International Journal of Computational Methods

The phenomenon of liquid drops impact on elastic surfaces widely exists in nature and industry. Theoretical description of this phenomenon is relatively difficult, due to its transient and fluid–structure interaction nature. In this study, a numerical model is proposed based on the smoothed particle hydrodynamics (SPH) method to simulate a liquid drop impact on hypoelastic solid surfaces. A key feature of the proposed model is that the surface tension effect is modeled by reconstructing the free surface of the droplet. We simulate water drops impact on super-hydrophobic cantilever beams. Interesting phenomena of droplet bouncing and beam vibration are reproduced by the model. The predicted behavior qualitatively agrees with the experimental observation. These analyses may be beneficial to engineering new materials and new devices in such areas as fabrics, agriculture, petroleum, and micro/nano technology.

In this paper, we studying the entropy generation in Sakiadis nanofluid flowing along a moving plate subject to magnetic field and a Cattaneo–Christov heat flux model that may predict the effects of thermal relaxation time on the boundary layer flow. The nonlinear transport equations are solved using a spectral quasi-linearization method. An analysis of the convergence of the method is presented, and the importance of various fluid and physical parameters concerning the behavior of the solutions is explored. Numerical analysis of the residual error and convergence properties of the method are also discussed. One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process. It is shown that the method converges fast and gives accurate results. The results show that entropy generation increases with an increase in the Reynolds number. The Bejan number is strongly affected by variations in the magnetic parameter, Brinkman number and temperature difference parameter.

In plasmas found in nuclear fusion energy and astrophysics, radiative properties play a pivotal role and they are needed in radiation hydrodynamic simulations of these plasmas. However, their calculation is a very complex problem involving very long computational times. One of the solutions is to perform parametrizations of the plasma radiative properties as a function of the plasma conditions which leads to considerable reductions in computational costs. In this work, we present models to generate and parametrize radiative properties databases as a function of plasma conditions which are valid for any plasma thermodynamic regime.

A simplified model for calculating the seismic responses of the shaft is proposed in this paper. Based on the theory of Winkler elastic foundation beam, the urban shaft is simplified as a vertical beam. The horizontal soil reaction and vertical shear tractions between the shaft circumference and the surrounding soils are considered through horizontal springs and rotating springs on the sidewall of the shaft. The translation and rocking motion of the shaft are considered through horizontal springs and rotating springs at the bottom of the shaft. Then, the dynamic analysis model of the shafts under seismic motion is established, and the control equation of the dynamic response of the shaft in frequency domain is deduced. The analytical solution of the steady state response of the shaft is obtained. Considering the randomness of the earthquake motion, this method can get the shaft kinematic responses under different ground motions efficiently in conceptual design process.

This study presents the boundary layer flow of a second grade fluid in a rotating reference frame. The model equations are solved numerically using the bivariate spectral quasi-linearization method to obtain the fluid properties. We investigate the effects of measurable quantities such as the rate of rotation, thermal diffusivity, energy dissipation, viscoelastic parameter and other material properties of the fluid on the flow. The results show that slow rotation leads to a quick decline in the thicknesses of the momentum, thermal and concentration boundary layers. There is also a region of reverse flow for fluids with high Prandtl number.

High-accuracy computer approximation of fractional derivatives and integrals by applying Grünwald–Letnikov formula generally requires a large number of input values. If required amount cannot be supplied, accuracy of approximation drops drastically. In this paper, we solve a difficult problem in this scope, i.e., when input data consists only of a small number of discrete values. Furthermore, some of the values may be unusable for computational purposes. Our problem solution includes an appropriate method of input data preprocessing, an interpolation algorithm with extrapolation abilities, a central point function discretization schema, recurrent computational method of coefficients and application of Horner’s schema for the core of the Grünwald–Letnikov method: coefficients and function’s values multiplication. Numerical method presented in the paper enables to compute fractional derivatives and integrals of complicated functions with much higher accuracy than it is possible when application of the default approach to Grünwald–Letnikov method computer implementation is applied. This new method usually takes only 10% of function’s values required by the default approach for the same computations and is much less restrictive for their quality. The general novelty of the method is an efficient configuration of existing numerical methods and enhancement of their abilities by applying modern programming language — Python and arbitrary precision arithmetic for computations.

Wind turbine installation vessel (WTIV) is a kind of special ship that has large upper deck and shallow draft, which is specifically designed for the installation of offshore wind turbines. However, accurately predicting the motion of WTIV is still a challenge. In this paper, computational fluid dynamics (CFD) is adopted to investigate the motion of WTIV under different wave conditions in a three-dimensional numerical wave tank using commercial software Star-CCM+. Reynolds Averaged Navier–Stokes (RANS) equations and $k-𝜀$ turbulent models are used for modeling the turbulent flow, and volume of fluid (VOF) method is applied to track the location and shape of transit-free surface. The overset grid technique is taken to handle the fluid–structure interaction (FSI) problem with large motion amplitude. The simulation results have been validated by comparing with the experimental data, and show potential to provide theoretical guidance and technical support for the motion of WTIV in waves.

Development of high-toughness composite materials requires careful microstructure design as geometric distribution of phases, constituent properties and interface attributes combine to influence the deformation and failure behavior of composites. In two-phase composite materials, reinforcement cracking and interface debonding are two competing fracture mechanisms observed during the crack–microstructure interactions. The activation of each fracture mechanism largely depends on the microstructure and ultimately determines the fracture toughness of composites. The objective of this study is to quantify the competition of the two fracture mechanisms as function of microstructure and find their intricate coupling with material fracture toughness. The multiscale material design framework developed here allows fracture toughness to be predicted through cohesive element-based fracture simulation and digital image correlation measurement. Based on the numerical and experimental results, two analytical models are developed for fracture mode determination of both brittle and ductile composites. Although calculations carried out concern ceramic composites Al₂O₃/SiC and metal matrix composites Al/SiC, the approach developed can be applied to other composite material systems.

In this work, a versatile computational package, named MIXKIP/RAPCAL/STOPP, developed to simulate and calculate the microscopy properties of plasmas as well as the characteristic parameters of the ion beam–plasma interaction processes is presented. The physical and numerical model implemented combines a set of theoretical and numerical approximations which still compare well with more elaborated codes and experimental data. In order to show the capabilities of the computational package, simulations of the spectrally resolved radiative properties of xenon plasmas doped with helium under the conditions of radiative shocks generated at the PALS laser as well as energy loss calculations of carbon ion beams in partially aluminum plasmas are presented.

Modeling of masonry confinement has been usually derived from concrete confinement, which was deeply tested in the last decades. However concrete and masonry have some crucial differences, e.g., ordinary concrete performance can be usually fully defined by the cylindrical compressive strength, while masonry does not. In the present work, a failure criterion is considered on a solid mechanics base. Such criteria are useful not only to introduce non-uniform stress states, as those developed in non-axisymmetric confined elements, but also to be implemented in FEM. The validity of the adopted failure criterion has been checked against actively confined clay brick masonry and a database of passive confinement tests available in the scientific literature.

Pollutant control is one of the key concerns in the design of buildings, for the sake of occupational health, safety and environment sustainability. In particular, risk analyses related to emergency leakage of chemicals from storage tanks or chemical processes have aroused increasing attentions in recent days, as well as the effectiveness of mitigation measures in order to eliminate, reduce and control the risks. In this paper, a CFD methodology with nonreactive chemical gases treated as passive scalars has been developed to simulate the gas dispersion across urban environments, subject to atmospheric boundary layer wind conditions. Special treatments to maintain the consistency in atmospheric boundary layer flow profiles, turbulence modeling and boundary conditions have also been accounted for. The proposed CFD methodology for gas dispersion has been implemented in the open source CFD code — OpenFOAM. It has been validated by modeling the gas dispersions for two urban-related test cases: the CODASC street canyon test case measured in a laboratory wind tunnel and the Mock Urban Setting Test (MUST) field experiment conducted in the desert area of Utah State. Effects of turbulent Schmidt number (Sc_t have been primarily addressed in this study. Statistical analyses about the discrepancies between predicted and experimental data have been carried out and statistical performance measures are used to quantify the accuracy of the proposed methodology. Simulations results from passive scalar transport equation demonstrate good agreement with experimental data, though tracer gases heavier than the atmospheric air were used in both the measurements. Furthermore, sensitivity tests also indicate that the accuracy of the simulation results is sensitive to the value of turbulent Schmidt number.

In the paper, the smoothed finite element method (S-FEM) based on linear triangular elements is used to solve 2D solid contact problems for functionally graded materials. Both conforming and nonconforming contacts algorithms are developed using modified Coulomb friction contact models including tangential strength and normal adhesion. Based on the smoothed Galerkin weak form, the system stiffness matrices are created using the formulation procedures of node-based S-FEM (NS-FEM) and edge-based S-FEM (ES-FEM), and the contact interface equations are discretized by contact point-pairs. Then these discretized system equations are converted into a form of linear complementarity problems (LCPs), which can be further solved efficiently using the Lemke method. The singular value decomposition method is used to deal with the singularity of the stiffness matrices in the procedure constructing the standard LCP, which can greatly improve the stability and accuracy of the numerical results. Numerical examples are presented to investigate the effects of the various parameters of functionally graded materials and comparisons have been made with reference solutions and the standard FEM. The numerical results demonstrate that the strain energy solutions of ES-FEM have higher convergence rate and accuracy compared with that of NS-FEM and FEM for functionally graded materials through the present contact analysis approach.

It has been observed by performing simple and diagonal compression tests of cob wallettes that the structural behavior of cob is highly nonlinear. This paper presents the results obtained of the simulation of cob’s nonlinear monotonic behavior using two well-known finite element commercial packages. Pros and cons of different available constitutive material models are identified and discussed. Concrete (CONCR) and Concrete Damaged Plasticity (CDP) are considered as the constitutive material models that provide the more satisfactory results reproducing cob’s nonlinear monotonic behavior when using ANSYS and ABAQUS, respectively.

The method to protect the whole station structure by installing flexible devices at the column end has been proved to be effective in typical station structures. However, the damping effects and application of this method to multi-story subway station structures still need further study. In this paper, a stochastic analysis method, probability density evolution method (PDEM), is adopted to estimate the damping effect of a four-story subway station structure with lead rubber bearings (LRBs) installed in the central column. Stochastic analysis results show that the internal forces and plastic energy dissipation of columns installed LRBs are greatly reduced and the reliability is improved. Internal forces and plastic energy dissipation of columns without the installation of LRBs increase and the reliability decrease. There is little difference in structural deformation and plastic energy dissipation of structural components when LRB is installed in the middle of the column or at the column ends. When LRBs are installed only in some of the stories, the overall reliability of the structure is lower than that of the structure without LRB. When LRBs are installed in the columns of all stories, the structural reliability is higher than that of the structure without LRB. Based on the above results, to obtain better seismic control effect by installing LRBs, the multi-story subway station structure should be installed with LRBs in the columns of all stories, and LRBs can be installed at the upper, middle and lower end of the columns.

To evaluate the safety of casing string is an important task in the oil exploitation. In this paper, the casing string with complex environment is investigated and the global sensitivity analysis (SA) technique is employed to identify the influential factors on the safety. Since the damage of casing string is of different kinds, three failure modes are mainly considered in the analysis. Then, the multivariate global SA technique is employed to identify the influential factors for the three failure modes simultaneously. Due to the full-size FE analysis of casing string which involves contact analysis of tread, being computationally expensive, a simplified model with full constraints are constructed. Then, to compute the multivariate global sensitivity efficiently, the neural network which is used to surrogate the FE model is employed to perform SA.

To investigate flexural vibration of structures in a fluid, a numerical algorithm was developed to relate the added mass and damping effects of the fluid to each mode of vibration. These are separate from the traditional added mass associated with rigid body motion, such as the translational motion along Cartesian axes. In this formulation, small-amplitude free surface waves were accounted for by using a nonsingular implementation of the free-surface Green’s function for a potential flow solver based on Boundary Element Method. The formulation was applied to the forced vibration of structures, namely, a hemispherical shell and a reinforced half cylinder with typical dimensions of ships and offshore structures, to obtain their dynamic response at various excitation frequencies. It is observed that resonance frequency of the structure, in contact with water, decreases due to the added mass effect. The influence of the free-surface wave on the fluid loading was investigated for large structures. It is simpler to relate the fluid added mass to mode shapes rather than distribution of fluid load over wetted surface of the structure in engineering simulations. Moreover, it is found that the vibration energy radiated away by the fluid surface wave has little influence on the vibration response of the shell structures.

Our principle aim in this paper is to present a new reconstruction of classical Chebyshev–Halley schemes having optimal fourth and eighth-order of convergence for all parameters $\alpha$ unlike in the earlier studies. In addition, we analyze the local convergence of them by using hypotheses requiring the first-order derivative of the involved function $f$ and the Lipschitz conditions. In addition, we also formulate their theoretical radius of convergence. Several numerical examples originated from real life problems demonstrate that they are applicable to a broad range of scalar equations, where previous studies cannot be used. Finally, a dynamical study of them also demonstrates that bigger and more promising basins of attractions are obtained.

In this paper, we present a local convergence analysis of some iterative methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. In the earlier study [Babajee et al. (2015) “On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations,” Algorithms 8(4), 895–909], demonstrate convergence of their methods under hypotheses on the fourth-order derivative or even higher. However, only first-order derivative of the function appears in their proposed scheme. In this study, we have shown that the local convergence of these methods depends on hypotheses only on the first-order derivative and the Lipschitz condition. In this way, we not only expand the applicability of these methods but also proposed the theoretical radius of convergence of these methods. Finally, a variety of concrete numerical examples demonstrate that our results even apply to solve those nonlinear equations where earlier studies cannot apply.

The complex layout and harsh working environment often encountered in aeronautical hydraulic pipeline system (AHPS) result in the requirement of a large number of constraints that are mainly utilized to avoid the damage caused by engine vibration and wing flutter. As a result, improvement of the mean time between failures (MTBF) of the AHPS considering all constraint locations is a costly process, and the management of such large-scale design variables is also frustrating. In this paper, a sensitivity analysis-based optimization is proposed. Firstly, the MTBF of AHPS under stochastic vibration is first deduced according to the first-passage theory-based dynamic strength reliability formula, and the corresponding optimization model is established. Secondly, a multiplicative-dimensional reduction method (M-DRM) based global sensitivity analysis (GSA) method is employed to screen out the constraint location coordinates that have little or no impact on MTBF. Lastly, the MTBF optimization is performed by considering only the remaining significant location coordinates as the design variables. The results show that the proposed sensitivity analysis-based optimization strategy shows advantages in efficiency and effect.

Two new computational algorithms for the Limit Analysis (LA) of large-scale 3D truss-frame structures recently proposed by the authors are reconsidered and adapted for a comparison prediction of the elastoplastic response of a strategic beautiful historic infrastructure, namely the Paderno d’Adda bridge (or San Michele bridge), a riveted wrought iron railway viaduct that was built in northern Italy in 1889. The first LA algorithm traces a fully exact evolutive piece-wise linear elastoplastic response of the structure, up to plastic collapse, by reconstructing the true sequence of activation of made-available plastic joints (as a generalization of plastic hinges), in the true spirit of LA. The second LA algorithm develops an independent kinematic iterative approach apt to directly determine the plastic collapse state, in terms of collapse load multiplier and plastic mechanism, based on the upper-bound theorem of LA. Specifically, the marvelous doubly built-in parabolic arch of the bridge is analyzed, under a static loading configuration at try-out stage, and its elastoplastic response is investigated, in terms of evolutive load-displacement curve, collapse load multiplier and plastic collapse mechanism. The two LA algorithms are found to much effectively run and perform, despite the rather large size of the computational model, with a number of dofs in the order of four thousands, by achieving good corresponding matches in terms of the estimate of the load-bearing capacity and of the collapse characteristics of the arch substructure, showing this to constitute a well-set structural element. Moreover, the direct kinematic method displays a rather dramatic performance, in truly precipitating from above onto the collapse load multiplier and rapidly adjusting to the collapse mode, in very few iterations, by a considerable saving of computational time, with respect to the complete evolutive elastoplastic analysis. This shall open up the way for further adoption of such advanced LA tools, with LA regaining a new momentum within the modern optimization analysis of structural design and form-finding problems.