Papers by Keyword: Analytic Solution

Abstract: The work formulates a particular problem on redistribution of an active element from brazing alloy into brazed materials with due account for thermodiffusion effect. The analysis of the solution has demonstrated that thermodiffusion can facilitate the acceleration of mass transfer from brazing alloy into brazed materials and cause the accumulation of components in the vicinity of contact boundaries.

Abstract: Conducting polymer actuators are of vital importance to the future of many engineering developments in a range of different fields especially micro applications. To allow for the use of conducting polymer actuators in practical applications a reliable and accurate model to predict the applied voltage, output force and bending motion relationship must be established. In current research, we are aiming to contribute to the fundamental understanding of the mechanical behaviour of such conducting polymer actuators under a range of different conditions and material properties. To achieve this goal it is vital to formulate a model that accurately represents the relationship between the applied voltage, output force and the resulting bending displacement of the conducting polymer actuator. Two different theoretical models have been developed and compared; one consisting of an analytical solution and the other involving a range of different finite element models solved using a commercial finite element analysis package–Abaqus. A new modelling method involving the meshing of a multilayered rectangular cross section that can be used for the analysis of a beam-like model is presented with satisfactory results. This numerical method allows for the complex structure of the conducting polymer actuator to be analysed using three dimensional beam elements available in Abaqus/Standard and allowing for the principles of classic beam theory to be implemented.

Abstract: Buried pipelines are important lifeline engineering. During war conventional weapons blasting in the air would induce indirect ground shock, and the shock to the buried pipeline can lead to the paralyzed of urban economic and social function. And the numerical simulation of the dynamic damage of buried pipeline is complicated and time consuming, so this article using the equivalent static load method proposes analytic solution method of stress calculation of buried pipeline under ground shock. Through comparing the results calculated by analytic solution method and numerical solution, it shows that the analytical solution is feasible in engineering application.

Abstract: The interval estimation for the presumption of structure concrete strength should be gained because of strong randomness of test data. For further exaltation of accuracy and credibility test concrete strength, analytic solution of inverse regression equation for evaluating concrete strength of building materials is presented herein based on the inverse regression model. The accurate solution for the presumption of concrete strength can be obtained through the analytic solution, detection precision and reliability for the presumption of structure concrete strength can be improved with respect to the traditional point estimation method.

Abstract: The basic theory of the rebound method is introduced, and analytic solution of inverse regression equation for evaluating concrete strength of building materials is presented herein based on the inverse regression model. Furthermore, two engineering examples are given, satisfactory results are obtained using the analysis method. The analysis method can be also used to gain the presumption of strength for others building materials and solutions of other inverse regression models.

Abstract: The previous studies show that the transverse distribution of pressure and temperature in microscale Poiseuille flow cannot be predicted by Navier-Stokes equation with the slip boundary condition. In this paper, we analyzed the planar microchannel force-driven Poiseuille flow by high order continuum model. The super-Burnett constitutive relations were used and the nonlinear ordinary differential Equations of higher-orders were obtained by the hypothesis of parallel flow. With a perturbations theory, we linearized the equations and obtained the analytic solutions. The results show that the solutions can capture the temperature dip which is the same as the DSMC result. However, we also find that the temperature profile near the wall does always not match with the DSMC result. Especially, the difference in the qualitative exists when the Knudsen number is large enough. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model such as super-Burnett one.

Abstract: Treat the upper plate and lower plate of ribbed hollow floor as the surfaces of sandwich panel, and the ribbed hollow layer as the central layer of sandwich panel; consider the bending stiffness of the surfaces and transverse shear deformation of the central layer; use Hoff laminated theory; based on the same stiffness principle; establish sandwich panel structure model of hollow floor; Derive partial differential equations of cast-in-place reinforced concrete two-way ribbed and thin-walled hollow floor under vertical uniform load and present the analytic solution of the equations with two opposite clamped edges and others simply supported edges. Analyze the mechanical properties of hollow floor. The results are very close to the results of using finite element method.

Abstract: This paper describes a method for generating a center of gravity trajectory of a biped humanoid robot under variable reference ZMP trajectory. A simple inverted pendulum model (SIPM) is used to calculate a center of gravity (CoG) trajectory from a reference zero moment point (ZMP) trajectory with an analytic form, which is based on the Fourier series. Fundamentally, we used a time segmentation based approach. For each segment, we defined its duration and boundary conditions, which are the key parameters of ZMP trajectory design. After designing the ZMP trajectory in each segment, we can automatically calculate the CoG trajectory by matching the boundary conditions and by calculating the coefficients between the time segments. The reference ZMP trajectory can be changed by updating the boundary conditions during walking. We successfully verified the proposed method through full-body dynamic simulations with variable step length.

Abstract: During the process of structure design, non uniform load on beam usually is considered as similar uniform load. Some analytic solution formulas of bending moment about beams acted on symmetric load are deduced. Table of equivalent uniform load coefficient according to the principle of bending moment equivalency is listed. The feasibility and beware are also discussed.

Abstract: In step with body Ⅱ, analytic solution and illustration of elastic energy releasing amount of rock mass dynamic destabilization are given for the first time in the form of precise and approximate catastrophe model. It is upgraded from qualitative understand to quantitative description that study on rock stability at the stage before and after earthquake and rockburst. The halting point’s position of rock mass dynamic destabilization is ascertained strictly, and it offers scientific basis for the calculation on earthquake efficiency, the study on earthquake energy magnitude released, earthquake stress drop, fault offset after earthquake and amount of elastic strain recovery of surrounding rock. The system possesses the capability of applying work to surroundings when it destabilizes, and earthquake wave energy is the work that destabilizing rock system applies to surroundings by way of destructive. The given illustration of elastic energy releasing amount implicates wealth of information, it produces credible evidence for confirming that the mathematical abstract of rock dynamic destabilization is fold catastrophe model.