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The purpose of this paper is to investigate the influence of the resolution with which interfaces of fractal geometry are represented, on the contact area and consequently on the contact interfacial stresses. The study is based on a numerical approach. The paper focuses on the differences between the cases of elastic and inelastic materials having as primary parameter the resolution of the interface.

A multi‐resolution parametric analysis is performed for fractal interfaces dividing a plane structure into two parts. On these interfaces, unilateral contact conditions are assumed to hold. The computer‐generated surfaces adopted here are self‐affine curves, characterized by a precise value of the resolution δ of the fractal set. Different contact simulations are studied by applying a horizontal displacement s on the upper part of the structure. For every value of s, a solution is taken in terms of normal forces and displacements at the interface. The procedure is repeated for different values of the resolution δ. At each scale, a classical Euclidean problem is solved by using finite element models. In the limit of the finest resolution, fractal behaviour is achieved.

The paper leads to a number of interesting conclusions. In the case of linear elastic analysis, the contact area and, consequently, the contact interfacial stresses depend strongly on the resolution of the fractal interface. Contrary, in the case of inelastic analysis, this dependence is verified only for the lower resolution values. As the resolution becomes higher, the contact area tends to become independent from the resolution.

The originality of the paper lies on the results and the corresponding conclusions obtained for the case of inelastic material behaviour, while the results for the case of elastic analysis verify the findings of other researchers.

Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer‐aided design (CAD) and computer‐aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to generate the necessary toolpath information. So this workflow cannot be applied for a fractal object. In this paper, to realize the fabrication of a fractal represented object by the LM technology, a methodology is proposed.

In the proposed methodology, a slab grid is generated in each layer of the object and it consists of a number of pixels. The interior property (corresponding to the fractal object) of each pixel in the slab grid is checked so that slab models of the fractal are created. The boundary of each slab is traced and refined so that the toolpath of the object can be generated from these boundaries.

Applying the proposed methodology, the LM toolpath information can be extracted from the mathematical model of the fractal and the tessellating or slicing processes are not needed to be performed. The problem of representing a fractal in a CAD platform can be eliminated.

The proposed methodology can be applied to iterative function system (IFS) or complex fractal. However, for some fractals constructed from more than one kind of fractal objects, such as multi‐IFS fractals, the methodology must be further developed.

The proposed methodology is a novel development for realizing the fabrication of fractal objects by the LM technology.

Outlines the development of the theory of fractal imaging technology and the evolvement of the theory into a practical technology for storing images. Describes the use of fractal imaging technology to store and index 44,000 images in the George Washington Wilson Collection, in the Queen Mother Library, University of Aberdeen. Indicates the long‐term applications of the technology.

The objective of the present work is to find an alternative approach for gearbox condition monitoring using wear particle characterization incorporated with image vision systems.

It is a quite well‐known phenomenon that wear generates whenever two metallic bodies have contact with each; other hence the present work tries to investigate the effect of improper lubrication in the gearbox due to wear particle generation between gear wheels. Since the identification of wear for machine condition monitoring needs much expertise knowledge and is time‐consuming using the conventional process, fractal mathematics with image morphological analysis has been utilized to overcome this situation in the present work.

The type of wear has been found for the present method by utilizing the lubricant used in the system ferrographically and a great deal of image processing has been done to characterize the type of particle so that the proper maintenance strategy can be undertaken.

Wear particle characterization is a quite common method in maintenance engineering, especially when fault diagnosis of any equipment is concerned. In the present work, the CCD acquisition of the images has been done for different particles, but one analysis amongst them has been shown in this paper. Among all other methodologies, the new technique of fractal mathematics has been used in the present work to minimize the imaging hazards and to make the system more user‐friendly.

Since the term was first coined in 1977, fractals seem to have pervaded every branch of science. Attempts to explain what fractals are and what they are being used for. Are they a fad or are they really useful? Considers factors including quantitative measurement, image compression and computer graphics. Concludes that the future will see an increase in the use of fractal graphics.

The purpose of this paper is to provide a static friction coefficient prediction model of rough contact surfaces based on the contact mechanics analysis of elastic-plastic fractal surfaces.

In this paper, the continuous deformation stage of the multi-scale asperity is considered, i.e. asperities on joint surfaces go through three deformation stages in succession, the elastic deformation, the elastic-plastic deformation (the first elastic-plastic region and the second elastic-plastic region) and the plastic deformation, rather than the direct transition from the elastic deformation to the plastic deformation. In addition, the contact between rough metal surfaces should be the contact of three-dimensional topography, which corresponds to the fractal dimension D (2 < D < 3), not two-dimensional curves. So, in consideration of the elastic-plastic deformation mechanism of asperities and the three-dimensional topography, the contact mechanics of the elastic-plastic fractal surface is analyzed, and the static friction coefficient nonlinear prediction model of the surface is further established.

There is a boundary value between the normal load and the fractal dimension. In the range smaller than the boundary value, the normal load decreases with fractal dimension; in the range larger than the boundary value, the normal load increases with fractal dimension. Considering the elastic-plastic deformation of the asperity on the contact surface, the total normal contact load is larger than that of ignoring the elastic-plastic deformation of the asperity. There is a proper fractal dimension, which can make the static friction of the contact surface maximum; there is a negative correlation between the static friction coefficient and the fractal scale coefficient.

In the mechanical structure, the research and prediction of the static friction coefficient characteristics of the interface will lay a foundation for the understanding of the mechanism of friction and wear and the interaction relationship between contact surfaces from the micro asperity-scale level, which has an important engineering application value.

This paper aims to study the relationship between normal contact stiffness and contact load. It purpose a new calculation model of the normal contact stiffness of joint surfaces by considering the elastic–plastic critical deformation change of asperities contact.

The paper described the surface topography of joint surfaces based on fractal geometry, and fractal parameters and of fractal function derived from measurement data. According to the plastic–elastic contact theory, the contact deformation characteristic of asperities was analyzed; the critical deformation estimation model was presented, which expressed critical deformation as the function of fractal parameters and contact deformation; the contact stiffness calculation model of single asperity was brought forward by considering critical deformation change.

The paper combined the surface topography description function, analyzed the asperity contact states by considering the critical deformation change, and calculated normal contact stiffness based on fractal theory and contact deformation analysis. The comparison between theoretical contact stiffness and experimental data indicated that the theoretical normal contact stiffness agreed with the experimental data, and the estimation model for normal contact stiffness was appropriate.

Owing to the possibility of plastic deformation during the loading process, the experimental curve between the contact stiffness and the contact load is nonlinear, resulting in an error between the experimental results and the theoretical calculation results.

The paper established the relationship between critical deformation and fractal surface topography by constructing asperity distribution function. The paper proposed a new normal contact stiffness calculation model of joint surfaces by considering the variation of critical deformation in contact process.

The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.

For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.

An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.

This law is only valid as long as the creep is of the size of the surface roughness. The modified model admits an analytical solution for the case when the behavior is linear viscoelastic. The proposed model shows a good agreement when compared with experimental results available in the literature.

The purpose of this paper is to develop a general mathematic approach to model the microstructures of porous structures produced by additive manufacturing (AM), which will result in fractal surface topography and higher roughness that have greater influence on the performance of porous structures.

The overall shapes of pores were modeled by triply periodic minimal surface (TPMS), and the micro-roughness details attached to the overall pore shapes were represented by Weierstrass–Mandelbrot (W-M) fractal representation, which was integrated with TPMS along its normal vectors. An index roughly reflecting the irregularity of fractal TPMS was proposed, based on which the influence of the fractal parameters on the fractal TPMS was qualitatively analyzed. Two complex samples of real porous structures were given to demonstrate the feasibility of the model.

The fractal surface topography should not be neglected at a micro-scale level. In addition, a decrease in the fractal dimension D_s may exponentially make the topography rougher; an increase in the height-scaling parameter G may linearly increase the roughness; and the number of the superposed ridges has no distinct influence on the topography. Furthermore, the synthesis method is general for all implicit surfaces.

The method provides an alternative way to shift the posteriori design paradigm of porous media to priori design mode through numeric simulation. Therefore, the optimization of AM process parameters, as well as the porous structure, can be potentially realized according to specific functional requirement.

The synthesis of TPMS and W-M fractal geometry was accomplished efficiently and was general for all implicit freeform surfaces, and the influence of the fractal parameters on the fractal TPMS was analyzed more systematically.

In this paper, a set of safe adaptive genetic algorithms (sGAs) is proposed based on the Splicing/Decomposable encoding scheme and the efficient speed‐up strategies developed by Xu et al.. The proposed algorithms implement the self‐adaptation of the problem representation, selection and recombination operators at the levels of population, individual and component which commendably balance the conflicts between “reliability” and “efficiency”, as well as “exploitation” and “exploration” existed in the evolutionary algorithms. It is shown that the algorithms converge to the optimum solution in probability one. The proposed sGAs are experimentally compared with the classical genetic algorithm (CGA), non‐uniform genetic algorithm (nGA) proposed by Michalewicz, forking genetic algorithm (FGA) proposed by Tsutsui et al. and the classical evolution programming (CEP). The experiments indicate that the new algorithms perform much more efficiently than CGA and FGA do, comparable with the real‐coded GAs — nGA and CEP. All the algorithms are further evaluated through an application to a difficult real‐life application problem: the inverse problem of fractal encoding related to fractal image compression technique. The results for the sGA is better than those of CGA and FGA, and has the same, sometimes better performance compared to those of nGA and CEP.