International Journal for Numerical Methods in Engineering最新文献

In this manuscript, we extend the quasi-static multi-phase-field method for composite materials to the dynamic case. In the dynamic multi-phase-field method, each phase of the composites has its individual phase field, and the degradation of each phase is governed by its respective phase field. The macroscopic response is then obtained by averaging and homogenization approaches through the reduced-order-homogenization (ROH) framework. Through the ROH and the Francfort-Marigo variational principle, we can obtain the equations that govern the motion of the composites and the evolution of each phase field. This method is capable of capturing the characteristics of dynamic fracture, such as crack branching, without the need for any additional bifurcation criterion. Moreover, it can capture dynamic fracture patterns in composite materials, including matrix cracking, fiber breakage, and delamination. The corresponding numerical algorithm that includes spatial and temporal discretization is developed. An implicit, staggered Newton-Raphson iterative scheme is implemented to solve the nonlinear coupled equations. Finally, this method is tested with several sets of dynamic fracture benchmarks, which demonstrates good agreement with the experiments and other numerical methods.

Advances in 3D-printing technology have enabled the fabrication of periodic microstructures that exhibit characteristic mechanical performances. In response, multiscale topology optimization, which finds the optimal design of microstructure for the macrostructure geometry and performance requirements, has become a hot topic in the field of structural optimization. While the basic optimization framework based on the homogenization theory spanning macro and microscales is available, it is computationally expensive and not easily applicable in practical scenarios such as high-resolution design for precision modeling and reliable design considering non-linearities. To address this issue, we focus on a homogenization analysis using a fast Fourier transform as an alternative approach to conventional finite element analysis and develop an optimization method with fast computing speed and low memory requirements. In this paper, we define a simple stiffness maximization problem with linear elastic materials and conduct two and three-dimensional optimization analyses to evaluate the validity and performance of the proposed method. We discuss the advantages of computational cost, the influence of the filtering process, and the appropriate setting of material contrast.

In this article, the Pareto front of multiobjective linear optimization problems (MLOPs) is approximated via a new neural network (NN) model. Karush-Kuhn-Tucker (KKT) optimality conditions for multiobjective linear optimization problems are applied to construct this neural network model. Compared with the available models in the literature, the proposed approach employs the KKT optimality conditions of the main MLOP, not a scalarized problem related to the MLOP. The stability of the suggested NN model in the sense of Lyapunov, is proved. Also, it is shown that the proposed NN is globally convergent to an efficient solution of the main MLOP. Moreover, we present two algorithms to attain some nondominated points with equidistant distribution throughout the Pareto front of bi-objective and three-objective optimization problems. In the suggested algorithms we apply some filters to attain a uniform approximation of the Pareto front. Illustrative results are provided to clarify the validity and performance of the introduced model for different categories of MLOPs. Numerical results satisfy the presented theoretical aspects. In order to have a comparison with other methods, three indicators, including Hypervolume (HV), Spacing, and Even distribution (EV), are utilized. Finally, we apply the proposed idea for the sustainable development of a multinational company in automotive engineering.

New semi-analytical shell elements are developed using the scaled boundary finite element method. A shell element is treated as a three-dimensional continuum whose midsurface, the generalized “boundary” of the continuum, is characterized with a quadrilateral spectral element. It is along the thickness direction ξ that the midsurface is scaled to represent the three-dimensional geometry and that the analytical displacement solution is sought. Neumann expansion is used to approximate the inverse of the Jacobian as a quadratic matrix polynomial of ξ while the assumed natural strain method is applied to alleviate the shear and membrane locking. The virtual work principle considering body forces is utilized to derive the scaled boundary finite element equation, which is directly solved via the differential quadrature method. Numerical examples show that the shell elements with five displacement sampling points along ξ can efficiently analyze thin to very thick general shells.

Reduced order modeling (ROM) is applied to the finite element thermo-mechanical simulation of metal additive manufacturing at part scale. This is a significant challenge because of the continuously evolving computational domain, on which a local reduced basis is required to apply the projection-based ROM. In this paper, ROM is applied to the mechanical resolution, which is much more time-consuming than the thermal one. Considering the modeling of DED processes (directed energy deposition), it is proposed to organize the training set of simulation snapshots according to an energy deposition length that represents the progress of the process. The full-order model consists of a transient thermomechanical model modified by use of the previously developed Inherent Strain Rate method. When applying the projection-based ROM to this full-order model, the constructed data sequence enables the design a local ROM depending on the energy deposition length and process parameters. The approach, in its present state, is limited to constructions with a constant transverse geometry and a constant set of process parameters. The simulation of the DED construction of a turbine blade mock-up, made of thirty layers with interlayer dwell times, revealed a computational speedup of about 100.

Thermal analysis of fractured porous media is of interest in environmental and reservoir engineering. The dual-porosity method is a common and cost-efficient approach for modeling fractured domain. In the case of thermal analysis, this method encounters two challenges; the high dependence on the matrix to fracture transfer parameter, “shape factor,” and numerical oscillations produced in the conventional Galerkin finite element formulation for convection dominant problems. To overcome these issues a Petrov-Galerkin dual porosity (PGDP) algorithm is presented for the analysis of 2D transient heat flow in fractured porous media. In the computational algorithm, an appropriate unit cell is selected from the primary domain and the corresponding thermal shape factor is evaluated with a time-varying function. Unlike conventional constant shape factor models, this shape factor accounts for not only the geometry of the blocks, but also the thermal properties of the domain and existing boundary conditions. Several case studies are simulated to investigate the validity and sensitivity of the time-dependent thermal shape factor to different parameters for square and non-square blocks. Moreover, the Petrov-Galerkin formulation is applied to effectively achieve the accurate spatial results for highly convective heat flows. Numerical simulations are performed to study the efficiency and accuracy of the proposed PGDP algorithm for different range of convection and conduction regimes. This study illustrates that the PGDP algorithm efficiently enhances the accuracy of the simulation in modeling of fractured domains, particularly in transient stages. Moreover, the capability of the proposed computational algorithm is demonstrated in modeling square and non-square matrix formations.

This study presents an improved version of the Extended Lumped Damage Mechanics (XLDM) formulation within a position-based approach of the Finite Element Method (FEM). In the XLDM, the strain field has been assessed from the elongations of numerical extensometers, which connect the finite element nodes. In addition, localisation bands positioned along the elements' boundaries depict the mechanical effects of material degradation. The position-based approach of FEM enables the accurate modelling of geometrically non-linear effects and its computational implementation is straightforward. In this approach, the equilibrium configuration has been evaluated in relation to the nodal positions instead of its displacements. Thus, one improvement proposed herein involves the coupling of the XLDM failure predictions within an exact geometrically non-linear framework. Besides, in this study, the XLDM has been further improved by incorporating the damage growth caused by compressive stresses. The non-linear formulation proposed herein enables the presence of reinforcements, which have been added by an embedded scheme and lead to another improvement in the XLDM context. Three applications demonstrate the accuracy of the proposed non-linear scheme, in which the numerical responses obtained by the proposed improved formulation have been compared to experimental results available in the literature.