Conditions for guaranteed destruction and explosion resistance of beam structural elements in the event of an explosion in water

По данным проведенных ранее исследований авторов найдены условия гарантированного разрушения и гарантированной взрывостойкости балки, свободно лежащей на недеформируемых опорах в воде. Импульсная динамическая нагрузка создана взрывом сосредоточенного заряда конденсированного взрывчатого вещества (ВВ), расположенного в воде на фиксированном расстоянии от балки. Под разрушением понимается потеря несущей способности балки вследствие возникновения в ней пластических зон (шарниров), трещин, разделений на фрагменты. Использован обобщенный на действия динамической нагрузки критерий разрушения, основанный на достижении максимальным изгибающим моментом критических значений. According to the data of the authors’ earlier studies, the conditions of guaranteed destruction and guaranteed explosion resistance of a beam freely lying on non-deformable supports in water were found. The impulse dynamic load is created by the explosion of a concentrated charge of a condensed explosive (HE) located in water at a fixed distance from the beam. Destruction is understood as the loss of the bearing capacity of the beam due to the appearance of plastic zones (hinges), cracks, and fragmentation in it. The criterion of destruction generalized to the action of dynamic load is used, based on the achievement of critical values by the maximum bending moment.

Elastic-Plastic Problem for a Stringer Plate with a Circular Hole

When calculating the strength of machines, structures and buildings with technological holes, it is important to take into account the plastic zones that emerge around the holes. However, the unknown shape and size of the plastic zone complicate the solution of elastic-plastic problems. This paper gives an approximate method and solution of the plane elastic-plastic problem of the distribution of stresses in a thin plate, reinforced with a regular system of stiffeners (stringers). The stringer plate under consideration has a circular hole, which is completely surrounded by the zone of plastic deformation. At infinity, the plate is subjected to a uniform tension along the stiffeners. A constant normal load is applied to the contour of the hole. The plate and stringer materials are assumed to be isotropic. The loading conditions are assumed to be quasi-static. It is assumed that the plate is in the plane-stressed state. Taken as the plasticity condition in the plastic zone is the Tresca-Saint-Venant plasticity condition. Methods of perturbation theory, analytic function theory, and the least squares method are used. The solution to the stated elastic-plastic problem consists of two stages. At the first stage, the stress-strain state for the elastic zone is found, and then the unknown interface between the elastic and plastic zones is determined using the least squares method. A closed system of algebraic equations has been constructed in each approximation, the numerical solution of which makes it possible to study the stress-strain state of a stringer plate, with the hole entirely surrounded by the plastic zone, as well as to determine the magnitudes of the concentrated forces that replace the action of the stringers. The interface between the elastic and plastic deformations has been found. The presented solution technique can be developed to solve other elastic-plastic problems. The solution obtained in this paper makes it possible to consider elastic-plastic problems for a stringer plate with other plasticity criteria.

Energy release induced rockbursts based on butterfly-shaped plastic zones in roadways of coal reservoirs

According to the theories of rockburst based on butterfly-shaped plastic zones, a plane strain mechanical model was established for stress distribution around the holes in homogeneous elastoplastic media. Based on the Mohr-Coulomb yield criterion and the generalized form of Hooke’s law, the equation for the elastic strain-energy density of units at a 3D stress state was deduced. On this basis, the energy absorption and release in rocks surrounding a roadway during the evolution thereof in a coal reservoir tend to rock bursting were quantified. Through Flac3D 5.0 numerical simulation software, the energy released from a homogeneous circular roadway at different development states of plastic zones was investigated. By investigating conditions at the 21141 working face in Qianqiu Coal Mine, Henan Province, China, subjected to rockburst, a numerical model was established to calculate the energy released by a rockburst working face. The calculated results approximated the data monitored at the outburst site, with the same energy level recorded. The theoretical calculation for energy release from the rock surrounding a roadway is expected to reference engineering practice.

Theoretical Analysis on Distribution Pattern of Plastic Zone in Surrounding Rock of High-Gas-Coal Roadway

The formation and expansion of the plastic zone is always accompanied by the deformation and failure of the roadway-surrounding rock. Based on elastoplastic theory, this paper considers the gas pressure parameters and uses the Mohr–Coulomb strength criterion to derive the implicit equation of the plastic zone boundary in the rock surrounding gas-coal roadways. The distribution characteristics of the plastic zone of gas-coal roadway-surrounding rock are studied, and the sensitivity to the gas pressure, cohesion, internal friction angle, and support strength of the roadway free face on the plastic zone of the surrounding rock is analyzed. The research results show that the plastic zone of the surrounding rock has four distribution patterns: circular, elliptical, rounded rectangle, and butterfly. Additionally, the lateral pressure coefficient, gas pressure, cohesion, and internal friction angle are found to jointly determine the distribution and range of the plastic zone. However, the support strength of the roadway free face does not change the distribution of the plastic zone but only affects its range. The circular and elliptical plastic zones are less sensitive to gas pressure, cohesion, and internal friction angle, whereas butterfly-shaped plastic zones are highly sensitive to these factors. The main manifestation of this sensitivity is that the four butterfly leaves degenerate rapidly with any decrease in the gas pressure or increase in the cohesion and internal friction angle. Larger butterfly leaves are prone to faster degeneration. The research results presented in this paper have important theoretical guiding significance and engineering application value for the design of high-gas-coal roadway support and gas drilling.

Plastic Limit Analysis Using the Simplified Theory of Plastic Zones

The simplified theory of plastic zones (STPZ) was mainly developed to determine strain ranges and accumulated strains in the state of shakedown at cyclic loading between prescribed levels of loading. Kinematic hardening is an indispensable feature of the STPZ. The plastic limit load, however, is defined for monotonic loading and elastic–plastic material behavior without hardening. Simply assigning a zero value or a numerically very low value of the tangent modulus when applying the STPZ is generally not possible due to arising numerical instabilities. It is, therefore, not immediately obvious how the STPZ can be used to determine the maximum load level that can be applied to a structure without developing a kinematic mechanism. This paper describes the theory and the analysis steps required and provides some illustrative examples. Typically, between one and three linear elastic analyses and some local calculations are required to provide either the exact value or at least a reasonable estimate of a range of the plastic limit load, as well as of the associated stress and strain fields and displacements that are not provided by classical limit analysis.