International Journal for Numerical Methods in Engineering最新文献

This work proposes a guaranteed error estimator for linear transient elastodynamics, accounting for both time and space discretization errors. The key lies in the definition of a novel dynamic constitutive relation error formulation, which is proven to be a strict bound of the discretization error. Moreover, based on the established dynamic constitutive relation error and the goal-oriented error estimation framework, strict upper and lower bounds on quantities of interest are also obtained. Numerical examples are conducted to verify the proposed strict bounds and to explore the application of these bounds to adaptive time stepping and mesh refinement.

We propose an explicit representation method using disk B-splines for Poisson's ratio metamaterial design. Disk B-spline representation generalizes the concept of the B-spline control point into a control disk, enhancing the ability to manipulate both the shape and thickness of the region. Therefore, this representation is frequently employed for shape optimization. The optimized metamaterials described by disk B-spline are decomposed into a sequence of circles constructing one implicit function. A novel optimization model based on disk B-spline representation is proposed, and the homogenization theory is used for calculating effective Poisson's ratio (PR). The numerical examples contained missing rib metamaterials, petal-like metamaterials, and extreme PR metamaterials, which are studies to illustrate the advantages and effectiveness. By explicitly manipulating the parameters of the disk's B-spline, a broad spectrum of unexpectedly negative Poisson's ratio from -0.1 to -0.9 sequences can be achieved, and arbitrary Poisson's ratios structures can be obtained through interpolating continuous parameters. It's also extended to encompass 3D structures. We validate the accuracy of our results by comparing them with simulations performed using commercial software.

Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu, and Shen, which has been broadly used to solve various challenging phase field problems. To design original energy-stable schemes, they have to solve a nonlinear algebraic equation to determine the introduced Lagrange multiplier, which can be computationally expensive, especially for large-scale and long-time simulations involving complex nonlinear terms. In this article, we propose an essential improved technique to modify this issue, which can be seen as a semi-implicit combined Lagrange multiplier approach. In general, the newly constructed schemes keep all the advantages of the Lagrange multiplier method and significantly reduce the computation costs. Besides, the new proposed second-order backward difference formula (BDF2) scheme dissipates the original energy, as opposed to a modified energy for the classic Lagrange multiplier approach. In addition, we establish a general framework for extending our constructed method to dissipative systems. Finally, several examples have been presented to demonstrate the effectiveness of the proposed approach.

The computational burden becomes unbearable when reliability analysis involves time-consuming finite element analysis, especially for rare events. Therefore, reducing the number of performance function calls is the only way to improve computing efficiency. This paper proposes a novel reliability analysis method that combines relevant vector machine (RVM) and improved cross-entropy adaptive sampling (iCE). In this method, RVM is employed to approximate the limit state surface and iCE is performed based on the constructed RVM. To guarantee the precision of RVM, the first level samples and the last level samples of iCE are used as candidate samples and the last level samples are regenerated along with the RVM updates. To prevent unnecessary updates of RVM, the proposed method considers the positions of the samples in the current design of experiment. In addition, based on the statistical properties of RVM and iCE, an error-based stopping criterion is proposed. The accuracy and efficiency of the proposed method were validated through four benchmark examples. Finally, the proposed method is applied to engineering problems which are working in extreme environment.

Surface texture is of great practical importance in applications due to its significant effect on the tribological performance of the sliding surface. In the present work, an explicit topology optimization framework for surface texture design is proposed. For this purpose, the moving morphable void (MMV)-based explicit topology optimization approach is used to maximize the load carrying capacity (LCC) of the bearing by optimizing the distribution of the surface texture. A multi-set of voids is established to describe the multi-film thickness of the texture. By using the explicit geometry information in MMV, the present work can be seamlessly linked to the CAD system, resulting in the accurate processing of complex surface textures. Besides some numerical examples to demonstrate the effectiveness of the proposed approach, experimental tests are also provided to verify the validity of the optimization results.

This article proposes an adaptive coupling strategy between the standard FEM and smoothed point interpolation methods (SPIMs) for the solution of phase-field fracture problems, where the SPIM discretization is used to model the fracture propagation regions. Adaptive strategies are an important tool for problems that demand highly refined meshes in localized regions, such as in phase-field problems. In the proposed strategy, the problem is initially discretized with a coarse FEM mesh, that is automatically replaced and refined by an SPIM discretization when and where fracture occurs. Five different benchmark tests are presented to illustrate the robustness of the proposed strategy. Brittle and quasi-brittle problems are simulated and evaluated in terms of phase-field contour plots and load-displacement paths, showing good agreement with literature results and with results obtained with previously refined FEM models. The numerical simulations consider different criteria for the identification of the regions where the discretization replacement and refinement must occur, different sizes of the substitution regions, and different SPIM strategies. The proposed strategy relies on three properties of the meshfree strategy: (i) the reduced connectivity that ease the adaptive refinement, (ii) the presence of the Kronecker-delta property, that makes the coupling with the FEM mesh straightforward, and (iii) the presence of nonpolynomial approximation functions, that provide a better approximation of the phase-field profile. As illustrated by the simulations, this new strategy results in computational times that are comparable with the ones of a previously refined FEM mesh, without requiring an a priori knowledge of the replacement regions.

In the nonlinear large deformation regime, the beam theory is usually based on the Timoshenko assumption which considers shear deformations. The formulation of a 3D Euler–Bernoulli beam has been significantly delayed and only recently it did attract the attention of few researchers. The main reason lies in the challenging complexities met once an attempt to develop such a theory is undertaken. The main obstacle in defining a three-dimensional Euler–Bernoulli beam theory lies in the fact that there is no natural way of defining a base system at the deformed configuration. In this article, we provide a novel methodology to do so leading to the development of a spatial rod formulation which incorporates the Euler–Bernoulli assumption. The first approach makes use of Gram–Schmidt orthogonalisation process coupled to a one-parametric rotation. The latter completes the description of the torsional cross sectional rotation and overcomes the nonuniqueness of the Gram–Schmidt procedure. In a second approach, the rotation tensor is defined based on first and second derivatives of the displacement vector of the centre line. It is followed by one parametric rotation. The proposed formulation is extended to the dynamical case and a stable, energy and momentum conserving time-stepping algorithm is presented as well. Specifically, the proof of conservation of angular momentum of the time stepping algorithm is highly demanding and is given here in full.