Stress-deformed state of the shell with a small initial deflection under the action of the end load

Purpose of work. Construction of method for calculating the stress-strain state of cylindrical shell with small initial deflection, to which an end load is applied, using the method of characteristics. Comparison of the calculation results of the obtained model with the works of other authors in this area. Research methods. For the calculation, the equations of motion of the Timoshenko type shell were used, taking into account both the shear deformation and inertia of rotation, and some nonlinear terms, to which the method of characteristics was applied. To obtain the equations of shell motion, the Hamilton-Ostrogradsky variational principle was used. Results method is proposed for calculating the stress-strain state of a cylindrical shell with a small initial deflection using characteristics. Comparative analysis of the calculation results with research in this area by other authors, which showed the effectiveness of the proposed method. Scientific novelty. The equations of the classical theory of shells, based on the Kirchhoff-Love hypotheses, which do not take into account the shear deformation and inertia of rotation, as well as linear equations of the Timoshenko type, have become widespread. In this work, a model of the stress-strain state of an axisymmetric shell with small initial deflections is constructed, taking into account both shear deformation and rotational inertia, and some nonlinear terms. Practical value. The proposed method can be used to calculate the stress-strain state of structures in which thin shells are present as elements, taking into account small initial deflection. This method makes it possible to study the influence of the characteristics of the initial deflection on the stress-strain state of the entire structure.

Особенности деформирования круглых тонкопленочных мембран и экспериментальное определение их эффективных характеристик

The features of thin-film membranes, which are formed above round holes in silicon substrates using the Bosch-process are considered. The membrane has a complex shape due to the presence of the stress state of the initial films. The analysis of the dependence of the membrane deflection w on the supplied overpressure P is used to calculate the mechanical characteristics of the membranes. In this case, it is necessary to determine directly on the membrane its diameter, the thickness of the constituent layers, the change in the relief of the membrane surface over its entire area as the excess pressure P. Determination of the membrane diameter and the thicknesses of the constituent layers is shown by the example of p-Si*/SiNx/SiO2 and SiNх/SiО2/SiNх/SiО2 membranes. We used spectral ellipsometry, energy-dispersive X-ray spectroscopy, optical profilometry, optical microscopy. The influence of the peculiarities of the fixing conditions on the stress-strain state of membranes is shown, and the assessment is carried out by means of numerical modeling. A technique has been developed for measuring and calculating the mechanical characteristics of membranes that have an initial deflection. The calculation result is shown on the example of a membrane with an initial deflection of 2 µm – SiNх/SiО2/SiNх/SiО2 and a membrane with an initial deflection of 30 µm – Al/SiO2/Al.

The influence of initial deflection angle on the tribological properties of gray cast iron rings with curve distributed pits under dry sliding

This study presents the influence of initial deflection angle (IDA) on the tribological properties of gray cast iron (GCI) rings with curve distributed pits in the radial direction (CDPRD). The thermal behavior of pits textured GCI rings with different initial deflection angles (0°, 30°, 45°, 60°, 75°) and fixed deflexional angle of adjacent pits (DAAP, 10°) were researched, through APDL programming. A pin-on-disc wear test rig was used to reveal the anti-wear performance of samples under dry sliding, at a rotating speed of 200 rpm, with a normal load of 70 N. An electronic balance and an optical microscope (OM) were used to obtain their wear losses and worn surfaces, respectively. The results show that: comparing with the smooth GCI ring, there are evident high temperature regions between two adjacent pits groups, called “temperature barrier and separation effect”. Among all textured samples, the von Mise’s stress of IDA45 is the most stable, and its temperature is almost the lowest. The friction coefficient curve and the wear loss of IDA45 are also the lowest, and much lower than the loss of smooth GCI ring, indicating the excellent anti-wear performance. This work can provide a valuable reference for the surface design of journal bearings.

Ultimate Strength and Collapse Behavior of Ring-Stiffened Cylindrical Shells Under External Pressure With Shell Buckling or Stiffener Torsional Buckling

A series of ultimate strength analyses of ring-stiffened cylindrical shells with various dimensions and scantlings is carried out applying the nonlinear finite element method. The detailed buckling/plastic collapse behavior including the influence of initial deflection applied in the ultimate strength analyses is investigated. In most past studies, detailed classification of collapse modes and investigation of the influence of the initial deflection mode have not been sufficiently conducted. In this study, firstly the ultimate strength analyses of 288 cases varying the dimensions of the ring-stiffened cylindrical shell and the attachment direction of the stiffeners, inside or outside, are performed. From the results, the collapse modes are classified into five modes, which are stiffener-torsional buckling collapse (localized deformation mode and mode to keep strength after the ultimate strength), shell buckling collapse (localized deformation mode and mode with kinking lines), and combined collapse of the buckling modes. A slenderness ratio is proposed using elastic buckling strength and pressure when the circumferential stress reaches the yield stress, and the possibility of estimating the ultimate strength is indicated.

Straightening of low-rigid cylindrical details. Part I. Justification of the type of loading and modes at transverse straightening

For straightening of low-rigid cylindrical details like shaft and axes different types of loadings are considered which form tension different in size and in distribution. As the perspective direction, it is possible to consider correction by a bend at the influence of the distributed loading with the subsequent hardening of a billet by superficial plastic deformation based on a cross cheesing of it by flat plates. Purpose of the work was to define tension of the billet at cross correction for the choice of more effective type of loading and processing rational modes. The mathematical apparatus was used based on laws of the theory of an elastoplastic solid and Ansys Workbench software package. Novelty is the research of effective methods of loading at cross correction of cylindrical details. As a result of analytical calculations, value of the residual tension providing correction of cylindrical details was determined. Residual tension necessary for correction of cylindrical details depends on an initial deflection, material and preparation rate. Tension of cylindrical details was defined depending on a type of the application of cross loadings. Bend tension for correction of a shaft at distributed loading is less, than tension from action of cross force. For correction of a shaft with a diameter of 10 mm, 200 mm long and an initial deflection of 0.5 mm it is necessary to create bend tension equal to about 370 MPa. An effective method of loading at cross correction of cylindrical details is the bend at influence of the distributed loading. The received extreme values of bend coefficients are from 5.3 to 5.5 for all cases of shaft rigidity at correction by cross bend at distributed loading with l/L relation equal to 0.8. The developed mathematical model gives quite reliable values of the residual tension providing correction of cylindrical details. The analytical dependence for determination of the size of general deflections and definition of an effective loading type can be recommended for practical use in production for achievement of precision accuracy of low-rigid details like shaft.

Improvement on Straightness of Micro-Motor Shaft Considering Stress Concentration Caused by the Grooves

Motor shaft is one of the most important parts of motor, which is widely used in industrial field. The straightness of the shaft has a potentially significant effect on motor performance, which is determined by the straightening process in the manufacturing process of the shaft. Considering the grooved characteristics on the micro-motor shaft and using the classical material mechanics principle, the stress and deformation models of the circular shaft with the grooves during the straightening process are established in this paper. By deriving the straighttening stroke-initial deflection model, an accurate and practical relationship between the straightening stroke and the initial deflection was provided. In order to verify the theoretical straightening model, some grooved shaft specimens are designed and manufactured for the straightening experiments. Through the simulation and experimental research, the straightening stroke-initial deflection model for the micro-motor shaft is compared and analyzed, and the correctness and feasibility of the model is verified.