For most strip-like plastic injection molded parts, whose cross section size is much smaller than their length, the traditional Hele-Shaw model and three-dimensional model do not work well in the prediction of the war...For most strip-like plastic injection molded parts, whose cross section size is much smaller than their length, the traditional Hele-Shaw model and three-dimensional model do not work well in the prediction of the warpage be- cause of their special shape. A new solution was suggested in this work. The strip-like plastic part was regarded as a little-curved beam macrnscopically, and was divided into a few one-dimensional elements. On the section of each elemental node location, two-dimensional thermal finite element analysis was made to obtain the non- uniform thermal stress caused by the time difference of the solidification of the plastic melt in the mold. The stress relaxation, or equivalently, strain creep was dealt with by using a special computing model. On the bases of in-mold elastic stress, the final bending moment to the beam was obtained and the warpage was predict- ed in good a^reement with practical cases.展开更多
The van Genuchten (vG) function is often used to describe the soil water retention curve (SWRC) of unsaturated soils and fractured rock. The objective of this study was to develop a method to determine the vG model pa...The van Genuchten (vG) function is often used to describe the soil water retention curve (SWRC) of unsaturated soils and fractured rock. The objective of this study was to develop a method to determine the vG model parameter m from the fractal dimension. We compared two approaches previously proposed by van Genuchten and Lenhard et al. for estimating m from the pore size distribution index of the Brooks and Corey (BC) model. In both approaches we used a relationship between the pore size distribution index of the BC model and the fractal dimension of the SWRC. A dataset containing 75 samples from the UNSODA unsaturated soil hydraulic database was used to evaluate the two approaches. The statistical parameters showed that the approach by Lenhard et al. provided better estimates of the parameter m. Another dataset containing 72 samples from the literature was used to validate Lenhard's approach in which the SWRC fractal dimension was estimated from the clay content. The estimated SWRC of the second dataset was compared with those obtained with the Rosetta model using sand, silt, and clay contents. Root mean square error values of the proposed fractal approach and Rosetta were 0.081 and 0.136, respectively, indicating that the proposed fractal approach performed better than the Rosetta model.展开更多
We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous...We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous heat bath at zero gravity.The width of particle size distribution is characterized by the only parameter,namely,the fractal dimension D.The energy dissipation of the mixture is increased as D increases or as e decreases.Furthermore,it is found that the steady-state properties of the mixture such as the collision rate,granular temperature,kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.展开更多
Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dim...Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the N-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures--fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of Ccr, the equivalent diameter of the formed crystals dcr and the intensity of internal energy source Ф, associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size d^r directly affects translation N, i.e., an increase in the number of sets of crystals of infinitely small size e, correspond to the size of the crystal lattice. In turn, translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.展开更多
In this paper, a discontinuous numerical model, namely SDDARF3D(three-dimensional spherical discontinuous deformation analysis for rock failure), is proposed for simulating the whole process of rock failure. Firstly, ...In this paper, a discontinuous numerical model, namely SDDARF3D(three-dimensional spherical discontinuous deformation analysis for rock failure), is proposed for simulating the whole process of rock failure. Firstly, within the framework of the classical discontinuous deformation analysis(DDA) method, the formulation of three-dimensional spherical DDA(3D SDDA) is deduced; secondly, a bonding and cracking algorithm is constructed and the SDDARF3 D model is proposed; thirdly, corresponding VC++ calculation code is developed and some verification examples are calculated. The simulated results can intuitively reproduce the failure phenomena of rock mass, indicating that the proposed SDDARF3 D numerical model is correct and effective.展开更多
基金Supported by the Key Program of National Natural Science Foundation of China(11432003)the Key Research Project for Henan Universities(15A430009)
文摘For most strip-like plastic injection molded parts, whose cross section size is much smaller than their length, the traditional Hele-Shaw model and three-dimensional model do not work well in the prediction of the warpage be- cause of their special shape. A new solution was suggested in this work. The strip-like plastic part was regarded as a little-curved beam macrnscopically, and was divided into a few one-dimensional elements. On the section of each elemental node location, two-dimensional thermal finite element analysis was made to obtain the non- uniform thermal stress caused by the time difference of the solidification of the plastic melt in the mold. The stress relaxation, or equivalently, strain creep was dealt with by using a special computing model. On the bases of in-mold elastic stress, the final bending moment to the beam was obtained and the warpage was predict- ed in good a^reement with practical cases.
基金Supported by the National Natural Science Foundation of China (Nos.50979106 and 50779067)
文摘The van Genuchten (vG) function is often used to describe the soil water retention curve (SWRC) of unsaturated soils and fractured rock. The objective of this study was to develop a method to determine the vG model parameter m from the fractal dimension. We compared two approaches previously proposed by van Genuchten and Lenhard et al. for estimating m from the pore size distribution index of the Brooks and Corey (BC) model. In both approaches we used a relationship between the pore size distribution index of the BC model and the fractal dimension of the SWRC. A dataset containing 75 samples from the UNSODA unsaturated soil hydraulic database was used to evaluate the two approaches. The statistical parameters showed that the approach by Lenhard et al. provided better estimates of the parameter m. Another dataset containing 72 samples from the literature was used to validate Lenhard's approach in which the SWRC fractal dimension was estimated from the clay content. The estimated SWRC of the second dataset was compared with those obtained with the Rosetta model using sand, silt, and clay contents. Root mean square error values of the proposed fractal approach and Rosetta were 0.081 and 0.136, respectively, indicating that the proposed fractal approach performed better than the Rosetta model.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10675048 and 1068006
文摘We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous heat bath at zero gravity.The width of particle size distribution is characterized by the only parameter,namely,the fractal dimension D.The energy dissipation of the mixture is increased as D increases or as e decreases.Furthermore,it is found that the steady-state properties of the mixture such as the collision rate,granular temperature,kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.
文摘Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the N-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures--fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of Ccr, the equivalent diameter of the formed crystals dcr and the intensity of internal energy source Ф, associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size d^r directly affects translation N, i.e., an increase in the number of sets of crystals of infinitely small size e, correspond to the size of the crystal lattice. In turn, translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.
基金supported by the Key Research Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-05-03)the National Basic Research Program of China("973"Project)(Grant No.2011CB710602)the National Natural Science Foundation of China(Grant Nos.51139004&40972201)
文摘In this paper, a discontinuous numerical model, namely SDDARF3D(three-dimensional spherical discontinuous deformation analysis for rock failure), is proposed for simulating the whole process of rock failure. Firstly, within the framework of the classical discontinuous deformation analysis(DDA) method, the formulation of three-dimensional spherical DDA(3D SDDA) is deduced; secondly, a bonding and cracking algorithm is constructed and the SDDARF3 D model is proposed; thirdly, corresponding VC++ calculation code is developed and some verification examples are calculated. The simulated results can intuitively reproduce the failure phenomena of rock mass, indicating that the proposed SDDARF3 D numerical model is correct and effective.
