Nonlinear contact problems for thin-walled elements of constructions

Some one-dimensional contact problems for plates and shells are considered for one-side contact with a rigid base. Contrary to analogous papers about the zone of contact, we use applied theories of contraction of Winkler type, which are obtained from equations of elasticity theory by asymptotic methods together with bending equations of thin-walled elements. The possibility of deviation of shells needs a definition of a contact zone in the process of solution of the problem from the condition of continuity of bending and its derivatives up to the second order inclusive. Some conclusions are made with respect to the optimal projects of reinforcement of shells taking into account their deviation.Translated from Dinamicheskie Sistemy, No. 8, pp. 40–45, 1989.     

Refined stability theory for sandwich shells with transversally stiff core. 2. Linearized equations of neutral equilibrium

Neutral equilibrium equations of the refined theory of stability for sandwich shells with a transversally stiff core are constructed and used for studying local mixed forms of stability loss (FSL), as well as admitting different variants of simplification, depending on the type of precritical state and realized FSL. The generalized Reissner variational principle used for deriving the stability equations allows us to refine transverse shear stresses in the core as compared to [1]. A method for a highly accurate definition of these stresses is proposed. Namely, after the integration of three-dimensional equilibrium equations over the transverse coordinate, the number of free constants and the number of static conditions to be satisfied are equalized according to the actual stress distribution across the thickness.Science and Technology Center for Study of Dynamics and Strength. Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 786–795, November–December, 1997.     

Effect of material properties on the stability of transversely isotropic shells with an elastic filler subjected to the action of mechanical loads and temperature

The effect of the low shear strength of the material (glass-reinforced plastic) on the stability of cylindrical shells with an elastic filler is investigated in relation to axial compression, external pressure, and heating. The equations of the thermoelastic problem of the theory of monotropic shells, constructed with allowance for the effect of tangential shearing stresses, are used in the calculations.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 903–907, September–October, 1970.     

Refined stability theory for sandwich shells with transversally stiff core. 1. Nonlinear equilibrium equations

A refined version of geometrically nonlinear relationships is proposed for the static thermoelastic response of sandwich shells with face sheets made of composite or homogeneous materials and a transversally stiff core. This theory has primary importance for studying mixed forms of buckling of the bearing sheets, which are mainly realized in the zones of a momentary stress-deformed state of the shell on the whole. An iteration procedure was developed for construction of the model. In the first step, assuming that the core is transversally soft, expressions are derived for the components of the displacement vector after integration of the three-dimensional equilibrium equations. In the second step, the tangential stresses are determined assuming a transversally stiff core to obtain the in-plane stresses and highly accurate transverse normal stresses. The proposed model admits a formal changeover to the model of a shell with a transversely soft core.Center for the Study of Dynamics and Stability. A. N. Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 513–524, July–August, 1996.     

Creep of a thermoplastic cylindrical shell under axisymmetric loading

The solution of the problem of creep of an axisymmetrically loaded thermoplastic cylindrical shell is considered. The strains and stresses for the zero-moment zone and with allowance for the edge effect are predicted on the basis of Kachanov's variational method using a computer. An algorithm is constructed for polyethylene and PVC shells at various values of the load. The analysis of the results obtained is illustrated by the calculation data for individual variants of the program.Leningrad Mozhaiskii Military Engineering Academy. Translated from Mekhanika Polimerov, No. 3, pp. 512–518, May–June, 1969.     

Analysis of the effect of transverse shear strains on the stability of multilayer cylindrical shells under external pressure

The effect of transverse shear strains on the critical pressure is investigated using the results of the solution obtained for the problem of the stability "in the small" of elastic multilayer cylindrical shells of regular structure with alternating light and stiff layers. Attention is drawn to the need to estimate the state of stress of the shells in the critical-load zone with the object of studying the desirability of taking the shear effect into account in the stability calculations. The results obtained can be used in calculating the stability of shells made from resin-based composites (glass-reinforced plastics, graphite-reinforced plastics, etc.). The numerical calculations were carried out using a computer.Translated from Mekhanika Polimerov, No. 6, pp. 1066–1070, November–December, 1973.     

Analysis of the transition zone in combined metal/reinforced-plastic shells

The bending stresses in the conical joint zone of cylindrical shells composed of two different materials are determined for the case of internal pressure. The effect of the length of the joint on these stresses is investigated using parameters typical of steel and glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 465–475, May–June, 1971.     

Refined stability theory for sandwich shells with transversally stiff core. 3. Simplest one-dimensional problems

The applicability and accuracy of stability equations of the refined theory for sandwich shells with a transversally stiff core proposed in [1] are investigated. The model problem of calculating the critical loads and stress fields in the core at mixed forms of the loss of stability is solved for an infinitely wide sandwich plate with an orthotropic core and composite load-carrying layers subjected to in-plane edge loads. The case of pure bending of the plate is considered in detail. The results obtained by variation of the physical-mechanical parameters are compared with the solutions of the three-dimensional theory for the core [2]. It is shown that the version of the refined theory [1] is more accurate than the other two-dimensional theories.For Pt. 2 see [1].Center for Study of Dynamics and Stability, Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 57–65, January–Feburary, 1998.     

Torsional stability of a glass-reinforced plastic cylindrical shell with an elastic core

The problem of the stability of a glass-reinforced plastic cylindrical shell with an elastic core subjected to twisting moments applied to the edges of the shell is considered. As in various other studies [4–6], the glass-reinforced plastic is treated as an elastically orthotropic material. The core is treated as an isotropic elastic cylinder, whose outer surface is bonded to the shell. Expressions for the critical stresses are obtained for an infinitely long shell and a shell of finite length.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1082–1086, November–December, 1970.     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

建筑用夹蕊板条的分析、数值和实验研究

由冷成型的薄壁钢面和刚性泡沫绝缘蕊子所组成的建筑用夹蕊板条,用来作为多功能建筑隔墙,日益普遍.本文总结了十多年来的研究工作,阐明了包括弯曲应力、挠度、弯曲折皱、轴向稳定、热应力以及振动在内的各种结构性能.研究中,采用了分析法(边界值法)、数值法(有限样条法、有限层法和有限棱柱体法等)以及实验法(全尺寸实物试验),写出了关键方程,并对各法所得结果进行了比较研究.     

Stresses in adhesive joints in cylindrical shells and panels

The stresses in adhesive joints in cylindrical shells and panels are determined for the general case of loading. The effects of joint length and the parameters of the adhesive, the shells, and the panels on the magnitude of these stresses are investigated.Aviation Technology Institute, Moscow. Translated from Mekhanika Polimerov, No. 6, No. 1093–1103, November–December, 1972.     

Optimization of cylindrical composite shells with regard to their critical mode of imperfections

This study deals with the optimum design of composite shells under external pressure with material strength and loss of stability according to the critical mode of imperfections taken as the failure criterion. The problem of optimum design is solved and the critical mode is obtained by nonlinear optimum programming for which the geometric and initial imperfection parameters are treated as variables. Numerical results are obtained for a cylindrical composite shell supported freely at its ends. The effect of shear forces between layers on the load-carrying capacity of the shell is also investigated.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 613–620, September–October, 1998.     

Multicycle fatigue resistance of brittle polymers

Conclusion A model of multicycle fatigue of polymers based on the hypothesis of self-simulation of the failure process was proposed and a method of predicting the durability was elaborated in the present study. It was found that in low-temperature conditions of self-heating, the crack is the basic cause of fatigue failure. A cyclic durability equation was obtained in the form of a modified time summation criterion for the stressed state in the failure zone in the vicinity of the apex of a fatigue crack. It was shown that in the case of brittle failure in multicycle fatigue, the maximum principal stresses which arise in the failure zone, one order of magnitude smaller than the size of the fatigue crack, are the criterion of failure.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 633–638, July–August, 1990.     

Influence of heating on the stability of fiberglass reinforced plastic shells during axial compression

Results are described of the experimental investigation of the patterns of change of carrying capacity and deformation of smooth thin-walled round cylindrical shells made from fiberglass reinforced plastic based on phenol-formaldehyde binder, loaded by an axial compressing force in a temperature field uniform with respect to the thickness of the wall and the surface. The experimental data are compared with calculated ones obtained according to the formulae of the theory of orthotropic shells. The influence of circumferential compressing stresses arising in the junction zone of the heated wall with less heated thicker parts at the edges (ribs) on the carrying capacity of the shells is evaluated.Professor N. E. Zhukovskii Central Aerodynamics Institute, Moscow Oblast. Translated from Mekhanika Polimerov, No. 5, pp. 838–845, September–October, 1972.     

On the theory of layered anisotropic cylindrical shells stiffened with ribs

The deformation, stability and vibration equations for anisotropic cylindrical shells stiffened with individual longitudinal and circumferential ribs are derived without introducing the hypothesis of nondeformable normals. The more general assumption adopted for layered materials (for example, glass-reinforced plastics) of a linear variation of the displacements over the thickness of the shell and the height of the ribs is used; in this case for the points of contact of the shell and the ribs after deformation the common normals form broken lines. The solution of the problem of the stability of a cylindrical shell stiffened with circumferential ribs is examined. For a shell with different, arbitrarily located ribs the problem is reduced to a homogeneous algebraic system of equations equal in number to three times the number of ribs.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 647–654, July–August, 1974.     

Temperature reversal of the reinforcing effect of fillers

A previous investigation [4] of the tear strength of filled systems based on SKS-85 butadiene-styrene copolymer over a broad temperature interval revealed a reversal of the reinforcing effect of fillers with a coefficient of thermal expansion different from that of the filled polymer. At Tg the strength of mixtures containing polymer fillers [Kapron (polycaprolactam) and cellophane powder] exceeds that of mixtures containing chalk and carbon black. The temperature reversal effect is attributed to the severe weakening of the adhesion of the polymer to the surface of the filler particles as a result of the concentration of shrinkage stresses in the polymer-filler contact zone. The presence of shrinkage stresses around the filler particles at Tg is qualitatively demonstrated on model systems using a photoelastic technique. Moreover, it is shown that the unbalance, and hence the residual stresses, in filled systems at temperatures below the glass transition temperature of the filled polymer is determined by the difference in the coefficients of thermal expansion.Moscow Technological Institute of the Meat and Dairy Industry. Translated from Mekhanika Polimerov, No. 4, pp. 579–583, July–August, 1969.     

Optimal position of a strut on a cylindrical shell

A solution is given for the problem of the optimal design of a rigid structure consisting of a spherical shell and two cylindrical shells linked by a strut. The volume of the structure is minimized under constraints on the maximal equivalent stresses in each of the shells and on the geometric parameters of the strut. Among the regulating parameters are the thickness of the shells, the geometric parameters of the strut, and the length of the first of the cylindrical shells. The problem is solved by the method of geometric programming.Translated from Matematicheskie Metody i Fiziko-Mekhanicheski Polya, No. 29, pp. 76–80, 1989.     

Optimization of reinforced cylindrical shells with nonuniform thickness

An optimum multilayer shell is designed whose stack of elementary layers has a nonuniform thickness. This optimization problem is solved numerically for the special cases of three-layer cylindrical shells with dynamic and static stability. The optimum variants of layer distribution in this model are compared with the optimum solutions in [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 298–303, March–April, 1976.     

Dynamics and optimization of cylindrical composite shells

The stability of cylindrical composite shells under dynamic external pressure is discussed. A criterion for determining the load-carrying capacity based on Malmeister's equation with respect to bending parts of deformation is proposed. Optimization of the shell mass relative to various structural parameters has been carried out as a nonlinear programming problem. Numerical results are given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 81–87, January–February, 1995.