International Journal for Numerical Methods in Engineering最新文献

This paper presents a time spectral generalized finite difference method (TS-GFDM) for three-dimensional (3D) transient heat conduction in functionally graded materials (FGMs) with space–time dependent coefficients. The time derivative of temperature in the governing equation is approximated as a linear combination of temperatures at Gaussian points within each time step, achieved via the inverse transform of spectral integration. Space derivatives of temperature are evaluated as linear combinations of nodal temperatures, constructed using Taylor series expansion in conjunction with the moving least squares (MLS) approximation. The proposed method allows for large time steps in the temporal direction while ensuring stability over long-time simulations. In the spatial domain, it eliminates the need for mesh generation, making it particularly well suited for heat conduction analysis in complex structures. The numerical results obtained using the TS-GFDM are compared with those from existing methods and the analytical solution, demonstrating the higher computational efficiency of the proposed approach.

This research develops a new topology optimization (TO) scheme to manipulate the trajectory of particle suspended in fluid by reverting fluid motion by fluid-structure interaction (FSI). The simulation of particle trajectory considering the effect of FSI is both challenging and largely unexplored in the context of TO, and the TO of particle-fluid-structure interaction system has not been considered yet. The drag force of particle being mainly determined by the relative velocity between the particle velocity and the fluid velocity, the change of the particle trajectory can be attributed to the change of the fluid velocity originated by the structural deformation. To consider this complex coupling from an optimization point of view, this research extends the monolithic simulation and optimization method for FSI to the particle optimization method. The monolithic design method for FSI developed for TO considers the structure deformation on fluid motion and allows to find out optimal topologies. The adjoint sensitivity analysis is developed and applied for this multiphysics system. The effectiveness of the proposed method is demonstrated through several transient topology optimization problems that highlight the influence of FSI on particle motion.

Neural networks (NNs) based constitutive modelling to extract stress–strain relationships from data have recently gained significant attention, driven by advancements in artificial intelligence. However, a generic NN that can directly extract new inelastic constitutive models from experimental data is still lacking. Additionally, integrating NN models into numerical simulations for boundary value problems (BVPs) while ensuring computational stability and efficiency presents a considerable challenge. This study proposes a novel postulate-driven NN (PNN) that leverages the basic constitutive modelling postulates of inelasticity and the strong nonlinear fitting ability of NNs to identify internal variables and constitutive relationships from stress–strain data automatically. The feasibility of PNN is demonstrated by successfully identifying internal variables and stress–strain responses in theoretical models of von Mises elastoplasticity and isotropic elasticity-based damage, as well as real-world clay experiments. The developed model is subsequently embedded into the finite element method (FEM) for solving BVPs by feeding the predicted stress and updated material tangential matrix. In particular, the PNN-based damage model is encoded into FEM to simulate bar damage. The results indicate that PNN is a promising alternative to directly identify internal variables and constitutive relations from experimental stress–strain data. Furthermore, its integration with FEM enables an efficient solution of BVPs while maintaining computational stability and cost-effectiveness.

A steady state Eulerian smoothed particle hydrodynamics (SPH) solver is proposed by integrating the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. By removing time dependent terms from the governing equations, the proposed approach directly solves for steady-state velocity, pressure, and temperature fields for incompressible flows using a matrix-based formulation. To efficiently handle the resulting large, sparse linear systems, a matrix-free Bi-CGSTAB iterative solver is employed and the overall computational algorithm is fully parallelized on GPUs to accelerate performance. The accuracy and efficiency of the proposed steady solver are validated through several benchmark tests, including pipe flow with and without obstacles, 2D/3D lid-driven cavity flow with and without heat transfer, and natural convection flow. Compared to conventional transient Eulerian SPH solvers, the proposed method achieves 8.97–17.36 times speedup while maintaining high accuracy, making it a promising tool for steady state CFD analysis and as a precursor to transient simulations.

The structural stability and stiffness are both crucial for maintaining aerodynamic profiles of stiffened thin-walled structures, especially in aerospace applications when subjected to extreme thermal loading. One of the challenges arises from significant compression loads induced by the restricted thermal expansion, leading to thermally induced buckling issues and severe thermal deformation. Existing methods lack choice and inevitably rely on room-temperature optimization models in thermal buckling designs, leading to an irreconcilable contradiction between the optimized thermal buckling and thermal stiffness performances. This study focuses on the collaborative design of buckling resistance and stiffness reinforcement for mitigating deformation failure in stiffened thin-walled structures and proposes a novel collaborative optimization model that maximizes the critical buckling load factor (BLF) under volume and regional strain energy constraints, namely BVR model. Compared with the conventional model that maximizes the critical BLF under volume and compliance constraints (BVC), the comparison results demonstrate the advantage of the proposed method in ensuring structural clarity, stability, and stiffness of optimal designs through typical and complex numerical examples. The failure reason for the conventional model is also given. For an aft deck structure under thermal loading, the proposed method increases the critical BLF by 98.7% and reduces the thermal deformation by 63.6%.

In this paper, we focus on numerical modeling of coupled processes of heat transfer and two-phase flow in porous media, which play a crucial role in many fields, particularly in thermally enhanced oil recovery and geothermal production. We first introduce a thermodynamically consistent numerical modeling framework for non-isothermal incompressible immiscible two-phase flow in porous media, which integrates the energy conservation equation with the newly developed two-phase flow equations. Applying the Gibbs fundamental relation, we rigorously derive an entropy equation, which demonstrates that the model obeys the second law of thermodynamics. To resolve numerical challenging aspects resulting from the inherent nonlinearity and strong coupling of the model, we apply subtle implicit and explicit mixed treatments and the energy factorization approach, in order to design a linearized and decoupled time marching scheme. The spatial discretization is constructed using the cell-centered finite volume method with carefully designed treatments. In particular, the averaging and upwind strategies are applied for discretizing the energy conservation equation to enforce the local energy conservation and the entropy stability (i.e., the adherence to the second law of thermodynamics). Taking advantage of the discrete versions of the Gibbs relation and the specific mean and difference splitting rules, we derive a discrete counterpart of the second law of thermodynamics, which yields the entropy stability without any restriction on time step sizes. Numerical experiments are performed to demonstrate the features and capabilities of the proposed scheme.