International Journal of Computational Methods

• (1)The RAOs of OC4-DeepCWind platform motions are more sensitive to the low-frequency wave than the high-frequency wave. The nonlinear motion responses for platform heave and pitch motions are comparatively remarkable.
• (2)The pitch motion of OC4-DeepCWind platform is much more apparently influenced by the height of center of gravity (COG) than surge and heave motions. The lower COG height within a suitable range leads to a smaller fluctuation amplitude of platform pitch motion in waves.
• (3)A large horizontal displacement abruptly occurs to the OC4-DeepCWind platform when one mooring line is failure. The risk of failure for the other mooring lines significantly increases.

To better understand the hydrodynamic performance of a floating support platform in various wave environments, a two-phase CFD solver naoe-FOAM-SJTU based on the open source CFD toolbox OpenFOAM is applied to investigate the hydrodynamic characteristics and motion performance of the OC4-DeepCWind platform. Moreover, the restoring force and moment of mooring lines are simulated using the solver in time domain. The studies of grid sensitivity and time step refinement are first conducted to determine an appropriate time step and mesh size. Then hydrodynamic responses of the floater in free-decay tests are analyzed and compared with experimental data, and the motion performance of the platform in regular waves with different parameters is also investigated. In addition, the platform motion responses with one mooring line broken and different heights of center of gravity are explored. It is shown that simulation results have good agreement with published data, and several conclusions can be drawn through the study. The RAOs of platform motions are found to be more sensitive to the low-frequency wave than the high-frequency wave. Nonlinear motion responses are comparatively remarkable in platform heave and pitch motions. Besides, the lower height of center of gravity within a suitable range is benefit to the stability of floating platform. Survival condition with broken mooring line should be paid enough attention to avoid the failure of other mooring lines.

An interval and random moment-based arbitrary polynomial chaos method (IRMAPCM) is proposed in this paper for the analysis of periodical composite structural-acoustic systems with multi-scale uncertain-but-bounded parameters. In IRMAPCM, the response of structural-acoustic system is approximated as moment-based arbitrary polynomial chaos (maPC) expansion. IRMAPCM can construct the polynomial basis according to the moment of the random variable without knowing the Probability Density Function (PDF), which can avoid the errors introduced by estimating the PDF. Numerical examples of a hexahedral box and an automobile passenger compartment are given to investigate the effectiveness of IRMAPCM for the prediction of the sound pressure response of structural-acoustic systems.

To accurately simulate the steady-state responses of a functionally graded piezoelectric structure (FGPS) and cure the “overly-stiff” of finite element method (FEM), the coupled thermal-electrical-mechanical inhomogeneous cell-based smoothed finite element method (CICS-FEM) is proposed. The gradient smoothing technique is introduced into FEM and a “close-to-exact” stiffness is obtained. Based on the basic theory of FGPS, the thermal field is introduced into the electrical-mechanical coupling field and the multi-physics coupling equations are given in conjunction with the cell-based smoothed finite element method. CICS-FEM is verified with several examples, and there is a satisfactory agreement between the current solution and the reference solution. Therefore, the developed method to solve the steady-state response of FGPS can provide a reference for the design and manufacture of smart devices.

Following a recent attempt by Waziri et al. [2019] to find an appropriate choice for the nonnegative parameter of the Hager–Zhang conjugate gradient method, we have proposed two adaptive options for the Hager–Zhang nonnegative parameter by analyzing the search direction matrix. We also used the proposed parameters with the projection technique to solve convex constraint monotone equations. Furthermore, the global convergence of the methods is proved using some proper assumptions. Finally, the efficacy of the proposed methods is demonstrated using a number of numerical examples.

The efficiency of contact search is one of the key factors related to the computational efficiency of three-dimensional sphere discontinuous deformation analysis (3D SDDA). This paper proposes an efficient contact search algorithm, called box search algorithm (BSA), for 3D SDDA. The implementation steps and data structure for BSA are designed, with a case study being conducted to verify its efficiency. The data structure also has been improved for parallelizing the computation in contact search. For the demonstration of the proposed algorithm (BSA), six cases with various sphere numbers are simulated. Simulation results show that the time consumed in contact search using BSA (CTofBSA) is much less than that by the direct search algorithm (DSA) (CTofDSA). For the case with 12,000 spheres, CTofBSA is 1.1h, which is only 1.3% of CTofDSA (84.62h). In addition, the proportion of the computation quantity of contact search in the entire computation (Pcs) is 91.3% by using DSA, while this value by BSA is only 12.4%, which demonstrates the contribution of BSA. The efficiency brought about by BSA (time consumed and computation quantity) may enable 3D SDDA to simulate large-scale problems.

In this paper, an optimized approach is proposed to enhance the performance of combined explicit–implicit time-domain analyses. In this context, an entirely automated explicit-implicit adaptive time-marching procedure is discussed as well as an optimization algorithm is introduced to compute the adopted time-step value of the analysis, so that the amount of explicit and implicit elements occurring along the model may be optimally provided, in terms of computational efficiency. The proposed formulation is very effective, allowing evaluating highly accurate responses considering much reduced computational efforts. At the end of the manuscript, numerical applications are presented, illustrating the excellent performance of the proposed formulation.

This paper is devoted to the development and quantitative evaluation of the properties of the numerical algorithm of the Cartesian grid method for three-dimensional (3D) simulation of shock-wave propagation in areas of varying shape. The detailed description of the algorithm is presented. The algorithm is relatively simple to implement and does not require solving the problem of determination of the shape of the body’s boundary intersection with regular computational cell. The accuracy of the algorithm is demonstrated by comparing the simulated and experimental data in the problems of the interaction of a shock wave (SW) with a nonmoving sphere and a moving particle.

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

This paper sets propelling a more current strategy for mechanical shape optimization by joining a coupled finite element (FE) method–meshfree method (MM) with swarm intelligence (SI)-based stochastic ‘zero-order’ search procedure. The arranged gathering massively fits as a structural shape optimization since MM is utilized here for structural examination shape analysis and to avoid a remeshing in view of fundamental mesh modification if there should be an occurrence of tremendous shape varieties, discontinuous secondary field variables across element boundaries, etc. while using FE. This is same as FE strategy that helps in beating the weaknesses of MM like high computational exertion and simplicity of forcing essential boundary conditions (EBCs). Populace-based stochastic optimization strategy, e.g., PSO abrogates computational burden, multifaceted nature and blunders aligned with structure affectability assessment Right now, plan limit portrayal Akima spline introduction has been considered on account of its improved persistence and smoothness over cubic spline. The convenience of present strategy, results got with current technique is contrasted and different strategies for past writing. The adequacy, legitimacy and execution of the present procedure are built up through mathematical instances of cantilever beam and fixed–fixed bar geometry for shape optimization with conduct limitations on displacement. For both these issues, h-refinement for opening issue geometry has been examined and furthermore impact of various design variables fit as a shape optimization has likewise been researched.

A new hybrid fundamental-solution-based finite element method (HFS-FEM) is developed for the transient heat conduction analysis of two-dimensional orthotropic materials. By using coordinate transformation and time-stepping approximation, the governing equation of the original problem is converted to the modified Helmholtz equation. In the solution procedure, the homogeneous solutions of the problem are sought by employing HFS-FEM while the particular solutions are approximated with the aid of radial basis function. HFS-FEM has many attractive features compared to the conventional FEM. The computational efficiency and convergence of the present method are examined through several numerical examples.

This paper presents a constraint handling approach without the need to use a penalty function, namely Optimization Without Penalty (OWP). This approach is used on a recent optimization algorithm based on morphological filters, called Optimization by Morphological Filters (OMF). This work consists of providing a simple and effective constraint-handling approach without the necessity of the penalty for any considered optimization problem. The proposed approach is applied to 03 hard mathematical functions, 18 benchmark constraint functions presented in CEC 2010 competition on constrained real-parameter optimization, and 7 constrained engineering design problems reported in the specialized literature. According to the statistical comparison results, the performance of the OMF algorithm with OWP-based approach is better or highly competitive on most of the studied problems.

In this paper, we report on a strategy for computing the numerical approximate solution for a class of ill-posed operator equations in Hilbert spaces: $K:E\to F,Kf=g$. This approach is a combination of Tikhonov regularization method and the finite rank approximation of $K^{\ast }K$. Finally, numerical results are given to show the effectiveness of this method.