Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique

Theoretical and experimental large deflection and stress analysis of a master leaf spring considering stress concentration effect of clamping is reported. The non-uniformly curved master leaf spring under three point bending subjected to moving boundaries is modeled. Geometrically nonlinear strain-displacement relations, as necessary for the theoretical analysis, are derived through visualization of physics behind the large deformation problem. An embedded curvilinear coordinate system is considered, to study the combined effects of non-uniform curvature, bending, stretching and shear deformation including cross-sectional warping. Governing equation of the non-uniformly curved beam system is derived in variational form using energy method, based on linear material constitutive relations and the derived nonlinear kinematic relations. An iterative solution scheme through successive geometry updation is developed and executed in MATLAB® software to solve the governing equation involving strong geometric nonlinearity together with complicating moving boundary effect. Experimental deflection profiles under static loading are obtained through manual image processing technique using AutoCAD® software. Whereas, strain measurements are performed using strain gauges with data acquisition system (HBM-MX840B). Comparison between the theoretical and experimental results lead towards observation on stress concentration effect due to presence of geometric discontinuity in form of a small hole in the physical system. A modified formulation is proposed using domain decomposition method incorporating effect of geometric discontinuity through an equivalent curved beam geometry of variable cross-section. The modified theoretical model is validated successfully with the experimental results, and observations on stress characteristics and effect of hole diameter to beam width ratio are made.

Prototyping of Straight Section Components Using Incremental Shape Rolling

Flexible Roll Forming (FRF) allows the forming of components with a variable cross-section along the length of the component. However, the process has only limited application in the automotive industry due to wrinkling in the flange which currently prevents the forming of high strength steels and limits the part shape complexity. This paper presents a new forming technology, Incremental Shape Rolling (ISR), where a pre-cut blank is clamped between two dies and then a single forming roll is used to incrementally form the material to the desired shape. The new process is similar to some Incremental Sheet Forming (ISF) approaches but with the difference that Incremental Shape Rolling (ISR) allows the manufacture of longitudinal components from high strength metal sheets. In this work, a numerical model of the ISR of a straight section is developed. Experimental prototyping trials are performed and are used to validate the numerical model which is then applied to analyse the new forming process. The results show that in ISR, tensile residual strains are developed in the flange. Flange wrinkling is observed and directly linked to the number of forming passes that are used in the process.

Installation for studying the parameters of localiInstallation for studying the parameters of localization of an electromagnetic wave in a waveguide of variable cross-section in the framework of the predictions of the 5-D extended space modelzation of an electromagnetic wave in a waveguide of variable cross-section in the framework of the predictions of the 5-D extended space model

The paper describes the creation and testing of an experimental setup for studying the parameters of localization of electromagnetic microwave radiation with a power of 0.001-0.004 W in the range of 36.0-79.0 GHz when propagating radiation in metal waveguides of variable cross-section. Measurements will also be carried out under conditions of filling the waveguide with dielectric materials with refractive indices from 1.46 to 4.0 for microwave radiation of the specified range. The installation is designed to measure the parameters of the localization of microwave radiation when it passes through a waveguide of variable cross-section, filled with materials with different refractive indices. Interpretation of the results will be carried out within the framework of the 5-D extended space model (ESM). The extended space model is formulated in (1+4)-dimensional space time-coordinate-interval. An additional spatial coordinate in the ESM is the interval. In the conjugate 5-D space, the energy-momentum-mass interval in the ESM corresponds to mass. In the ESM formalism, the question of the appearance of a nonzero variable mass in a photon and its localization under the influence of an external field is studied.

INTENSIFICATION AND STUDY OF HEAT TRANSFER AND FRICTION IN THE PLATE HEATING SURFACES OF THE KMS-2 AIR HEATER WITH A PRESSURE GRADIENT

A numerical study of heat transfer and friction in the heat exchanger channels in the presence of a variable pressure gradient is performed. The research was carried out in software complexes (Code_Saturne, Salome). The results of the validation of the research method are presented and they showed that the deviation of the numerical simulation results from the calculation data according to the known criterion equations is within the error of generalization of the experimental data by the criterion equations. According to the results of studies at Red=3000, Red=4177, Red=6000, it was found that the average value of the heat transfer coeffi cient of the channel of variable cross-section is up to 20 % higher than for the channel at dp/dx0. At the same time, the thermal-hydraulic effi ciency of the alternating channel (L=117 mm, l=58.5 mm, n=2) in the initial section at x =0...0.08 is lower than in the channel with dp/dx>0 by 26.7 %, and at x =0.08...1 it is higher by 5 ... 15 %, at dp/dx

Theoretical development of a stiffness decomposition method for calculating the displacement of complex bending structures

It is very difficult to provide analytical displacement solutions for complex bending structures, such as beams with variable cross-sections, in structural analysis. The common methods used for such analysis—the direct integration method and the conventional graph multiplication method—have disadvantages of inefficiency and large computational costs. Therefore, a new approach called the stiffness decomposition method was proposed to overcome these shortcomings. The fundamental principle of this new approach was derived based on the unit load method. The general calculation equation of displacement was derived and provided for general n-segment complex bending structures, and an operational procedure for this method was constructed to facilitate its application. Then, the method was applied to two case studies involving classic complex bending structures. The results showed the correctness and effectiveness of the proposed method. The stiffness decomposition method was simpler and more efficient than the other two methods: the number of computations required by the stiffness decomposition method accounted for only 47.4% to 84.0% of the number of computations required by the other methods in the two case studies. The clear mathematical and mechanical derivation of the proposed method makes it easy to understand. Furthermore, the simplicity and practicality of this method make it extensively applicable.

Discrete-continuous three-element model of impact device

There have been examined the mathematic model of the impact device provided for geological materials destruction. Basic elements of the impact device are variable cross-section tool, striker and impact device body. The interaction of these elements is described as a movement of two discrete mass and the rod in the presence of rigid and dissipative connections. One equation in partial derivatives and two ordinary differential equations associated by initial and boundary conditions represent the initial-boundary problem. The numerical method parameters of which are determined at tests problems solution by Fourier method is used for looking for solutions of mixed initial-boundary problem. Researches are made, and parameters determining the damping efficiency of tool, striker and impact device body oscillations are evaluated.

Longitudinal-transverse thermal- force bending and stability layered inhomogeneous profiled rod

The solution to the problem of the stress-strain state of an inhomogeneous profiled rod is based on the use of nonlinear equilibrium conditions and physical relations of a layered thermo elastic thin rod. A differential equation of bifurcation inhomogeneous rod stability of variable cross-section is obtained. The equation has variable functional coefficients. In the initial state, the rod is subjected to bending with the implementation of one of the asymmetric shapes. The critical state occurs under the action of a longitudinal load corresponding to one of the lowest symmetrical shapes, orthogonal to the initial shape. In the first series, numerical calculations of an inhomogeneous I-rod with a variable cross section height are performed. Shelves and wall I-rod are made of steel, aluminum and titanium alloys. The graphs of maximum deflection and normal stresses acting at the calculate points at the boundaries of the layers are plotted depending on the longitudinal load at the given levels of transverse loads and thermal field. A significant influence of the rod physical structure, the profiling its form and the factor of nonlinearity of static relations on the stress fields has been established. A homogeneous temperature field with a nominal value of 80°C creates fields of self-balanced stresses in an inhomogeneous rod. The components of normal stresses in this case reach 20-40% of the materials permissible resistance level. The presence of rod parts with a significant difference in the coefficients of thermal expansion in the composition enhances this effect. In the second, the stability analysis of an inhomogeneous I-rod with a variable width cross section was performed. The transition of the initial S-shaped bend to an unstable state is shown.