International Journal for Numerical Methods in Engineering最新文献

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.

This work establishes a thermo-mechanical coupling model for thermally induced cracks in quasi-brittle materials within the framework of localizing gradient damage theory. The constitutive relation considering the thermal expansion effect, and the heat conduction equation integrating the volumetric strain and damage evolution, are formulated based on the Clausius–Duhem inequality to ensure thermodynamic consistency. In particular, to accommodate the tension-compression strength asymmetry across different quasi-brittle materials, a modified Mazars strain is proposed as the driving force for the micro equivalent strain, where the first invariant of strain tensor and an adjustable ratio of compressive strength to tensile strength ($��k�$) are introduced. The numerical implementation employs the generalized-α method for time domain discretization and the staggered scheme for decoupling. Numerical simulations demonstrate a nice feasibility of the modified Mazars strain in capturing both tensile and mixed-mode failures, and the proposed model proves capable of characterizing complex crack behaviors under thermal loading in both quasi-static and dynamic scenarios. The quenching test simulations of ceramic plates highlight the bidirectional coupling effects on crack patterns. Unidirectional coupling models that ignore the influence of volumetric strain and damage evolution on the temperature field would underestimate the temperature gradient, resulting in larger crack spacing and fewer cracks. In the thermal shock tests of cylindrical specimens, the transition in crack patterns from spiral shear bands to an annular damage zone with increasing compression-tension strength ratio ($��k�$) is precisely captured, demonstrating the generality of the proposed model for various quasi-brittle materials with tension-compression strength asymmetry.