In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micr...In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.展开更多
In this study,the relationship of tropical cyclone(TC)size change rate(SCR),within 24 hours,with size,intensity,and intensity change rate(ICR)are explored over the western North Pacific.TC size is defined as the azimu...In this study,the relationship of tropical cyclone(TC)size change rate(SCR),within 24 hours,with size,intensity,and intensity change rate(ICR)are explored over the western North Pacific.TC size is defined as the azimuthally averaged radius of gale-force wind of 17 m s−1(R17)based on the Multiplatform Tropical Cyclone Surface Winds Analysis data.The majority of SCRs are mainly distributed in the range from−20 to 80 km d−1.The correlation coefficients between SCR and size(SCR-R17),intensity,and ICR(SCR-ICR)are−0.43,−0.12,and 0.25,respectively.The sensitivity of the SCR-R17 and SCR-ICR relationships to size,intensity,and evolution stage are further examined.Results show that the SCR-R17 relationship is more sensitive to variations of size and evolution stage than that of intensity.The relationship of SCR-ICR is largely modulated by the evolution stage.The correlation coefficient of SCR-ICR can increase from 0.25 to 0.40 when only considering the lifetime stages concurrently before and after the lifetime maximum size(LMS)and lifetime maximum intensity.This demonstrates that ICR is a potential factor in predicting SCR during these evolution stages.Besides,the TC size expansion(shrinkage)is more likely to occur for TCs with smaller(larger)size and weaker(stronger)intensity.The complexity of size change during a TC's lifetime can be attributed to the fact that shrinkage or expansion could occur both before and after LMS.展开更多
When two contacting solid surfaces are tightly closed and invisible to the naked eye, the discontinuity is said to be microscopic regardless of whether its length is short or long. By this definition, it is not suffic...When two contacting solid surfaces are tightly closed and invisible to the naked eye, the discontinuity is said to be microscopic regardless of whether its length is short or long. By this definition, it is not sufficient to distinguish the difference between a micro- and macro-crack by using the length parameter. Microcracks in high strength metal alloys have been known to be sev- eral centimeters or longer. Considered in this work is a dual scale fatigue crack growth model where the main crack can be mi- cro or macro but there prevails an inherent microscopic tip region that is damaged depending on the irregularities of the micro- structure. This region is referred to as the ＂micro-tip＂ and can be simulated by a sharp wedge with different angles in addition to mixed boundary conditions. The combination is sufficient to model microscopic entities in the form of voids, inclusions, precipitations, interfaces, in addition to subgrain imperfections, or cluster of dislocations. This is accomplished by using the method of ＂singularity representation＂ such that closed form asymptotic solutions can be obtained for the development of fa- tigue crack growth rate relations with three parameters. They include： （1） the crack surface tightness o-＊ represented by Cro/Cr~ = 0.3-0.5 for short cracks in region I, and 0.1-0.2 for long cracks in region II, （2） the micro/macro material properties reflected by the shear modulus ratio/1＂ （=,L/micro/]-/macro varying between 2 and 5） and （3） the most sensitive parameter d＊ being the micro-tip characteristic length d＊ （=d/do） whose magnitude decreases in the direction of region I ---~II. The existing fatigue crack growth data for 2024-T3 and 7075-T6 aluminum sheets are used to reinterpret the two-parameter da/dN=C（AK）n relation where AK has now been re-derived for a microcrack with surfaces tightly in contact. The contact force will depend on the mean stress ~m or mean stress ratio R as the primary parameter and on the stress amplitude era as the secondary parameter.展开更多
基金Projects(50975092,50805052,U0834002) supported by the National Natural Science Foundation of ChinaProject(9151030101000007) supported by the Natural Science Foundation of Guangdong Province,ChinaProject(2009ZZ0041) supported by the Fundamental Research Funds for the Central Universities in China
文摘In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.
基金This study was supported by the National Natural Science Foundation of China[grant numbers 41975071 and 41775063].
文摘In this study,the relationship of tropical cyclone(TC)size change rate(SCR),within 24 hours,with size,intensity,and intensity change rate(ICR)are explored over the western North Pacific.TC size is defined as the azimuthally averaged radius of gale-force wind of 17 m s−1(R17)based on the Multiplatform Tropical Cyclone Surface Winds Analysis data.The majority of SCRs are mainly distributed in the range from−20 to 80 km d−1.The correlation coefficients between SCR and size(SCR-R17),intensity,and ICR(SCR-ICR)are−0.43,−0.12,and 0.25,respectively.The sensitivity of the SCR-R17 and SCR-ICR relationships to size,intensity,and evolution stage are further examined.Results show that the SCR-R17 relationship is more sensitive to variations of size and evolution stage than that of intensity.The relationship of SCR-ICR is largely modulated by the evolution stage.The correlation coefficient of SCR-ICR can increase from 0.25 to 0.40 when only considering the lifetime stages concurrently before and after the lifetime maximum size(LMS)and lifetime maximum intensity.This demonstrates that ICR is a potential factor in predicting SCR during these evolution stages.Besides,the TC size expansion(shrinkage)is more likely to occur for TCs with smaller(larger)size and weaker(stronger)intensity.The complexity of size change during a TC's lifetime can be attributed to the fact that shrinkage or expansion could occur both before and after LMS.
文摘When two contacting solid surfaces are tightly closed and invisible to the naked eye, the discontinuity is said to be microscopic regardless of whether its length is short or long. By this definition, it is not sufficient to distinguish the difference between a micro- and macro-crack by using the length parameter. Microcracks in high strength metal alloys have been known to be sev- eral centimeters or longer. Considered in this work is a dual scale fatigue crack growth model where the main crack can be mi- cro or macro but there prevails an inherent microscopic tip region that is damaged depending on the irregularities of the micro- structure. This region is referred to as the ＂micro-tip＂ and can be simulated by a sharp wedge with different angles in addition to mixed boundary conditions. The combination is sufficient to model microscopic entities in the form of voids, inclusions, precipitations, interfaces, in addition to subgrain imperfections, or cluster of dislocations. This is accomplished by using the method of ＂singularity representation＂ such that closed form asymptotic solutions can be obtained for the development of fa- tigue crack growth rate relations with three parameters. They include： （1） the crack surface tightness o-＊ represented by Cro/Cr~ = 0.3-0.5 for short cracks in region I, and 0.1-0.2 for long cracks in region II, （2） the micro/macro material properties reflected by the shear modulus ratio/1＂ （=,L/micro/]-/macro varying between 2 and 5） and （3） the most sensitive parameter d＊ being the micro-tip characteristic length d＊ （=d/do） whose magnitude decreases in the direction of region I ---~II. The existing fatigue crack growth data for 2024-T3 and 7075-T6 aluminum sheets are used to reinterpret the two-parameter da/dN=C（AK）n relation where AK has now been re-derived for a microcrack with surfaces tightly in contact. The contact force will depend on the mean stress ~m or mean stress ratio R as the primary parameter and on the stress amplitude era as the secondary parameter.
