The simulation of real contact area between materials is foundationally important for the contact mechanics of mechanical structures. The Greenwood and Williamson(GW) model and the Majumdar(MB) model are the basic mod...The simulation of real contact area between materials is foundationally important for the contact mechanics of mechanical structures. The Greenwood and Williamson(GW) model and the Majumdar(MB) model are the basic models in this field, which are widely accepted and proven to be valid in many experiments and engineering. Although the contact models have evolved considerably in recent years, the verifications of the models are most based on the indirect methods such as electrical conductivity and contact stiffness, because of the lack of effective methods to directly measure the variation of contact surface. In this paper, the total reflection(TR) method is introduced into the verification of contact models.An experiment system based on TR method is constructed to measure the real contact area of two PMMA specimens. The comparison analysis between the results of experiment and models suggests that the experiment result has the same trend with simulation, the MB model has better agreement with the experimental result because this method can take into account the variation of radius and the merging of asperities, while the GW model has a huge deviation because of the dependence on resolution and the lack of considering the variation of radius and asperity's merging process. Taking the interaction of asperities into account could give a better result that is closer to the experiment. Our results and analysis prove that the experimental methods in this paper could be used as a more direct and valid method to quantitatively measure the real contact area and to verify the contact models.展开更多
Marx,as one of the founders of Marxism,experienced a significant transformation in his thought during the period of 1843-1844.The Introduction to Critique of Hegel’s Philosophy of Right(hereafter referred to as the I...Marx,as one of the founders of Marxism,experienced a significant transformation in his thought during the period of 1843-1844.The Introduction to Critique of Hegel’s Philosophy of Right(hereafter referred to as the Introduction)is one of Marx’s most representative works from this time.Lenin noted that this text,along with Marx’s On the Jewish Question,marks Marx’s transition from idealism and revolutionary democracy to materialism.In this renowned text,Marx offers a rational critique of the absolute authority of religion,articulates a vision for human emancipation,and envisages the possibility of free and comprehensive human development.During this intellectual shift,Marx absorbed the essence of German classical philosophy and,from a positivist perspective,began employing critical thinking and materialist expression.This enabled him to embark on a path of critique addressing both the religious and real social worlds.In the new era,systematically studying Marxist classic works allows for the exploration of their contemporary relevance.By aligning these classics with specific directions outlined in reports such as those from the 20th CPC Central Committee’s Third Plenary Session,the vitality of these works can be reinvigorated for the modern age.展开更多
In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn [...In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn [1] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the existence theorem of the solution along with partially total unimodularity and nonnegativeness of the incidence matrix to prove that the simplex method facilitates solving these problems. We also provide insights as to how a partition including a particular unit may be obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11872033)the Beijing Natural Science Foundation,China(Grant No.3172017)
文摘The simulation of real contact area between materials is foundationally important for the contact mechanics of mechanical structures. The Greenwood and Williamson(GW) model and the Majumdar(MB) model are the basic models in this field, which are widely accepted and proven to be valid in many experiments and engineering. Although the contact models have evolved considerably in recent years, the verifications of the models are most based on the indirect methods such as electrical conductivity and contact stiffness, because of the lack of effective methods to directly measure the variation of contact surface. In this paper, the total reflection(TR) method is introduced into the verification of contact models.An experiment system based on TR method is constructed to measure the real contact area of two PMMA specimens. The comparison analysis between the results of experiment and models suggests that the experiment result has the same trend with simulation, the MB model has better agreement with the experimental result because this method can take into account the variation of radius and the merging of asperities, while the GW model has a huge deviation because of the dependence on resolution and the lack of considering the variation of radius and asperity's merging process. Taking the interaction of asperities into account could give a better result that is closer to the experiment. Our results and analysis prove that the experimental methods in this paper could be used as a more direct and valid method to quantitatively measure the real contact area and to verify the contact models.
文摘Marx,as one of the founders of Marxism,experienced a significant transformation in his thought during the period of 1843-1844.The Introduction to Critique of Hegel’s Philosophy of Right(hereafter referred to as the Introduction)is one of Marx’s most representative works from this time.Lenin noted that this text,along with Marx’s On the Jewish Question,marks Marx’s transition from idealism and revolutionary democracy to materialism.In this renowned text,Marx offers a rational critique of the absolute authority of religion,articulates a vision for human emancipation,and envisages the possibility of free and comprehensive human development.During this intellectual shift,Marx absorbed the essence of German classical philosophy and,from a positivist perspective,began employing critical thinking and materialist expression.This enabled him to embark on a path of critique addressing both the religious and real social worlds.In the new era,systematically studying Marxist classic works allows for the exploration of their contemporary relevance.By aligning these classics with specific directions outlined in reports such as those from the 20th CPC Central Committee’s Third Plenary Session,the vitality of these works can be reinvigorated for the modern age.
文摘In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn [1] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the existence theorem of the solution along with partially total unimodularity and nonnegativeness of the incidence matrix to prove that the simplex method facilitates solving these problems. We also provide insights as to how a partition including a particular unit may be obtained.
