International Journal of Computational Methods

A new multidimensional drift flux mixture model was developed to simulate gas–liquid droplet two-phase flows. The new drift flux model was modified by considering the centrifugal force on the liquid-droplets. Therefore the traditional 1D drift flux model was upgraded to multidimension, 2D and 3D. The slip velocities between the continual phase (gas) and the dispersed phase (liquid droplets) were able to calculate through the multidimensional diffusion flux velocities based on the new modified drift flux model. Through the numerical simulations comparing with the experiments and the simulations of other models on the backward-facing step and the water mist spray two-phase flows, the new model was validated.

Impellers of centrifugal compressors are generally loaded by fluctuating aerodynamic pressure in operations. Excessive vibration of the impellers can be induced by unsteady airflows and lead to severe fatigue failures. Traditional transient stress analyses implemented in time domain generally require multiple load-step, very time-consuming computations using input of temporal pneumatic force previously obtained from Computational fluid dynamics (CFD) analyses. For quick evaluation of structural integrity of impellers, it is necessary to develop random vibration models and solution approaches defined in frequency domain. In this paper, the Pseudo-Excitation Method (PEM) is used to obtain power spectral density of three-dimensional, dynamic displacement and stress of impellers. A finite element model of an unshrouded impeller of a centrifugal compressor is generated based on the result of unsteady CFD analysis. Compared with the direct transient stress analyses in time domain, the pseudo-excitation method provides accurate and fast estimation of dynamic response of the impeller, making it an applicable and efficient method for analyzing random vibration of impellers.

It is generally assumed that influence of the red blood cells (RBCs) is predominant in blood rheology. The healthy RBCs are highly deformable and can thus easily squeeze through the smallest capillaries having internal diameter less than their characteristic size. On the other hand, RBCs infected by malaria or other diseases are stiffer and so less deformable. Thus it is harder for them to flow through the smallest capillaries. Therefore, it is very important to critically and realistically investigate the mechanical behavior of both healthy and infected RBCs which is a current gap in knowledge. The motion and the steady state deformed shape of the RBCs depend on many factors, such as the geometrical parameters of the capillary through which blood flows, the membrane bending stiffness and the mean velocity of the blood flow. In this study, motion and deformation of a single two-dimensional RBC in a stenosed capillary is explored by using smoothed particle hydrodynamics (SPH) method. An elastic spring network is used to model the RBC membrane, while the RBC's inside fluid and outside fluid are treated as SPH particles. The effect of RBC's membrane stiffness (k_b), inlet pressure (P) and geometrical parameters of the capillary on the motion and deformation of the RBC is studied. The deformation index, RBC's mean velocity and the cell membrane energy are analyzed when the cell passes through the stenosed capillary. The simulation results demonstrate that the k_b, P and the geometrical parameters of the capillary have a significant impact on the RBCs' motion and deformation in the stenosed section.

In this paper, a two-step Taylor Galerkin smoothed finite element method (TG-SFEM) is presented to deal with the two-dimensional Lagrangian dynamic problems. In this method, the smoothed Galerkin weak form is employed to create discretized system equations, and the cell-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stability and the adaptation of elements aberrations presented in the two-step TG-SFEM are studied through detailed analyses of numerical examples. In the analysis of wave propagation, the proposed method can provide smoother displacement and stress than the common SFEM does, and energy fluctuations are found to be minimal. In the large deformation problems, the TG-SFEM can acclimatize itself to the mesh distortion effectively and stay bounded for long durations because the isoparametric elements are replaced, and area integration over each smoothing cells is recast into line integration along edges and no mapping is needed. Therefore, the stability, flexibility of elements distortion and the property of energy conservation of the TG-SFEM applied on two-dimensional solid problems are well represented and clarified.

This paper presents a numerical study of gas and solid flow in an internally circulating fluidized bed (ICFB). Two-fluid Eulerian model with kinetic theory of granular flow option for solid phase stress closure and various drag laws were used to predict the hydrodynamic behavior of ICFB. 2D and 3D geometries were used to run the simulations. The 2D simulation results by various drag laws show that the Arastoopour and Gibilaro drag models able to predict the fluidization dynamics in terms of flow patterns, void fractions and axial velocity fields close to the experimental data. The effect of superficial gas velocity, presence of draft tube on solid hold-up distribution, solid circulation pattern, and variations in gas bypassing fraction for the 3D ICFB are investigated. The mechanism governing the solid circulation and solids concentration in an ICFB has been explained based on gas and solid dynamics obtained from the simulations. Predicted total granular temperature distributions in the draft tube and annular zones qualitatively agree with experimental data. The total granular temperature tends to increase with increasing solids concentration in the dilute region (ε < 0.1) and decreases with an increase of solids concentration in the dense region (ε > 0.1). In the dense zone, the decreasing trend in the granular temperature is mainly due to the reduction of the mean free path of the solid particles.

This paper proposes a probability-interval mixed uncertainty model considering parametric correlations and a corresponding structural reliability analysis method. First of all, we introduce the sample correlation coefficients to express the correlations between different kinds of uncertain variables including probability and interval variables. Then dependent parameters are transformed into independent ones through a matrix transformation. A reliability analysis model is put forward, and an efficient method is built to obtain the reliability index or failure probability interval of the structure. Finally, four numerical examples are provided to verify the validity of the method.

Damage identification of structures is always attractive to researchers because it plays an important role in the health monitoring in many civil engineering structures. When carrying out a health monitoring, sensors are usually laid on a beam to record acceleration signals, in which the modes of the beam can be extracted to construct indicators for detecting damage of the investigated beam. It should be noted that it is difficult to measure rotational signals of the beam at a position where sensors are laid, thus only the modal translations are available. Although the modal translations can be used to construct indicators without modal rotations and often it is the case, an indicator taking into account modal rotations is suggested in application to resist the effect of noise on the accuracy of measurement. In this paper, modal rotations were reconstructed by modal translations using the principle of static condensation and QR decomposition. Then both modal translations and rotations were used to build an indicator based on element modal strain energy with the help of data fusion theory. The modal translations were extracted from accelerations recorded on a beam using stochastic subspace identification (SSI). Studies were carried out on choosing values of parameters in SSI in order to eliminate the effect of noise as nearly as possible. The simulation given by a FEM model and analyses of accelerations recorded on a reinforced concrete beam show that the proposed damage indicator with the efforts of eliminating noise is able to detect the locations of damage in the investigated beams.

Boundary slip effect caused by low gas density has an important influence on the thermal environment of the vehicles. Numerical studies on the boundary slip effect and accommodation for moment and energy have been carried out in this paper. The simulations considering slip boundary and surface catalysis are validated with Arc-jet test data. Mechanism and rules of impact on surface heat flux by different boundary slip level (Knudsen number from 0.0028 to 0.05) has been investigated in typical hypersonic flow conditions. The results show that mechanisms of boundary slip effect on mass diffusion heat flux and convective heat flux are different; slip boundary diminishes the convective heat, whereas enhances the mass diffusion heat flux. Smaller moment and energy accommodation coefficient is equivalent to more rarefaction. As Knudsen number goes up, the influences of accommodation on heatflux are enhanced, it mainly affects the convective heat flux.

In this study, the impact responses of concrete debris against soil are investigated. Three types of concrete debris are shot at soil with different incident conditions in experiments. A numerical modeling for the impact process is established and calibrated by the experimental results. A further study on the effect of debris size is then carried out based on the calibrated numerical modeling. A set of formulation is presented to predict the outgoing velocity and the outgoing angle in terms of the incident velocity and the incident angle. Critical lethality curves are derived based on the assumption of a critical kinetic energy of 79 J.

With the demand of lightweight structure, more and more metal foams were employed as impact protection and efficient energy absorption materials in engineering fields. But, results from different impact experiments showed that the strain rate sensitivity of metal foams were different or even controversial. In order to explore the true hiding behind the controversial experimental data about the strain rate sensitivity of metal foams, numerical simulations of split Hopkinson pressure bar (SHPB) tests of the metal foams were carried out by finite element methods. In the analysis, cell structures of metal foams were constructed by means of 3D Voronoi, and the matrix metal was assumed to be no strain rate sensitivity, which helps to learn the strain rate effects quantitatively by the foam structures. Numerical simulations showed that the deformation of the metal foam specimen is not uniform during the SHPB tests along the specimen, and the strain–stress relations of the metal foams at two ends of the specimen are different; there exists strain rate sensitivity of the metal foams even the matrix metal has no strain rate sensitivity, when the strain of the metal foams is defined by the displacement difference between the ends of the specimen; localized deformation of the metal foams and the inertia effect of matrix metal are the two main contributions to the strain rate sensitivity of the metal foams.

An edge-based smoothed finite element method (ES-FEM) using 3-node triangular element was recently proposed to improve the accuracy and convergence rate of the standard finite element method (FEM) for 2D elastic solid mechanics problems. In this research, ES-FEM is extended to large-deformation plasticity analysis, and a selective edge-based/node-based smoothed finite element (selective ES/NS-FEM) method using 3-node triangular elements is adopted to address volumetric locking problem. Validity of ES-FEM for large-deformation plasticity problem is proved by benchmarks, and numerical examples demonstrate that, the proposed ES-FEM and selective ES/NS-FEM method possess (1) superior accuracy and convergence properties for strain energy solutions comparing to the standard FEM using 3-node triangular element (FEM-T3), (2) better computational efficiency than FEM-T3 and similar computational efficiency as FEM using 4-node quadrilateral element and 6-node quadratic triangular element, (3) a selective ES/NS-FEM method can successfully simulate problems with severe element distortion, and address volumetric locking problem in large-deformation plasticity analysis.

In this paper, unidirectional fiber reinforced composites with periodic square array of circular and hexagonal fibers is studied by a novel fundamental-solution-based hybrid finite element model. Due to the periodicity of composites, a representative unit cell containing a single fiber with circular or hexagonal cross section is taken into consideration and analyzed using the proposed hybrid finite element model. In the present numerical model, special polygonal fiber elements with arbitrary number of sides are developed by coupling the independent element interior and frame displacement fields. The element interior displacement fields are approximated by the combination of fundamental solutions to prior satisfy the governing equation of the problem, so that the domain integral appeared in the weak-form hybrid functional in terms of dual variables is converted into boundary integrals. Independently the element frame displacement fields are approximated by the conventional shape functions to guarantee the continuity of adjacent elements. Following this, special polygonal fiber elements are constructed to reduce mesh effort in the fiber region and achieve good accuracy with fewer elements. Finally, numerical tests are carried out for assessing the performance of the present special elements.

This work formulates the node-based smoothed radial point interpolation method (NS-RPIM), a typical model of smoothed point interpolation method, for the elastoplastic analysis of two-dimensional solids with gradient-dependent plasticity. The NS-RPIM uses radial point interpolation shape functions for field approximation and node-based gradient smoothing for strain field construction. The formulation is based on the parametric variational principle (PVP) in the form of complementarity with the gradient-dependent plasticity being represented by means of the linearization of the yield criterion and the flow rule. Numerical study results have demonstrated the accuracy and stability of the proposed approach for elastoplastic analysis.

The rigid bodies-spring model (RBSM) has been developed as a numerical model to generalize limit analysis in plasticity, in which the structure to be analyzed is idealized as an assemblage of rigid bodies connected by normal and tangential springs. Originally, this approach was a discrete model for handling static problem. In this paper, we illustrate the formulation of an explicit dynamic method for each element using the principle of hybrid-type virtual work. Additionally, we propose a new RBSM approach for contact mechanism and friction characteristics. Finally, we verify the accuracy of dynamic analysis by RBSM with some numerical examples.

The paper presents the formulation and recent development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. In the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the original plate element DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the cell-based strain smoothing technique (CS-FEM) is used to smooth the strains on these three sub-triangles. The numerical examples illustrate four superior properties of the CS-FEM-DSG3 including: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) giving high accurate solutions for problems with skew geometries in the static analysis; (3) giving high accurate solutions in free vibration analysis; (4) providing accurate values of high frequencies of plates by using only coarse meshes. Due to its superior and simple properties, the CS-FEM-DSG3 has been now developed for various analyses such as: flat shells, stiffened plates, functionally graded plates, composite plates, piezoelectricity composite plates, cracked plate and plates resting on the viscoelastic foundation subjected to moving loads, etc.

The geometry of high-dimensional spaces is very different from low dimensional spaces and possesses some counter-intuitive features. It is shown that, for high dimensions, the sampling points fall far away from the origin and concentrate within an intersection between a very thin shell and a suitable equatorial slab. The well-known First-Order Reliability Method (FORM), originally formulated for low dimensions, may work well in many engineering problems of high dimension. But it is not able to reveal the level of achieved accuracy. Considering the features of high-dimensional geometry, a novel linear response surface based on Support Vector Method (SVM) is proposed for structural reliability problems of high dimension. The method is shown to outperform FORM for structural reliability problems of high dimension in terms of robustness and accuracy.

Vibration of double-walled carbon nanotubes (DWCNTs) with one end fixed and the other end free is studied by using different beam models of continuum mechanics and the molecular dynamics (MD) simulations. The models of the double-Euler beams (DEB) and the double-Timoshenko beams (DTB) of cantilevered case, with the van der Waals interaction between layers taken into consideration, are applied to predict the natural frequencies of DWCNTs. An analytical solution is first obtained for the DTB model with cantilevered boundary condition. The fundamental frequencies obtained by the DEB model and the DTB model are very close, for the relatively long DWCNTs. The MD simulations show that these two models can predict the natural frequencies well. However, the difference between the DEB model and the DTB model becomes obvious, for the vibration of the relatively short DWCNTs. The DTB model can offer a much better prediction than the DEB model when the DWCNT is very short especially for high-order frequencies.