析元运动求解无限次碰撞问题——湖南省2022年学业水平选择性考试物理卷第14题第(3)问的探析

湖南省2022年学业水平选择性考试物理卷第14题以“篮球运动”为背景,对常规模型赋予新的物理情境,实现高考选拔功能.然而,在解题时,学生对第(3)问普遍感觉难度较大,无从下手.建立情境分析与转化的实施路径,探讨无限次碰撞问题的有效策略:情境分析,模型建构;析元运动,推理论证;探究规律,数学处理;搭架简化,解释检验.同时,作为教学思考,对高三复习备考提出建议.

Rigorous back analysis of shear strength parameters of landslide slip

A rigorous back analysis of shear strength parameters of landslide slip was presented. Kinematical element method was adopted to determine factor of safety and critical failure surface, which overcomes the disadvantage of limit equilibrium method. The theoretical relationship between the combination of shear strength parameters and stability state was studied. The results show that the location of critical slip surface, F/tan f and F/c depend only on the value of c/tan f. The failure surface moves towards the inside of slope as c/tan f increases. According to the information involving factor of safety and critical failure surface in a specific cross-section, strength parameters can be back calculated based on the above findings. Three examples were given for demonstrating the validity of the present method. The shear strength parameters obtained by back analysis are almost consistent with their correct solutions or test results.

CONCISE SOLUTION OF FORWARD KINEMATICS ANALYSIS OF PARALLEL MECHANISM IN 6-SPS SIMILAR PLATFORM

The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.

Finite element analysis of effect of soil displacement on bearing capacity of single friction pile

Effect of soil displacement on friction single pile in the cases of tunneling,surcharge load and uniform soil movement was discussed in details with finite element method.Lateral displacement of the pile caused by soil displacement reached about 90% of the total displacement,which means that P-Δ effect of axial load can be neglected.The maximum moment of pile decreased from 159 kN·m to 133 kN·m in the case of surcharge load when the axial load increased from 0 to the ultimate load.When deformation of pile caused by soil displacement is large,axial load applied on pile-head plays the role of reducing the maximum bending moment in concrete pile to some extent.When pile is on one side of the tunnel,soil displacements around the pile are all alike,which means that the soil pressures around the pile do not decrease during tunneling.Therefore,Q-s curve of the pile affected by tunneling is very close to that of pile in static loading test.Bearing capacities of piles influenced by surcharge load and uniform soil movement are 2480 kN and 2630 kN,respectively,which are a little greater than that of the pile in static loading test(2400 kN).Soil pressures along pile increase due to surcharge load and uniform soil movement,and so do the shaft resistances along pile,as a result,when rebars in concrete piles are enough,bearing capacity of pile affected by soil displacement increases compared with that of pile in static loading test.

Upper-bound and finite element analyses of multi-row sprocket during cold semi-precision forging process

The cold semi-precision forging of a multi-row sprocket was investigated using upper-bound （UB） and finite element methods combined with experiments. Based on the design of a new tooth profile for the sprocket, a cold semi-precision forging process and a kinematically admissible velocity field for filling the die cavity were proposed. Using the UB method, the velocity fields of the sprocket billet in the forming process were divided theoretically and calculated. The process of forging a multi-row sprocket was simulated using the FEM package Deform-3D V6.1 to obtain the distributions of the velocity field and the effective stress field in filling the die cavity. Similar to the simulated results, the experiment on cold forging a 5052 aluminum alloy sprocket was successfully performed. By comparing the calculated （UB method）, experimental and simulated load-stroke curves, the calculated and simulated results were basically in accordance with the experimental results. The study provides a theoretical foundation for the development of the precision forging of multi-row sprockets.

Structure reliability analysis based on supercavity vehicle steady motion

Taking the steady motion status as a starting point,according to the modeling of actual state of theoretical analysis,a predigested model of supercavity vehicle was established,and relationship expressions of these angles were obtained when the movement of supercavity vehicle was stable.A theoretical analysis on the stability of underwater high-speed movement in the movement simulation program was conducted and the simulation results were given.Then the force status of the supercavity vehicle was elicited from the results.The finite element analysis was carried out based on the stability at all angles obtained from simulation results.Taking a pilot model as example,the Monte Carlo method was adopting to analyze the reliability with the given state of force and displacement.The result indicates that this method is feasible.

The Effect of Separatism on the Society： Quantitative Analysis on the World Values Survey

In the 21st century, world politics appeared to far from resolved condition in terms of power sharing among the elites, thus created separatism movements in many parts of the world. These movements caused some changes in the society that is nowadays seen as a multicultural. Using World Values Survey＇s data, this study revealed that separatism would cause people to less likely agree on ethnic diversity benefit. Further, when the result is tested by elaboration model, economic condition was found as important factor on how people saw ethnic diversity benefit among the society.

Analysis of the Adjacent Terrain Effect on the Properties of Ground Motion

The explicit finite element analysis method combined with the artificial transmitting boundary theory is performed to evaluate the adjacent terrain effects on ground motion,and the influence of the distance between adjacent terrains on the topographical amplification effects on ground motion is studied. The results show that:( 1) Compared to the case of a single hill,the presence of adjacent hills has little effect on the shape of the spectral ratio curve,but has a significant effect on the value of spectral ratio,which is dependent on the locations of observation points.( 2) The presence of adjacent hills has a greater effect on high-frequency ground motion,and with the increase of the distance between adjacent hills,such an effect weakens gradually,and the effect of the composite topography combined with multiple hills on ground motion gradually approaches that of a single hill.