Papers by Keyword: Boundary Element Method

Abstract: In this paper, the boundary element method (BEM) is investigated and computer simulations are conducted to study the patterns of structure formation of non-isometric elements. The modeling of this study covered various aspects, including shape, radius, angle from the stable radius, porosity, average coordination number, simulation time, component falling force, and electrostatic constant. The simulation results provided important information about the properties and interaction of non-isometric components under different conditions. It was found that the obtained parameters can be effectively predicted for further research. It should also be noted that important processes, such as deformation and material behavior, colloidal aspects, dynamic modeling of the movement of components with complex shapes, and features of nanotechnology, were observed in parallel with computer simulation.

Abstract: The research work is devoted to the study of the stress-strain state of a structure comprising a cylinder with a sphere using numerical approaches and Green’s functions. The results obtained include the analysis of stress distribution, study of deformations and determination of stress concentration zones. Safety factors are assessed and the influence of boundary conditions on the behaviour of the structure is revealed. The application of numerical methods allowed for a detailed study of the interaction of the sphere, providing an opportunity to analyse the exact properties and assess the influence of various factors in complex structures. It should be noted that the results obtained, which were evaluated taking into account all factors, affect the real system and can be predicted with a deviation error of 1%.

Abstract: The paper concerns the problems related to applying the complex variable step method for the sensitivity analysis of the steady temperature field in the solid body domain due to the perturbations of the geometrical and physical parameters. The optimization problem using the approach proposed is also discussed. At the stage of numerical modelling, the boundary element method is used. The first part of the paper is devoted to the shape sensitivity. The results obtained are compared with the solution resulting from the implicit approach of sensitivity analysis. In the second part, the practical problem concerning optimizing the geometry of continuous casting mould cross-section is considered. The project variable vector contains the cooling pipes' radius and the volume flow rate of the cooling water. The numerical results and the conclusions are presented in the final part of the paper.

Abstract: The application of the numerical-analytical boundary elements method (NA BEM) to the calculation of shells is considered. The main problem here is due to the fact that most of the problems of statics, dynamics and stability of shells are reduced to solving an eighth-order differential equation. As a result, all analytical expressions of the NA BEM (fundamental functions, Green functions, external load vectors) turn out to be very cumbersome, and intermediate transformations are associated with eighth-order determinants. It is proposed along with the original differential equation to consider an equivalent system of equations for the unknown state vector of the shell. In this case, calculations of some analytical expressions related to high-order determinants can be avoided by using the Jacobi formula. As a result, the calculation of the determinant at an arbitrary point reduces to its calculation at the point , which leads to a significant simplification of all analytical expressions of the numerical-analytical boundary elements method. On the basis of the proposed approach, a solution is obtained of the problem of bending a long cylindrical shell under the action of an arbitrary load, the stress-strain state of which is described by an eighth-order differential equation. The results can be applied to other types of shells.

Abstract: In this contribution, we propose a cohesive grain-boundary model for hydrogen-assisted inter-granular stress corrosion cracking at the grain-scale in 3D polycrystalline aggregates. The inter-granular strength is degraded by the presence of hydrogen and this is accounted for by employing traction-separation laws directly depending on hydrogen concentration, whose diffusion is represented at this stage through simplified phenomenological relationships. The main feature of the model is that all the relevant mechanical fields are represented in terms of grain-boundary variables only, which couples particularly well with the employment of traction-separation laws.

Abstract: In this work, a novel grain boundary formulation for inter-and trans-granular cracking of polycrystalline materials is presented. The formulation is based on the use of boundary integral equations for anisotropic solids and has the advantage of expressing the considered problem in terms of grain boundary variables only. Inter-granular cracking occurs at the grain boundaries whereas trans-granular cracking is assumed to take place along specific cleavage planes, whose orientation depends on the crystallographic orientation of the grains. The evolution of inter-and trans-granular cracks is then governed by suitably defined cohesive laws, whose parameters characterize the behavior of the two fracture mechanisms. The results show that the model is able to capture the competition between inter-and trans-granular cracking.

Abstract: In order to effectively evaluate the acoustic vibration characteristics of viscoelastic sandwich composite cylindrical shell, based on FEM and BEM method, the vibration acoustic radiation of the viscoelastic sandwich panel and metal shell are calculated, and the results agree well with the experimental results. The dynamic mechanical parameters of viscoelastic core are obtained by dynamic thermodynamic experiments and the equivalent principle of temperature and frequency. The finite element method is used to simulate the coupling of water and shell. Finally, the indirect boundary method is used to calculate the radiated sound field under point excitation and the results show that the average and peak value of the acoustic power of the viscoelastic sandwich composite shell is 21.2dB and 46.4dB lower than that of the steel shell. In the range of low frequency,the radiation sound power is sensitive to the change of the layer angle,which is opposite in the range of high frequency. In the range of high frequency,the shear loss of the viscoelastic core is relatively obvious,which is opposite in the range of low frequency.

Abstract: Theoretical and experimental estimation of elastic properties of two-phase composites containing matrix material and arc-shaped cylindrical fibers is given. Theoretical aspect consists in hybrid micro-macro formulation of problem with consideration of two associated subproblems –nume­rical simulation of fiber influence on the representative volume element and effective strain-stress field approximation by the averaging procedures. Boundary element method is applied for the solution of micro-level subproblem as well as Mori-Tanaka model is adopted for the overall description of composite properties at the macro-level. Then interfacial displacements are involved into solution scheme only. The effective elastic moduli of arc-fiber-reinforced composites are analyzed for the different materials combinations and fiber fractions. For the validation of numerical results, the prismatic concrete specimen filled by the curvilinear shaped cylindrical steel fibers under compression is investigated experimentally. Comparison of theoretical and experimental data is made.

Abstract: This work presents a numerical formulation to compute wear in ber-reinforced composite materials that are subjected to fretting wear contact conditions. The formulation is based on authors' previous works [1, 2] and presents contact and wear constitutive laws which consider micromechanical aspects such as the ber orientation relative to the sliding direction, the ber volume fraction or the ber length. The formulation uses the Boundary Element Method (BEM) for computing the elastic in uence coef cients and contact operators over the augmented Lagrangian to enforce contact constraints. The proposed formulation is applied to compute and study wear in different carbon berreinforced bulk and fi lm con gurations.

Abstract: Crystal plasticity plays a crucial role in the mechanics of polycrystalline materials and it is commonly modeled within the framework of the crystal plasticity finite element method (CPFEM). In this work, an alternative formulation for small strains crystal plasticity is presented. The method is based on a boundary integral formulation for polycrystalline problems and plasticity is addressed using an initial strains approach. Voronoi-type micro-morphologies are considered in the polycrystalline case. A general grain-boundary incremental/iterative algorithm, embedding the flow and hardening rules for crystal plasticity, is developed. The key feature of the method is the expression of the micro-mechanical problem in terms of inter-granular variables only, resulting in a reduction of the number of DoFs, which may be appealing in multi-scale applications. Some numerical results, showing the potential of the technique, are presented and discussed.