A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem

The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep characteristics of the viscoplastic stage from the perspective of internal energy to analyze the mechanism of rock creep failure and determine the threshold of accelerated creep initiation.Based on the kinetic energy theorem,Perzyna viscoplastic theory,and the Nishihara model,a unified creep constitutive model that can describe the whole process of decaying creep,stable creep,and accelerated creep is established.Results reveal that the energy consumption and creep damage in the process of creep loading mainly come from the internal energy changes of geotechnical materials.The established creep model can not only describe the viscoelasticeplastic creep characteristics of rock,but also reflect the relationship between rock energy and creep deformation change.In addition,the research results provide a new method for determining the critical point of creep deformation and a new idea for studying the creep model and creep mechanical properties.

Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method

The supposedly missing dark energy of the cosmos is found quantitatively in a direct analysis without involving ordinary energy. The analysis relies on five dimensional Kaluza-Klein spacetime and a Lagrangian constrained by an auxiliary condition. Employing the Lagrangian multiplier method, it is found that this multiplier is equal to the dark energy of the cosmos and is given by where E is energy, m is mass, c is the speed of light, and λ is the Lagrangian multiplier. The result is in full agreement with cosmic measurements which were awarded the 2011 Nobel Prize in Physics as well as with the interpretation that dark energy is the energy of the quantum wave while ordinary energy is the energy of the quantum particle. Consequently dark energy could not be found directly using our current measurement methods because measurement leads to wave collapse leaving only the quantum particle and its ordinary energy intact.

Thermal-induced snap-through buckling of simply-supported functionally graded beams

The instability of functionally graded material(FGM)structures is one of the major threats to their service safety in engineering applications.This paper aims to clarify a long-standing controversy on the thermal instability type of simply-supported FGM beams.First,based on the Euler-Bernoulli beam theory and von K′arm′an geometric nonlinearity,a nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated.Second,an approximate analytic solution to the nonlinear integro-differential boundary value problem under a thermal-induced inhomogeneous force boundary condition is obtained by using a semiinverse method when the coordinate axis is relocated to the bending axis(physical neutral plane),and then the analytical predictions are verified by the differential quadrature method(DQM).Finally,based on the free energy theorem,it is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes;furthermore,the nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect.These results are expected to provide new ideas and references for the design and regulation of FGM structures.

Dynamic Response of Ocean Trestle to Horizontal Impact of Moving Mass

Based on the Winkler hypothesis, a model for analysis of the flexural response of an ocean trestle embedded in layered soil to horizontal impact of a moving mass is developed. By use of the transfer matrix in Lime domain, one can calculate the flexural dynamic response of a single pile. Then, by use of the boundary conditions of piles at the pile top, the dynamic response of the structure is analyzed. By use of the model proposed in this paper, the interactive force between the moving mass and the structure can be computed based on Work's kinetic energy theorem and Newton iterative method. Thus the approach does not have to assume the interactive force, while the traditional method have to. The approach more accords with the engineering practice than the traditional method and it is convenient for engineering design.

A Combined Numerical-Experimental Study on the Noise Power Spectrum Produced by an Electromagnetic Sensor for Slurry Flow

The signals generated by electromagnetic flow sensors used for slurry fluids are often affected by noise interference produced by interaction with the slurry itself.In this study,the power spectrum characteristics of the signal are studied,and an attempt is made to determine the relationship between the characteristics of the related noise and the velocity and concentration of the slurry fluid.Dedicated experiments are conducted and the related power spectrum curve is obtained processing the signal measured by the sensor with Matlab.Numerical simulations are also carried out in the frame of an Eulerian approach in order get additional insights into the considered problem through comparison with the experimental results.The following conclusions are drawn:(1)The intensity of noise is directly proportional to the number of solid particles colliding with the electrode of the electromagnetic flow sensor per unit time,and to the square of the average velocity of the flow layer near the pipe wall.(2)With an increase in the slurry noise intensity,the power spectrum curve shifts upward in the logarithmic coordinate system(and vice versa).

Research on the Optimal Strategy of"Working Together with One Heart"Project

The"Working Together with One Heart"project,also known as the"One Heart Drum"project,is a collaboration skill development project,which assesses the collaboration skills of its team members.In this paper,the method of combining actual problems with physical model analysis is used to determine the influence of different factors in the project operation,and a geometric analysis model is also established.Through MATLAB simulation and assignment operation,the optimal strategy of the project is finally obtained.

THE DERIVATION OF EXACT STATIC CONDITIONS AT THE CORNER POINTS FOR THE BENDING OF THICK RECTANGULAR PLATES

In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].

On the Mathematical Nature of Wireless Broadcast Trees

Trees are arguably one of the most important data structures widely used in information theory and computing science. Different numbers of intermediate nodes in wireless broadcast trees may exert great impacts on the energy consumption of individual nodes, which are typically equipped with a limited power supply in a wireless sensor network; this limitation may eventually determine how long the given wireless sensor network can last. Thus, obtaining a deep understanding of the mathematical nature of wireless broadcast trees is of great importance. In this paper, we give new proof of Cayley＇s well-known theorem for counting labeled trees. A distinct feature of this proof is that we purely use combinatorial structures instead of constructing a bijection between two kinds of labeled trees, which is in contrast to all existing proofs. Another contribution of this work is the presentation of a new theorem on trees based on the number of intermediate nodes in the tree. To the best of our knowledge,this work is the first to present a tree enumeration theorem based on the number of intermediate nodes in the tree.