Solving the Nonlinear Heat Equilibrium Problems Using the Local Multiquadric Radial Basis Function Collocation Method

In this article, the nonlinear heat equilibrium problems are solved by the local multiquadric (MQ) radial basis function (RBF) collocation method. The system of nonlinear algebraic equations is solved by iteration based on the residual norm-based algorithm, in which the direction of evolution is determined by a linear equation. In addition, the role of the collocation point and source point is clearly defined such that in our proposed method the field value of any interested point can be expressed. Six numerical examples are shown to check the performance of the proposed method. As the number of supporting points (mp) increases, the accuracy of numerical solution increases. Among all examples, mp = 50 can perform well. In addition, the selection of shape parameter, c, affects the accuracy. However, as c < 2 the maximum relative absolute error percentage is less than 1%.

Modeling and Thermal Analysis of a Moving Spacecraft Subject to Solar Radiation Effect

The impact of solar radiation on spacecraft can increase the cooling load, degrade the material properties of the structure and possibly lead to catastrophic failure of their missions. In this paper, we develop a computational model to investigate the effect of the exposure to solar radiation on the thermal distribution of a spacecraft with a cylindrical shape which is traveling in low earth orbit environment. This is obtained by the energy conservation between the heat conduction among the spacecraft, the heating from the solar radiation, and the radiative heat dissipation into the surroundings while accounting for the dynamics of the space vehicle (rotational motion). The model is solved numerically using the meshless collocation point method to evaluate the temperature variations under different operating conditions. The meshless method is based on approximating the unknown field function and their space derivatives, by using a set of nodes, sprinkled over the spatial domain of the spacecraft wall and functions with compact support. Meshless schemes bypass the use of conventional mesh configurations and require only clouds of points, without any prior knowledge on their connectivity. This would relieve the computational burden associated with mesh generation. The simulation results are found in good agreement with those reported in previously-published research works. The numerical results show that spinning the spacecraft at appropriate rates ensures low and uniform temperature distribution on the spacecraft, treated as thick-walled object of different geometries. Therefore, this would extend its lifetime and protect all on-board electronic equipment needed to accomplish its mission.

Applying potential-based panel method for steady flow analysis across a wing with finite span

In the paper hereby, an incompressible irrotational steady flow across a submerged body with finite dimensions will be studied. For this purpose, it is necessary to solve Laplace’s differential equation about a potential function in order to obtain the conservative velocity vector field. A general solution to the problem utilizing the Green identity implies the double layer potential function at an arbitrary point not belonging to the boundary surface. The potential is expressed by source/sink and doublet singularities distributed over the body surface and a wake attached to the trailing edge. The wake ensures that the Kutta condition is fulfilled. The submerged body geometry is approximated further by quadrilateral panels in order to compute the surface integrals for each panel exactly. To form a linear non-homogenous algebraic system, it is essentially to compute each panel influence to a collocation point of interest. The obtained coefficient matrix is diagonally dominant. The system is solved iteratively by means of the Gauss-Seidel method. The goal is development of a non-proprietary source code in order to work out a solution to the stated problem. The developed source code is authentic. Auxiliary libraries have not been used. Validation case and numerical results are depicted and discussed in the paper.

Study on the Single Scattering of Elastic Waves by a Cylindrical Fiber with a Partially Imperfect Bonding Using the Collocation Point Method

The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP) method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P- and SV-waves is studied. Results indicate that (i) the total scattering cross section (SCS) is almost symmetric about the axis α=π/2 with respect to the location (α) of the imperfect interface, (ii) imperfect interfaces located at α=0 and α=π highly reduce the total SCS under a P-wave incidence and imperfect interfaces located at α=π/2 reduce the total SCS most significantly under SV-incidence, and (iii) under a P-wave incidence the SCS has a high sensitivity to the bonding level of imperfect interfaces when α is small, while it becomes more sensitive to the bonding level when α is larger under SV-wave incidence.

A Rolling Simulation System for Reversing Rolling Mills

In this work a rolling simulation system has been developed for rolling schedules which consists of multiple reversing rolling mills. A slice model approach is applied where the position of a slice can only be determined by considering total deformation. Each slice is parallel to each other and perpendicular to the rolling direction. The solution of coupled thermal and mechanical models over each slice, at a given time and position, are achieved by a novel meshless Local Radial Basis Function Collocation Method (LRBFCM). Mechanical material model obeys ideal plastic flow rule defined by Von Mises. Unknown fields over the slices are interpolated by a certain number of collocation points distributed over the physical domain and its boundary. A system of equations is solved for each collocation point considering its local neighbouring points in the range between 5 and 7. A non-linear system of equations is solved by direct iteration. Groove geometries of each roll are implemented in a compatible way with the slice model and every roll has a horizontal orientation. In between each rolling pass the billet is rotated either 90 or 45 degrees clockwise or counter clockwise. Reduction at each of the passes can be very high, and in such cases, the material completely fills up the groove. This requires a special attention regarding the contact boundary conditions and the collocation node distribution due to numerical instability issues. Coulomb model of friction or sticking boundary conditions are used at the contact boundaries and Gauss-Seidel iterative elliptic node generation algorithm is used for redistributing collocation nodes over the physical domain, when necessary. The simulation results for arbitrary initial position of the slice in the billet are shown in terms of temperature, displacement, strain and stress fields as well as roll forces and torques. A user friendly computer application is created for industrial use based on C# and .NET.

Scattering Attenuation of SH-Waves in Fiber-Reinforced Composites with Partial Imperfectly Bonded Interfaces

The influence of partial imperfectly bonded interfaces between each fiber and the matrix on the scattering attenuation of coherent SH-waves in fiber-reinforced composites is investigated. The imperfection of interfaces is modelled using the spring model, in which the level of imperfection is characterized by a parameter K, which is called the stiffness of the imperfect interfaces. First, the single scattering of SH-waves by a cylindrical fiber with such a partial imperfectly bonded interface to the matrix is formulated and subsequently solved using the collocation point (CP) method. Later on, based on the analysis of the corresponding single scattering problem, effects of several parameters (i.e., frequency of the incident wave, level of imperfection of interfaces, and width of the imperfect interfaces) on the far-field scattering magnitude, scattering cross section, and scattering attenuation coefficients of coherent SH-waves are shown graphically. The potential application of the current results to nondestructive evaluation of interfaces in composites is also discussed.

Estimation of the interaction effects of backfill on the shell in the soil-steel structure based on deformation of the shell

A characteristic feature of the soil-steel structure, in contrast to conventional bridges, is a greatly influence of the backfill ground and the road surface as a load-bearing elements. In the model with soil-steel structure, there are two structural parts: steel shell with corrugated plates and backfilling ground with road surface. The interaction between them is modelled as a contact interaction (interface), which is a normal and tangential force to the surface of the shell. These normal interactions are variable during the construction phase as well as during operation. In this paper, the collocation condition is use to determine these interactions, based on the fact that the calculation result obtained from the model of the geometry of the shell is to be consistent with the result of the measurement of the movement of the collocation point in the real structure. The physical characteristics of the soil in layers of backfill and especially the technology of laying and compacting is taken into account. This is the advantage of this algorithm. The results of these analyses can be the basis for comparing the effectiveness of conventional geotechnical models.

Atypical late-time singular regimes accurately diagnosed in stagnation-point-type solutions of 3D Euler flows

We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point type introduced by Gibbon et al. (Physica D, vol. 132, 1999, pp. 497–510). By employing the method of mapping to regular systems, presented by Bustamante (Physica D, vol. 240 (13), 2011, pp. 1092–1099) and extended to the symmetry-plane case by Mulungye et al. (J. Fluid Mech., vol. 771, 2015, pp. 468–502), we establish a curious property of this solution that was not observed in early studies: before but near singularity time, the blowup goes from a fast transient to a slower regime that is well resolved spectrally, even at mid-resolutions of $512^{2}.$ This late-time regime has an atypical spectrum: it is Gaussian rather than exponential in the wavenumbers. The analyticity-strip width decays to zero in a finite time, albeit so slowly that it remains well above the collocation-point scale for all simulation times $t<T^{\ast }-10^{-9000}$, where $T^{\ast }$ is the singularity time. Reaching such a proximity to singularity time is not possible in the original temporal variable, because floating-point double precision (${\approx}10^{-16}$) creates a ‘machine-epsilon’ barrier. Due to this limitation on the original independent variable, the mapped variables now provide an improved assessment of the relevant blowup quantities, crucially with acceptable accuracy at an unprecedented closeness to the singularity time: $T^{\ast }-t\approx 10^{-140}$.