MASS CONVERTED FROM THE ENERGY OF MOTION

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

MASS CONVERTED FROM THE ENERGY OF MOTION

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

On the Motion of Two Microspheres in a Stokes Flow Driven by an External Oscillator Field

Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.

NUMERICAL APPROACH FOR SIMULATING THE TENSIONING PROCESS OF COMPLEX PRESTRESSED CABLE-NET STRUCTURES

The stability of cable-net structures depends on the prestress of the system. Due to the large displacement and mutual effect of the cables, it is difficult to simulate the tensioning process and control the forming accuracy. The Backward Algorithm (BA) has been used to simulate the tensioning process. The traditional BA involves complicated and tedious matrix operations. In this paper, a new numerical method based on the Vector Form Intrinsic Finite Element (VFIFE) method is proposed for BA application. Moreover, the tensioning sequence of a complex cable-net structure is introduced. Subsequently, a new approach for BA application in the simulation of the tensioning process is presented, which combines the VFIFE approach and the notion of form-finding. Finally, a numerical example is simulated in detail and the results of different tensioning stages are analyzed to verify the feasibility of the proposed approach. This study provides a significant reference for improving the construction control and forming accuracy of complex prestressed cable-net structures.

openVFIFE: An Object-Oriented Structure Analysis Platform Based on Vector Form Intrinsic Finite Element Method

The vector form intrinsic finite (VFIFE) method is a new and promising structural analysis technique that has many advantages as compared with the conventional finite element method (FEM) in analyzing the complex behaviors of a structure. However, despite the popularization of its application in civil and infrastructure engineering, there is no available unified general analysis framework for it, which limits the applications and developments of VFIFE. This work develops and implements a platform (termed openVFIFE) based on a new proposed object-oriented framework to facilitate the development and application of the vector form intrinsic finite method as well as the efficient and accurate analyses of complex behaviors for civil structures. To validate the platform, a series of numerical examples are conducted. Furthermore, to extend the applications of VFIFE, the nonlinear dynamic and collapse processes of a transmission tower under earthquake load are studied using openVFIFE. The results of these numerical examples simulated by the developed truss or beam elements are consistent with theoretical solutions, previous research or conventional finite element models. The failure modes of the transmission tower under earthquake load simulated by the platform is consistent with those observed in real cases. In addition, the results of nonlinear dynamic analyses of the transmission tower show that the computational efficiency of the proposed platform is 6-10 times higher than that of the conventional finite element method. The results provide sufficient evidence to prove the accuracy and efficiency of the proposed platform in the static, dynamic and elastoplastic analyses of truss and frame structures, especially in the structure analysis characterized by strong geometry nonlinearity. It is noteworthy that in addition to the link and beam elements, further work is undergoing on implementing more elements, such as shell and solid elements. The openVFIFE also allows researchers who are interested in this topic to put their creative ideas into this platform and continuously improve the completeness and applicability of the VFIFE method.