Engineering Analysis with Boundary Elements最新文献

Accurate and efficient calculation of all second-order wave load components in six degrees of freedom (6DoF) remains a challenging task, in particular for structures with sharp edges. Based on Gauss theorem, we have tailor-made an efficient method for direct time-domain solvers utilizing, for instance, boundary element methods. Unlike other methods based on momentum conservation or Gauss theorem that require control surfaces, this method only involves integrals on the structure and free surfaces. The accuracy and efficiency of the method are firstly verified for the mean and sum-frequency wave forces on a hemisphere and a truncated vertical cylinder. Subsequently, an application to study the motion responses of a semi-submersible floating offshore wind turbine (FOWT) in focused waves is presented, where experimental results are also available. The results indicate that the proposed method can greatly improve the computational efficiency in accurately predicting second-order loads on offshore structures with sharp edges in direct time-domain solvers. For the FOWT in focused waves, this alternative method is essential in achieving accurate prediction of hydrodynamic responses near the focus time.

For the reaction–diffusion equation (RDE) based topology optimization of elastoplastic structure, exactness in volume constraint can be crucial. As a non-traditional numerical method, the recently proposed exact volume constraint requires iterations to determine the precise Lagrangian multiplier. Conversely, conventional inexact volume constraint methods resemble a time-forward scheme, potentially leading to convergence issues. An approximate topological derivative for the 2D elastoplastic problem is derived and utilized to investigate the difference between employing exact and inexact volume constraint methods. A comprehensive examination is conducted by varying parameters such as mesh density, design domain aspect ratio, applied load, constrained volume ratio, and the diffusion coefficient $\tau$. Results indicate that the inexactness of volume constraint can lead to more severe issues in elastoplasticity compared to elasticity. The exact volume constraint method not only yields significantly improved convergence in structural optimization but also reduces structural compliance and computational runtime. There might be speculation that the fluctuation caused by the traditional inexact treatment of volume constraints could prevent the optimization process from being trapped in a local minimum. However, contrary to this assumption, in elastoplastic cases, it often has the opposite effect, frequently driving the structure away from a global optimum. Particularly noteworthy is the observation that inexact volume constraint quite often results in very poor structures with exceedingly high compliance. On the other hand, increasing the normalization parameter can lead to substantial improvements in results. These findings underscore the necessity of exact volume constraint for nonlinear topology optimization problems.

Geometric nonlinearities, material nonlinearities, and volume locking are the notable challenges faced in hyperelastic analysis. Traditional methods in this regard are complex and laborious for implementation as they require linearization and formulation of global matrix equations while simultaneously addressing volumetric locking. A mixed node's residual descent method (NRDM) proposed herein can effectively address the numerical challenges associated with geometric nonlinearities, material nonlinearities, force nonlinearities, and incompressibility. First, the implementation of the NRDM is considerably simplified as unlike traditional incremental–iterative methods, it's a matrix-free iterative method that does not require incremental linear equations. Second, the NRDM addresses the geometric and material nonlinearities with relative ease as it flexibly describes the deformation with the initial configuration or assumed deformed configuration as the reference frame. Third, the NRDM prevents the occurrence of volumetric locking by employing hydrostatic pressure as an independent variable. Furthermore, the NRDM can easily treat the force nonlinearities and boundary nonlinearities by controlling the relation between load and deformation during iteration. Moreover, a notable accuracy of the NRDM is confirmed through numerical verifications, and several critical matters are discussed, including the scheme for adjusting the basic independent variables, treatment of displacement boundaries, scheme for imposing loads, and computational parameter setting.

In this paper, we propose a novel model for the discrimination of complex three-dimensional connected regions. The modified model is grounded on the Allen–Cahn equation. The modified equation not only maintains the original interface dynamics, but also avoids the unbounded diffusion behavior of the original Allen–Cahn equation. This advantage enables us to accurately populate and extract the complex connectivity region of the target part. The model is discretized employing a semi-implicit Crank–Nicolson scheme, ensuring second-order accuracy in both time and space. This paper provides a rigorous proof of the unconditional energy stability of our method, thereby affirming the numerical stability and the physical rationality of the solution. We validate the discriminative ability of the proposed model for 3D complex connected regions.

In this research work, we apply a numerical scheme based on the first-order time integration approach combined with the modifications of the meshless approximation for solving the conservative Allen–Cahn–Navier–Stokes equations. More precisely, we first utilize a first-order time discretization for the Navier–Stokes equations and the time-splitting technique of order one for the dynamics of the phase-field variable. Besides, we use the local interpolation based on the Matérn radial function for spatial discretization. We should solve a Poisson equation with the proper boundary conditions to have the divergence-free property during the numerical algorithm. Accordingly, the applied numerical procedure could not give a stable and accurate solution. Instead, we solve a regularization system in a discrete form. To prevent the instability of the numerical solution concerning the convection term, a biharmonic term with a small coefficient based on the high-order hyperviscosity formulation has been added, which has been approximated by a scalable interpolation based on the combination of polyharmonic spline with polynomials (known as the PHS+poly). The obtained full-discrete problem is solved using the biconjugate gradient stabilized method considering a proper preconditioner. We investigate the potency of the numerical scheme by presenting some simulations via uniform, hexagonal, and quasi-uniform nodes on rectangular and irregular domains. Besides, we have compared the proposed meshless method with the standard finite element method due to the used CPU time.

An enhanced computational approach is formulated to assess the service performance of active phased array antenna (APAA). For this approach, the discretized system equation of the thermo-mechanical coupling analysis is firstly constructed by the node-based gradient smoothing technique. Then, the stabilization terms are introduced to further improve the computational accuracy and stability, which are related to the temperature and strain gradient of APAA. Finally, the thermo-mechanical-electromagnetic (TME) coupling model is established by quantitatively analyzing the relationship between electromagnetic performance and thermal deformation of APAA. The accuracy, efficiency, convergence speed and mesh distortion insensitivity of the developed approach are deeply studied and its effectiveness in addressing the multi-physics coupling analysis of APAA is fully demonstrated through comparisons with traditional methods.

In this study, the effects of partitioning a square cavity with both vertical and horizontal porous walls on conjugate natural convection heat transfer are investigated numerically using a non-linear Darcy-Brinkman-Forchheimer model. The primary objective is to establish benchmark solutions and a dataset for validating Computational Fluid Dynamics (CFD) simulations. The governing equations, including mass, Navier-Stokes, and energy, are discretized using a staggered grid system based on the control volume method. To handle porous media, a FORTRAN code is developed based on the non-linear Darcy-Brinkman-Forchheimer model and initially validated against three challenging benchmark cases. These cases involve mixed and natural convection heat transfer in a square porous cavity, with and without a magnetic field. Through comparative analysis with existing data, the accuracy and robustness of the numerical model in capturing complex flow and heat transport phenomena in porous media are confirmed. Subsequently, the validated numerical model is applied to examine conjugate natural convection heat transfer in a square cavity partitioned with both vertical and horizontal porous matrices. In the final stage of the investigation, the influence of a magnetic field on the heat transfer rate within the partitioned enclosure is also explored. The results reveal significant impacts of the Darcy number and porous region orientation on the thermal and hydrodynamic characteristics of the system. Moreover, substantial variations in heat transfer rate and flow intensity within the computational domain are observed with decreasing the Darcy number and increasing Hartman numbers.

This article presents a local mesh-less procedure for simulating the Galilei invariant fractional advection–diffusion (GI-FAD) equations in one, two, and three-dimensional spaces. The proposed method combines a second-order Crank–Nicolson scheme for time discretization and the second-order weighted and shifted Grünwald difference (WSGD) formula. This time discretization scheme ensures unconditional stability and convergence with an order of $O\left({\tau }^2\right)$. In the spatial domain, a mesh-less weak form is employed based on the direct mesh-less local Petrov–Galerkin (DMLPG) method. The DMLPG method employs the generalized moving least-square (GMLS) approximation in conjunction with the local weak form of the equation. By utilizing simple polynomials as shape functions in the GMLS approximation, the necessity for complex shape function construction in the MLS approximation is eliminated. To validate and demonstrate the effectiveness of the proposed algorithm, a variety of problems in one, two, and three dimensions are investigated on both regular and irregular computational domains. The numerical results obtained from these investigations confirm the accuracy and reliability of the developed approach in simulating GI-FAD equations.

Effective thermal conductivity of porous media is a crucial parameter for heat transfer within them. Many studies have characterized various porous media by adjusting the control parameters generated through the Quartet Structure Generation Set method. The porous media effective thermal conductivity is then determined through Computational Fluid Dynamics calculations, which, however, necessitate significant computational resources and time. Thus, following an exploration of the influence of control parameters (i.e., porosity, core growth probability, and their coupling) on the effective thermal conductivity of isotropic porous media generated by the Quartet Structure Generation Set method, this study developed a multi-layer perceptron prediction model. The aim was to establish a prediction model from the porous media control parameters to effective thermal conductivity, thereby reducing the time spent on iterative calculations. The findings indicate that the effective thermal conductivity does not uniformly increase with the growth of core probability, and instead fluctuates after a certain threshold. Notably, the trained model exhibits a high prediction accuracy, with average deviations of 0.0887 and 0.0748 for the training and testing datasets, respectively.

Dynamic fracture is a critical concern in the design and reliability assessment of concrete structures. This study presents a numerical prediction of dynamic fractures in concrete composites using a nonlocal multiscale damage model and the scaled boundary finite element method (SBFEM). The nonlocal multiscale damage model accurately captures the damage behavior of concrete materials by considering the nonlocal effects and predicting fractures under dynamic loading conditions. The SBFEM combined with quadtree meshes, efficiently models and discretizes concrete composites, enhancing computational efficiency, and capturing local details. The concrete mesostructure consists of aggregates, mortar matrix, and interface transition zone. The random aggregates are generated using the popular Monte Carlo simulation and take-and-place methods. By slightly offsetting the boundaries of the generated aggregates, a virtual thickness interface is obtained to approximately characterize the weakest regions. This study extensively investigates the effects of loading rate, aggregate content and shape, and interface thickness on fracture properties. The loading rate significantly influences crack morphology, with low rates suppressing crack branching, and higher rates resulting in crack branching. Moreover, an increased aggregate content in the concrete results in greater maximum reaction force. Additionally, the range of the maximum reaction force is higher when polygonal aggregates are used as compared to circular aggregates. This study examines the impact of the interface thickness on the fracture characteristics. Increasing the interface thickness makes the interface region more fragile, resulting in additional minimally damaged areas alongside the completely damaged cracked sections. This behavior can be attributed to the energy degradation functions employed in the model, thereby decreasing the load-bearing capacity of these regions. These findings contribute to a better understanding of the dynamic fracture phenomena and aid in optimizing the design and improving the reliability of concrete structures.