Shapes of a square Kirchhoff plate with a clamped edge are obtained and analyzed, before and after losing stability in the case of a compound bending (uniform transverse loading in combination with edge compressive loading), as well as equilibrium forms and critical loadings only with clamping in the plate’s surface. Hyperbolic trigonometric series are used for solving. It was established that transverse loading causing small deformations does not affect the plate’s stability. The range of the critical state corresponds with an unlimited increase in bends of interior points of a plate. As critical loading, we suggest taking the one at which the bends at the plate’s center tend to infinity the most rapidly. As balanced loading, we suggest taking the one at which the plate acquires a new stable equilibrium form. A range of critical and balanced loadings of a square plate with a clamped edge was presented. The corresponding 3D forms of supercritical equilibrium of the given plate were obtained. A comparison with the results of other authors is given.

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The issue of determining the reliability of the hulls of inland and river-sea-going vessels after a known number of years of operation under given condition is considered. It is accepted that fault detection of a ship’s hull is a survey, measurement and evaluation of defects in each element of the ship’s hull in order to establish the methods and scope of repairs that ensure its reliable operation until the next regular survey under specified operating conditions. It is shown that the volume of residual thicknesses can be significantly reduced using the statistical data on wear rates presented in the Rules of the Russian River Register. At the same time, the reduction in the scope of measuring the parameters of defects retains the probability of detecting all defects of the hull elements to the level of 0.95, and the probability of failure-free operation of the hull until the next survey, after the elimination of the identified defects will be at least 0.95. A form of table for processing the values of the residual thicknesses of all elements in the inspection report and instructions for filling it out are given. Explanations for using the results of measurements and calculations at determining the technical condition of certain elements in the group and the ship’s hull as a whole are given. The last column of the table indicates the method of eliminating the defect of an element and groups of elements, and in the conclusion of the inspection report, the method of repair and its scope for the entire hull of the ship providing a suitable assessment of the condition after repair are indicated. The main advantage of this paper, in difference from the previous studies of the authors in this area, is that user-friendly (the designer of the defect report tables) nomograms, which allow you to reduce the number of measurements of the residual thicknesses of hull structure elements in the online mode, have been created. The performed study, allowing you to reduce the number of measurements while guaranteeing the reliable operation of the ship’s hull, will let the shipowner to reduce the cost of repair work by reducing the number of days of ship standing on the slipway (in the dock). In addition, the ship repair company will be able to free up its production facilities for the purpose of their subsequent loading with other ship repair or shipbuilding orders, which will increase the efficiency of their activities.

The required level of reliability of modern forced engines can be provided only on condition of their high-quality design, which is based on the strong calculation of the most loaded parts, which include parts crank mechanism. The article shows the importance of kinematic and dynamic analysis of crank mechanism in the process of designing an internal combustion engine and their role in ensuring the reliability of the engine, describes ways to solve the problem of kinematic and dynamic analysis of crank mechanism. The comparative analysis of static and dynamic models of crank-crank mechanisms is given. Calculation schemes, the sequence of kinematic and dynamic analysis of the mechanism, the system of equations, allowing to determine the forces acting in the crank mechanism, are presented. On the basis of the vector diagrams of loads on the crankshaft connecting rod presented in the article the expediency of application of dynamic models of crank mechanisms with SIM-metric and asymmetric connecting rods for analytical calculations of piston engines is proved. The results of analytical calculations of the dynamics of crank mechanism of four-stroke diesel supercharged size 13/14 are presented. It is shown that with the modern development of computer technology and software, the complexity of such calculations practically does not increase, and the results are close to those obtained by numerical analysis of dynamics using three-dimensional solid-state models. Recommendations on the use of "light" software products Ltd, which allows to perform kinematic and dynamic analysis of mechanisms in the educational Pro-process and solution design tasks. The results presented in the article prove the appropriateness of using the coordinate method to determine the kinematic parameters of the third replacement weight of the connecting rod and the ability to ensure the required accuracy of the calculations performed on the basis of the analysis of rod systems.

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