The present work formulated a materials design approach,a cluster-formula-embedded machine learning(ML)model,to search for body-centered-cubic(BCC)β-Ti alloys with low Young’s modulus(E)in the Ti–Mo–Nb–Zr–Sn–Ta...The present work formulated a materials design approach,a cluster-formula-embedded machine learning(ML)model,to search for body-centered-cubic(BCC)β-Ti alloys with low Young’s modulus(E)in the Ti–Mo–Nb–Zr–Sn–Ta system.The characteristic parameters,including the Mo equivalence and the cluster-formula approach,are implemented into the ML to ensure the accuracy of prediction,in which the former parameter represents the BCC-βstructural stability,and the latter reflects the interactions among elements expressed with a composition formula.Both auxiliary gradient-boosting regression tree and genetic algorithm methods were adopted to deal with the optimization problem in the ML model.展开更多
A tapered rod mounted at one end (base) and subject to a normal force at the other end (tip) is a fundamental structure of continuum mechanics that occurs widely at all size scales from radio towers to fishing rods to...A tapered rod mounted at one end (base) and subject to a normal force at the other end (tip) is a fundamental structure of continuum mechanics that occurs widely at all size scales from radio towers to fishing rods to micro-electromechanical sensors. Although the bending of a uniform rod is well studied and gives rise to mathematical shapes described by elliptic integrals, no exact closed form solution to the nonlinear differential equations of static equilibrium is known for the deflection of a tapered rod. We report in this paper a comprehensive numerical analysis and experimental test of the exact theory of bending deformation of a tapered rod. Given the rod geometry and elastic modulus, the theory yields virtually all the geometric and physical features that an analyst, experimenter, or instrument designer might want as a function of impressed load, such as the exact curve of deformation (termed the elastica), maximum tip displacement, maximum tip deflection angle, distribution of curvature, and distribution of bending moment. Applied experimentally, the theory permits rapid estimation of the elastic modulus of a rod, which is not easily obtainable by other means. We have tested the theory by photographing the shapes of a set of flexible rods of different lengths and tapers subject to a range of impressed loads and using digital image analysis to extract the coordinates of the elastica curves. The extent of flexure in these experiments far exceeded the range of applicability of approximations that linearize the equations of equilibrium or neglect tapering of the rod. Agreement between the measured deflection curves and the exact theoretical predictions was excellent in all but several cases. In these exceptional cases, the nature of the anomalies provided important information regarding the deviation of the rods from an ideal Euler-Bernoulli cantilever, which thereby permitted us to model the deformation of the rods more accurately.展开更多
基金It was supported by the National Natural Science Foundation of China[No.91860108 and U1867201]the National Key Research and Development Plan(2017YFB0702401)+1 种基金Natural Science Foundation of Liaoning Province of China(Grant No.2019-KF-05-01)the Fundamental Research Funds for the Central Universities(DUT19LAB01).
文摘The present work formulated a materials design approach,a cluster-formula-embedded machine learning(ML)model,to search for body-centered-cubic(BCC)β-Ti alloys with low Young’s modulus(E)in the Ti–Mo–Nb–Zr–Sn–Ta system.The characteristic parameters,including the Mo equivalence and the cluster-formula approach,are implemented into the ML to ensure the accuracy of prediction,in which the former parameter represents the BCC-βstructural stability,and the latter reflects the interactions among elements expressed with a composition formula.Both auxiliary gradient-boosting regression tree and genetic algorithm methods were adopted to deal with the optimization problem in the ML model.
文摘A tapered rod mounted at one end (base) and subject to a normal force at the other end (tip) is a fundamental structure of continuum mechanics that occurs widely at all size scales from radio towers to fishing rods to micro-electromechanical sensors. Although the bending of a uniform rod is well studied and gives rise to mathematical shapes described by elliptic integrals, no exact closed form solution to the nonlinear differential equations of static equilibrium is known for the deflection of a tapered rod. We report in this paper a comprehensive numerical analysis and experimental test of the exact theory of bending deformation of a tapered rod. Given the rod geometry and elastic modulus, the theory yields virtually all the geometric and physical features that an analyst, experimenter, or instrument designer might want as a function of impressed load, such as the exact curve of deformation (termed the elastica), maximum tip displacement, maximum tip deflection angle, distribution of curvature, and distribution of bending moment. Applied experimentally, the theory permits rapid estimation of the elastic modulus of a rod, which is not easily obtainable by other means. We have tested the theory by photographing the shapes of a set of flexible rods of different lengths and tapers subject to a range of impressed loads and using digital image analysis to extract the coordinates of the elastica curves. The extent of flexure in these experiments far exceeded the range of applicability of approximations that linearize the equations of equilibrium or neglect tapering of the rod. Agreement between the measured deflection curves and the exact theoretical predictions was excellent in all but several cases. In these exceptional cases, the nature of the anomalies provided important information regarding the deviation of the rods from an ideal Euler-Bernoulli cantilever, which thereby permitted us to model the deformation of the rods more accurately.
