The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The supp...The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.展开更多
Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner m...Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.展开更多
We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy ofcircular Rydberg states of hydrogen atoms in the intermediate magnetic Geld.This scheme can produce high accuracye...We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy ofcircular Rydberg states of hydrogen atoms in the intermediate magnetic Geld.This scheme can produce high accuracyenergy levels and valid for an arbitrary magnetic field.Energy levels of hydrogen are presented for circular Rydbergstates with azimuthal quantum numbers \m\ = 10-70 as a function of magnetic field strengths ranging from zero to2.35 x 109 T.The variation of spatial distributions of electron probability densities with magnetic field strengths isdiscussed and competition between Coulomb and magnetic interactions is illustrated.展开更多
为预估和延长双圆弧谐波减速器刚轮插齿刀有效长度,论文建立了双圆弧刚轮齿廓数学模型,根据运动学法,建立了插刀加工数学仿真模型;根据齿廓法线法,建立了砂轮磨削加工数学模型,推导了刃磨后插刀的等效齿形与加工误差,确定了插刀的有效...为预估和延长双圆弧谐波减速器刚轮插齿刀有效长度,论文建立了双圆弧刚轮齿廓数学模型,根据运动学法,建立了插刀加工数学仿真模型;根据齿廓法线法,建立了砂轮磨削加工数学模型,推导了刃磨后插刀的等效齿形与加工误差,确定了插刀的有效长度。在此基础上,论文通过优化砂轮齿形与插刀齿数,延长了插刀有效长度。结果表明:优化前55齿插刀有效长度为2.1 mm, 0截面插刀加工出刚轮齿形误差为2μm;优化后0截面插刀加工出刚轮齿形误差的最大值为0.14μm。优化后插刀齿数越多,插刀有效长度越长;优化后42齿、55齿、68插刀有效长度分别增加了4.8%、52%、81%。展开更多
文摘The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.
文摘Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.
基金Support from National Science Foundation of USA under Grant No. 0630370National Natural Science Foundation of China under Grant Nos. 90403028 and 11074260
文摘We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy ofcircular Rydberg states of hydrogen atoms in the intermediate magnetic Geld.This scheme can produce high accuracyenergy levels and valid for an arbitrary magnetic field.Energy levels of hydrogen are presented for circular Rydbergstates with azimuthal quantum numbers \m\ = 10-70 as a function of magnetic field strengths ranging from zero to2.35 x 109 T.The variation of spatial distributions of electron probability densities with magnetic field strengths isdiscussed and competition between Coulomb and magnetic interactions is illustrated.
文摘为预估和延长双圆弧谐波减速器刚轮插齿刀有效长度,论文建立了双圆弧刚轮齿廓数学模型,根据运动学法,建立了插刀加工数学仿真模型;根据齿廓法线法,建立了砂轮磨削加工数学模型,推导了刃磨后插刀的等效齿形与加工误差,确定了插刀的有效长度。在此基础上,论文通过优化砂轮齿形与插刀齿数,延长了插刀有效长度。结果表明:优化前55齿插刀有效长度为2.1 mm, 0截面插刀加工出刚轮齿形误差为2μm;优化后0截面插刀加工出刚轮齿形误差的最大值为0.14μm。优化后插刀齿数越多,插刀有效长度越长;优化后42齿、55齿、68插刀有效长度分别增加了4.8%、52%、81%。
