International Journal of Computational Methods

Laser Powder Bed Fusion (LPBF) is an additive manufacturing method that manufactures high density and quality metal products. We present a coupled grain growth and heat transfer modeling technique to understand the materials microstructure evolution in metals during the cooling process of LPBF. The phase-field model is combined with a transient heat transfer equation to simulate the solidification and crystallization of the melt pool simultaneously. Specifically, the variable domain and driving force of the order parameters in the phase-field calculation are defined using current temperature distribution. Additionally, the latent heat generated by crystallization is introduced as a heat source to affect temperature evolution in the cooling process. The finite element method with a staggering strategy is employed to solve the coupled governing equations on an irregular computational domain. The computational framework is verified in a one-dimensional solidification problem by comparing the velocity of the fluid-solid interface. The two-way coupling solution of solidification and crystallization is studied in an example of LPBF of Aluminum alloys.

The dynamic characteristics of a hub-functionally graded material beam undergoing large overall motions are studied. The deformation field of the flexible beam is described by using the assumed mode method (AMM), the finite element method (FEM) and the point interpolation method (PIM). Assuming that the physical parameters of functionally graded materials follow certain kind of power law gradient distribution and vary along the thickness direction. The longitudinal deformation and transversal deformation of the beam are both considered, and the nonlinear coupling term which is known as the longitudinal shortening caused by transversal deformation is also taken into account. The rigid-flexible coupling dynamics equations of the system described by three different discrete methods which have a uniform form are derived via employing Lagrange’s equations of the second kind. The validity of the point interpolation method established in this paper is verified by comparing with the numerical simulation results of the assumed mode method and the finite element method. On this basis, the influence of the functional gradient distribution rules on the dynamic characteristics of flexible beams undergoing large overall motions is discussed. The results show that the assumed mode method cannot deal with large deformation problem. Remaining other physical parameters of functionally graded materials beam unchanged, the maximum displacement of the beam increases with the increase of functionally graded materials index. The natural frequency of transverse bending of beam increases with the increase of rotational speed, when rotational speed is constant, the natural frequency will decrease with the increase of functional gradient index.

The paper proposes a novel automatic adaptive recovery stress edge-smoothed finite element method (ES-FEM) that determines the maximum load capacity of inelastic structures at plastic collapse. This approach performs solely a series of elastic ES-FEM analyses with systematic modulus variations (considering the influences of stress singularity) to converge the collapse load solutions. The smoothed $C^0$-continuous recovery stress field ensures the satisfaction of static admissible stress and yield conformity conditions underpinning lower-bound limit analysis theorems. A modified modulus error function within the newest node bisection algorithm enables automatic mesh refining and coarsening constructions, and fast convergence to the lower-bound collapse limit.

A new optimal formulation of the selective cell-based smoothed finite element method using 10-node tetrahedral elements (SelectiveCS-FEM-T10) is proposed for nearly incompressible large deformation problems. SelectiveCS-FEM-T10 is a generic name for S-FEM formulations that apply the selective reduced integration (SRI) and the cell-based S-FEM (CS-FEM) simultaneously to the 10-node tetrahedral (T10) elements, and thus it has various formulation variations. The conventional SelectiveCS-FEM-T10 naturally subdivides a T10 element into twelve 4-node tetrahedral (T4) subelements with a dummy node at the element center. Meanwhile, the new SelectiveCS-FEM-T10 radially subdivides it into sixteen T4 subelements around the dummy node. Owing to this radial element subdivision, all the edges of the subelements, including the frame edges, are subjected to strain smoothing only via the edge-based S-FEM (ES-FEM) within an element. Besides, SelectiveCS-FEM-T10 can be implemented into general finite element codes as a T10 element because it is a CS-FEM, which only applies intra-element strain smoothing. Our demonstrative analyses reveal that the new SelectiveCS-FEM-T10 is more robust than the best available T10 element against severe large deformation. They also show that the accuracy of the new SelectiveCS-FEM-T10 is almost equal to the conventional T10 elements as it does not cause shear/volumetric locking and pressure checkerboarding.

A mathematical analysis method is employed to solve the bending problem of slip clamped shallow spherical shell on elastic foundation. Using the slip clamped boundary conditions, the differential equations of the problem are simplified to a biharmonic equation. Using the $R$-function, the fundamental solution and the boundary equation of the biharmonic equation, a function is established. This function satisfies the homogeneous boundary condition of the biharmonic equation. The biharmonic equation of the slip clamped shallow spherical shell bending problem on elastic foundation is transformed to Fredholm integral equation of the second kind by using Green’s formula. The vector expression of the integral equation kernel is derived. Choosing a suitable form of the normalized boundary equation, the singularity of the integral equation kernel is overcome. To obtain the numerical results, the discretization of the integral equation of the bending problem is conducted. The treatment of singular term in the discretization equation is to use the integration by parts. Numerical results of rectangular, trapezoidal, pentagonal, L-shaped and concave shape shallow spherical shells show high accuracy of the proposed method. The numerical results show fine agreement with the ANSYS finite element method (FEM) solution, which shows the proposed method is an effective mathematical analysis method.

The flight of a water rocket involves complicated flows such as a gas–liquid two-phase flow in a pressure tank and a jet flow in an ejection hole. It can be applied to various phenomena by developing a method of reproducing and analyzing complicated phenomena. We simulated the flight of a calculation model of a water rocket by computational fluid dynamics. We conducted the simulation to estimate the thrust data of the calculation model and fluid–structure interaction. The simulated flight trajectory qualitatively matched that obtained from a previous experiment. In addition, it was possible to confirm changes in the attitude of the water rocket and vortices generated around it by simulating the pressure distribution on the surface of it and the flow around it. Therefore, it was possible to simulate the flow around a flying water rocket, which cannot be obtained through conventional theoretical calculations and experiments.

Microfluidics have shown great promise in multiple applications, especially in biomedical diagnostics and separations. While the flow properties of these microfluidic devices can be solved by numerical methods such as computational fluent dynamics (CFD), the process of mesh generation and setting up a numerical solver requires some domain familiarity, while more intuitive commercial programs such as fluent and StarCCM can be expensive. Hence, in this work, we demonstrated the use of a U-Net convolutional neural network as a surrogate model for predicting the velocity and pressure fields that would result for a particular set of microfluidic filter designs. The surrogate model is fast, easy to set-up and can be used to predict and assess the flow velocity and pressure fields across the domain for new designs of interest via the input of a geometry-encoding matrix. In addition, we demonstrate that the same methodology can also be used to train a network to predict pressure based on velocity data, and propose that this can be an alternative to numerical algorithms for calculating pressure based on velocity measurements from particle image velocimetry measurements. Critically, in both applications, we demonstrate prediction test errors of less than 1%, suggesting that this is indeed a viable method.

Surrogate models are commonly used in place of computationally expensive simulations in engineering design and optimization, and the predictive performance of surrogate models is usually influenced by the quality of design of experiments (DoE). One way to eliminate the effect of the randomness of DoE is to average multiple prediction accuracies over multiple DoEs. However, how many DoEs are needed to obtain stable prediction results for problems with different dimensionalities remains a challenging issue. Mathematical test functions have been employed in a large body of literatures to identify the predictive performance of surrogate models. In this work, 30 test functions ranging from 1 dimension to 16 dimensions are selected to investigate the relationship between the number of DoEs needed for a stable prediction accuracy and the number of sample points. A convergence condition is used to determine whether a reliable model accuracy has been obtained. In this paper, the number of DoEs required for estimating the model accuracy is provided as a suggestion for those who develop surrogate models and select test functions to validate the performance of models.

This paper presents a time-domain boundary element method (BEM) for viscoelastic wave scattering by many cavities in 3D infinite space. The convolution quadrature method (CQM) is applied to the convolutions of the time-domain boundary integral equation in order to improve the numerical stability of BEM. Scattering of an incident wave by cavities in a viscoelastic solid is solved by the developed time-domain BEM. The incident wave propagating in a viscoelastic solid in time-domain is obtained using the inverse Fourier transform of that in frequency-domain. In addition, the hybrid parallelization using OpenMP and MPI is used to save the computational time and memory.

The model of stochastic volatility with contemporaneous jumps is written for pricing under a partial integro-differential equation (PIDE) having a double integral and a nonsmooth initial value. To tackle this problem, first, a new radial basis function (RBF) as a convex combination of two known RBFs is given. Second, the weighting coefficients of the RBF generated finite difference (FD) method are contributed and the associated error equations are derived. To deal with the integral part, the new idea is to apply an estimate for the unknown function for every cell and do an integration of the density function. The contributed approach is competitive and reduces both the calculational efforts and elapsed time.