In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solutio...In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.展开更多
The theory of the fractal structure characterizing propagation of a crack through identification of its generator is presented. It’s generating fractal, the peculiarities of its construction and the way to measure it...The theory of the fractal structure characterizing propagation of a crack through identification of its generator is presented. It’s generating fractal, the peculiarities of its construction and the way to measure its segments are defined, and a theorem on the inverse scale property of such and other of the axial symmetry property of the fractal generator are presented and demonstrated. The theory is applied on 6061-T6 aluminum samples, using SENB probes. Direction of crack propagation and its fractal dimension are calculated numerically. Results obtained from modeling the direction of crack propagation through mechanics of elastic linear fracture and the one proposed here, called geometrical fractal fracture, are compared, thus developing the mirror case.展开更多
Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal pa...Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal parameters into the mixed lubrication equation, the relationship between flow factors and fractal dimensions is analyzed. The results show that the pressure flow factors' values increase, while the shear flow factor decreases, with the increasing length to width ratio of a representative asperity γ at the same fractal dimension. It can be also found that these factors experience more irregular and significant variations and show the higher resolution and the local optimal and the worst fractal dimensions, by a fractal dimension D , compared with the oil film thickness to roughness ratio h/R q . As an example of application of the model to solve the lubrication of the piston skirt in an engine, the frictional force and the load capacity of the oil film in a cylinder were analyzed. The results reveal that the oil film frictional force and the load capacity fluctuate with increasing fractal dimension, showing big values at the small D and smaller ones and slightly variable in the range of bigger one, at the same crank angle.展开更多
Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affin...Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.展开更多
Fractal dimension fd, was used as one of the parameters to describe dessicationcracking pattern of a remolded Black Cotton soil (Eutric Vertisol). The fractal dimension computed from filtered, thinned and skeletonized...Fractal dimension fd, was used as one of the parameters to describe dessicationcracking pattern of a remolded Black Cotton soil (Eutric Vertisol). The fractal dimension computed from filtered, thinned and skeletonized binary images of soil cracks using the Fractal3 software provided an insight into temporal variability of fd as well as its relationship with the Crack Intensity Factor (CIF) and Soil Moisture Content (SMC). The results showed that even for single crack, the fd prior to filtering and thinning were higher than after. Cracking patterns were observedfroma chosen soil sample during dessication and the corresponding relationship between fd and CIF compared and monitored. As the critical SMC decreased during drying (45% to 27%), the CIF soil increased (0.023% - 5.75%), so did the fd (1.233 to 1.7193). The fd showed a positive linear correlation with CIF at r<sup>2</sup> = 0.247 (P fd with SMC was best described using a polynomial function at r<sup>2</sup> = 0.969 (P fd was sensitive to dessication cracking and therefore on SMC changes. Visual observation of dessication cracking showed that CIF increased and attained stability after day 4 while the computed and logarithmic transformed crack area attained stability between days 7 to 10 gradually decreasing to values below 2%. The estimated crack Cover or Brightness of the digitized binary images also gave better approximation of the CIF though this was slightly higher. Our results showed that dessication cracking of the Eutric Vertisol was independent of antecedent critical SMC and was time-constrained. Further soil cracking therefore stopped once maximum CIF was attained and only widening and deepening of pre-existing cracks continued.展开更多
文摘In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.
文摘The theory of the fractal structure characterizing propagation of a crack through identification of its generator is presented. It’s generating fractal, the peculiarities of its construction and the way to measure its segments are defined, and a theorem on the inverse scale property of such and other of the axial symmetry property of the fractal generator are presented and demonstrated. The theory is applied on 6061-T6 aluminum samples, using SENB probes. Direction of crack propagation and its fractal dimension are calculated numerically. Results obtained from modeling the direction of crack propagation through mechanics of elastic linear fracture and the one proposed here, called geometrical fractal fracture, are compared, thus developing the mirror case.
基金ThisresearchwassupportedbytheNationalNaturalScienceFoundationofChina (No .5 9990 472 )
文摘Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal parameters into the mixed lubrication equation, the relationship between flow factors and fractal dimensions is analyzed. The results show that the pressure flow factors' values increase, while the shear flow factor decreases, with the increasing length to width ratio of a representative asperity γ at the same fractal dimension. It can be also found that these factors experience more irregular and significant variations and show the higher resolution and the local optimal and the worst fractal dimensions, by a fractal dimension D , compared with the oil film thickness to roughness ratio h/R q . As an example of application of the model to solve the lubrication of the piston skirt in an engine, the frictional force and the load capacity of the oil film in a cylinder were analyzed. The results reveal that the oil film frictional force and the load capacity fluctuate with increasing fractal dimension, showing big values at the small D and smaller ones and slightly variable in the range of bigger one, at the same crank angle.
基金supported by the National Natural Science Foundation of China (Grant Nos.60972004 and 60402004)
文摘Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.
文摘Fractal dimension fd, was used as one of the parameters to describe dessicationcracking pattern of a remolded Black Cotton soil (Eutric Vertisol). The fractal dimension computed from filtered, thinned and skeletonized binary images of soil cracks using the Fractal3 software provided an insight into temporal variability of fd as well as its relationship with the Crack Intensity Factor (CIF) and Soil Moisture Content (SMC). The results showed that even for single crack, the fd prior to filtering and thinning were higher than after. Cracking patterns were observedfroma chosen soil sample during dessication and the corresponding relationship between fd and CIF compared and monitored. As the critical SMC decreased during drying (45% to 27%), the CIF soil increased (0.023% - 5.75%), so did the fd (1.233 to 1.7193). The fd showed a positive linear correlation with CIF at r<sup>2</sup> = 0.247 (P fd with SMC was best described using a polynomial function at r<sup>2</sup> = 0.969 (P fd was sensitive to dessication cracking and therefore on SMC changes. Visual observation of dessication cracking showed that CIF increased and attained stability after day 4 while the computed and logarithmic transformed crack area attained stability between days 7 to 10 gradually decreasing to values below 2%. The estimated crack Cover or Brightness of the digitized binary images also gave better approximation of the CIF though this was slightly higher. Our results showed that dessication cracking of the Eutric Vertisol was independent of antecedent critical SMC and was time-constrained. Further soil cracking therefore stopped once maximum CIF was attained and only widening and deepening of pre-existing cracks continued.
