Engineering Analysis with Boundary Elements最新文献

The multi-scale numerical procedure proposed in our previous work based on smoothed dissipative particle dynamics (SDPD) is employed, and a new multi-phase interaction model based on the inter-particle force (IPF) that includes a consistent repulsion force is presented and verified. A comparative investigation utilizing smoothed particle hydrodynamics (SPH), SDPD, and our multi-scale methods is then carried out and the computational efficiency, droplet morphology, wetting flow field, and advantages of the multi-scale method are demonstrated. In addition, the droplet thickness is derived from the Navier–Stokes equations with a stochastic force, demonstrating the effect of thermal fluctuations on the mesoscopic scale. Finally, the wetting states are simulated at different surface roughness values, and the transition of states and some new mechanisms are clarified. When the roughness scale is smaller than the interaction range between particles, the wetting state may change significantly, and this effect becomes weaker when the roughness scale exceeds the interaction range. The results also show that the horizontal roughness (direction of droplet spreading) is more decisive than vertical one (perpendicular to the direction of droplet spreading), usually leading to a transition of the wetting states, while the vertical roughness usually plays a reinforcing role.

The interval model, which requires less prior information than probabilistic and fuzzy models, is used to describe the uncertainty of the material and geometric parameters of soft biological tissues. A quadtree scaled boundary finite element method (quadtree SBFEM) and an optimization-based numerical algorithm are developed for the interval damage analysis of soft biological tissues. The material is hyperelastic, and the damage behavior is described by a gradient-enhanced damage model without mesh dependence. The deterministic problem is solved by the image-based quadtree SBFEM, and the interval problem is solved via an optimization based bounds estimation, which is reliable and insensitive to the scale of the intervals. A Legendre polynomial surrogate (LPS) is constructed to approximate the SBFEM-based deterministic solutions to reduce the computational cost of the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed approaches, and the uncertain behavior of the Cauchy stress and damage function.

Traditional RBF interpolation involves solving a linear system, making it computationally expensive for large datasets. Iterative-based quasi-interpolation combines RBF interpolation with iterative methods to enhance accuracy and convergence. To enhance efficiency and accuracy, we in this paper propose a novel method for RBF quasi-interpolation that combines Anderson acceleration with the asynchronous DCPI, termed Anderson-DCPI. The method alternates between the preconditioning iterative method and Anderson extrapolation, aiming to improve convergence rates. We demonstrate the convergence of Anderson-DCPI for positive definite RBF kernel functions and validate its effectiveness through a series of numerical examples.

In this paper, a new approach was presented for the transient analysis of SH-wave scattering problems by the dual reciprocity boundary element method (DR-BEM). In the use of static fundamental solutions and the concept of estimator functions, the effect of domain inertia integrals was applied in the boundary integral equations (BIEs). Then, the solvable form of the BIE was obtained by adding the free-field displacement to satisfy the stress-free boundary conditions on the surface. By implementing the formulation in a time-domain computer code, the accuracy and efficiency of the approach were evaluated by solving different examples including the embedded circular cavity, the semi-circular valley, and the twin hump hill subjected to obliquely propagating incident SH-wave. In this regard, a comprehensive comparative study was carried out with the half-space time-domain BEM (TD-BEM), previously presented by the corresponding author, to observe the accuracy of the results as well as the analysis time. The results showed that although the presented method had more complex models compared to the half-space TD-BEM, the analysis time was significantly reduced with the use of a simple formulation. This approach can be applied to prepare half-space models in the field of geotechnical earthquake engineering in substituting other time-consuming methods.

In this paper, we introduce a meshless method for numerical simulation of nonlinear Klein–Gordon equations. The method begins with a temporal discretization to address time derivatives. The stability and error of the temporal discretization scheme are theoretically analyzed. Subsequently, meshless algebraic systems of Klein–Gordon solitons are established by using the superconvergent finite point method (SFPM) for spatial discretization. The moving least squares approximation and its smoothed derivatives are adopted in the SFPM to ensure the high accuracy and remarkable superconvergence. Accuracy and convergence of the meshless numerical simulation for nonlinear Klein–Gordon equations are analyzed in theory. Numerical results validate the superconvergence and effectiveness of the method and confirm the theoretical analysis.