieves 7-18-fold reductions in degrees of freedom (DOFs) and 24350-fold reductions in computational time compared to standard FEM, demonstrating its high accuracy and efficiency in simulating high-frequency narrowband and broadband wave propagation.

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.