International Journal for Numerical Methods in Engineering最新文献

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.

This study proposes a hybrid collocation approach for simulating heat conduction problems in anisotropic functionally graded materials over extended time intervals. In this approach, the Krylov deferred correction (KDC) scheme is employed for the temporal discretization of dynamic problems, featuring a novel numerical implementation designed to ensure the precise satisfaction of boundary conditions. The localized radial basis function (LRBF) collocation method is modified and utilized to solve the resulting boundary value problems. A new radial basis function is developed and combined with an optimization strategy for the distribution of source points to enhance the performance of the LRBF scheme. This method synergizes the KDC technique, which supports large time step sizes, with the LRBF collocation method, characterized by its truly meshless nature, to address dynamic problems over long durations. Additionally, the coefficient matrix produced by the LRBF method is sparse and depends solely on the spatial distances between collocation points and source points, which is advantageous for long-term simulations. Numerical simulations spanning thousands of time steps demonstrate the accuracy, stability, and convergence of the hybrid approach. The developed numerical framework shows significant improvements over existing methods, particularly in handling dynamic problems with substantial temperature variations.

This paper aims to optimize both the topology of microstructure and macrostructure, by using the Moving Iso- Surface Threshold (MIST) method under the framework of Isogeometric Analysis (IGA). To achieve this, the physical response and the equivalent properties of the microstructure are solved by IGA. The physical response functions are defined at the control points. The NURBS fitting method is used to fit the physical response function, generating a NURBS surface for describing the physical response function, that is, the explicitly described physical response function surface. An iso-surface cut the NURBS physical response surfaces to obtain the explicitly described structure topology. In addition, the standard IGS files of the NURBS physical response surface and iso-surface can be transferred to Computer-Aided-Design (CAD) software without post-processing. The multiscale structure can be easily assembled in CAD software using the proposed method. Finally, several numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function.

Sensitivity analysis plays a vital role in understanding the impact of control parameter variations on system output, particularly in cases where an objective functional evaluates the output's merit. The adjoint method has gained popularity due to its efficient computation, especially when dealing with a large number of control parameters and a few functionals. While the discrete form of the adjoint method is prevalent, exploring its continuous counterpart can offer valuable insights into the underlying mathematical problem, particularly in characterizing the boundary conditions. This paper presents an investigation into the continuous form of the adjoint method applied to time-dependent viscous flows, where the time dependence is either imposed by boundary conditions or arises from the system dynamics itself. The proposed approach enables the computation of sensitivities with respect to both geometric and operational control parameters using the same adjoint solution. For time-periodic flows, a special formulation is developed to mitigate the computational costs associated with time integration. Results demonstrate that the methodology proposed in a previous work can be successfully extended to time-dependent flows with fixed time spans. In such applications, time-accurate simulations of physics and adjoint fields are sufficient. However, periodic flows necessitate the application of the Leibniz Rule because the period might depend on the control parameters, which introduces additional terms to the adjoint-based sensitivity gradient. In that case, time integration can be limited to a minimum common multiple of all appearing periods in the flow. Although the accurate estimation of such multiple poses a challenge, the approach promises significant benefits for sensitivity analysis of fully established periodic flows. It leads to substantial cuts in computational costs and avoids transient data contamination.

In this paper, we present a stable generalized finite element method (SGFEM) to address the approximation of the discontinuous solutions of interface problems with nonhomogeneous interface conditions. We propose a set of enrichment functions based on the Heaviside and Distance functions on the patches that intersect the interface. The enrichment based on the Heaviside function is used to strongly enforce the given nonhomogeneous interface condition, that is, the jump in the solution, and only the enrichment based on the product of the Heaviside and Distance functions contributes to the degrees of freedom. Consequently, the number of degrees of freedom in this approach is the same as that is required for an interface problem with homogeneous interface conditions. The chief merit is that the proposed method totally confors and does not use conventional techniques for the nonhomogeneous interface condition in the literature, such as the penalty method or the Lagrange multiplier. Our experiments show that this method yields optimal order of convergence, its conditioning is not worse than that of the standard finite element method, and it is robust.