Deformation of cylindrical composite shells under combined dynamic loading

Conclusions A procedure has been shown for calculating the stress-strain state of cylindrical multilayer shells made from composite materials under the combined action of dynamic axial compression and dynamic external pressure, as well as with different variants of combined loading with static and dynamic forces. An investigation has been made of the effect on the mode of the buckled shell surface of the ratio of the application rate of dynamic loads; ranges of loading rates have been established in which stresses predominate caused either by axial compression or external pressure. It has been shown that, as a result of preliminary static loading, a marked change occurs in the initial imperfections of the shell mode which affects subsequent dynamic buckling. To calculate the time when the first defect occurs and its location in the shell body, a procedure has been devised for layer-by-layer strength analysis employing a tensor-polynomial criterion. It was demonstrated that the level of preliminary static loading noticeably affects the time until the first failure of the layer, not only a reduction of this time being possible with an increase in the static loads, but also an increase in it.We should also point out the work in [10] where it is shown that it is possible to weaken the susceptibility of the shell to initial imperfections when internal pressure is applied.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 461–473, May–June, 1981.     

Dynamic stability of axisymmetrically heated glass-reinforced plastic cylindrical shells bonded to elastic cylinders

The dynamic stability of glass-reinforced plastic shells subjected to the action of a longitudinal pulsating force and an external, uniformly distributed load is examined. The shells are orthotropic, and their elastic properties are temperature-dependent and vary over the thickness of the wall. It is assumed that the elastic cylinder forms a Winkler foundation. Three boundary conditions are investigated.Moscow Institute of Chemical-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 331–337, March–April, 1972.     

Validation of a Structural Optimization Algorithm Transforming Dynamic Loads into Equivalent Static Loads

Generally, structural optimization is carried out based on external static loads. However, all forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is almost impossible in a large-scale problem. Therefore, in engineering practice, dynamic loads are often transformed into static loads via dynamic factors, design codes, and so on. Recently, a systematic transformation of dynamic loads into equivalent static loads has been proposed in Refs. 1–3. Equivalent static loads are made to generate at each time step the same displacement field as the one generated by the dynamic loads. In this research, it is verified that the solution obtained via the algorithm of Refs. 1–3 satisfies the Karush–Kuhn–Tucker necessary conditions. Application of the algorithm is discussed.     

Methods of taking into account the nonlinearity of the deformation properties of the material in calculating thick-walled composite rings

The results of an investigation of the deformation properties of unidirectional composites are presented, and engineering models which take into account the effect of the nonlinearity of the properties in the radial direction on the state of stress of rings under pressure are proposed. The relations obtained are checked theoretically — by means of a refined calculation based on the nonlinear theory of elasticity — and experimentally — by loading rings with internal and external pressure by means of rubber cuffs in specially designed apparatus.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 73–84, January–February, 1976.     

Acoustic measurements in rubberlike polymers during compressive deformation

Problems associated with the method of measurement of acoustical properties of viscoelastic materials and the influence of various external factors (temperature, pressure) on these materials have been examined. The results of measurements of propagation speeds and damping coefficients of waves of the sonic and ultrasonic regions in resins are given for discrete excitation frequencies and during simultaneous static action on the specimen. It is shown that uniaxial compression of the resin results in the appearance of dispersion of the dynamic elastic modulus. A possible explanation of this phenomenon is suggested.Dnepropetrovsk Civil Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 149–156, January–February, 1974.     

Dynamic Robust Output Min–Max Control for Discrete Uncertain Systems

Min–max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min–max control is a static state feedback law. Recently, the applicability conditions of discrete static min–max control through the output have been derived. In this paper, the results for output static min–max control are further extended to a class of output dynamic min–max controllers, and a general parametrization of all such controllers is derived. The dynamic output min–max control is shown to exist in many circumstances under which the output static min–max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min–max controllers, constructed from an asymptotic observer which is insensitive to uncertainties and a state min–max control, is derived. The latter is shown to be a particular case of the dynamic min–max control when the nominal system has no zeros at the origin. In the case where the insensitive observer exists, it is shown that the observer-controller has the same stability properties as those of the full state feedback min–max control.     

Minimizing the mass of cylindrical shells formed from a composite material with an elastic filler and designed for strength and stability under a combined loading

The mass of a multilayer cylindrical shell, formed from a composite material with an elastic filler and designed for strength and stability under the combined action of axial compression and external pressure, is minimized. The problem is formulated as one of nonlinear programming and is solved by Rossen's method of projection gradients. The strength of the material is established from analysis of the strength of the layers making up the entire bundle. Failure of an individual layer is determined from Malmeister's criterion. The structure of a shell with different external loads and the dependence of minimal mass on the stiffness of the filler and on the volume coefficient of reinforcement are investigated in numerous examples.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. K. Preikshas Shyaulyaisk Pedagogical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 289–297, 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.     

Determination of the elastic and damping properties of the human femur in bending

The results of an experimental investigation of the deflection of the human femur subjected to a bending moment are presented. The existence of two principal bending planes is established. The equivalent flexural rigidity of the dry bone is calculated for both static and dynamic loading. It is found that the human femur has a nonlinear elastic characteristic. The stiffness and damping properties obtained in static and dynamic testing are compared.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 642–646, July–August, 1975.     

State of stress deformation of an orthotropic fiberglass shell in consideration of the creep of the material

Based on Volterra's principle we analyzed the axisymmetrical curvature of cylindrical orthotropic shells under the effect of sustained external pressure in consideration of the creep due to interlaminar shift. To solve the viscosity-elasticity problem, the known elastic solution is approximated by means of simple analytical dependences, taking the lateral shifts into account. Numerical examples are presented.Translated from Mekhanika Polimerov, No. 3, pp. 552–555, May–June, 1970.     

Longitudinal vibrations of a composite isotropic plate

Approximate integration of the longitudinal vibrations equations for composite plates is considered. A numerical investigation is performed of the potential energy distribution in a two-layered ring when a pulsating pressure acts on the inner contour.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 63–67, 1989.     

Viscous-elastic properties of amorphous polymers used in the polarization-optical method for investigation of stresses

The present article gives the results of an investigation of the mechanical properties of certain optically sensitive polymers under static and dynamic loading. It is shown that the Kelvin-Voight model can be used to describe the behavior of the materials investigated over limited time intervals corresponding to the duration of static or dynamic experiments.B. E. Vedeneev All-Union Scientific-Research Institute of Hydraulic Engineering, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 585–596, July–August, 1972.     

Large deflections and rigidity of a long cylindrical orthotropic glass-plastic panel subjected to intermittent-uniform loads

Large deflections and the stability of a long slanting orthotropic cylindrical panel, subjected to an external pressure uniformly distributed over a section of the panel width, are discussed. Relationships are used, taking into account lateral-shift deformation and normal stress _z. A closed-loop solution is obtained by means of generalized functions. A numerical evaluation has been made to assess the error of Kirchhoff's hypothesis. Similar solutions, taking into account the lateral-shift deformation are presented in [4, 5] for cases involving continuous uniform pressure and local linear loads.Kazan Physicotechnic Institute, Academy of Sciences of the USSR. Translated from Mekhanika Polimerov, No. 5, pp. 829–837, September–October, 1972.     

Boundary-value problem of thermoelasticity in displacements for an elongated spheroid

The static problem for an elongated spheroid with the temperature distribution and the displacement vector given on its surface is formulated and an exact solution is obtained. The internal and external problems are solved for the spheroid.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 81–90, 1988.     

Dynamic properties of wing panels made of composite materials

The dynamic characteristics of an elastic wing panel made of composite material are investigated in relation to the transient processes in a gas flow. The problem is solved using the geometrically nonlinear equations of shallow orthotropic shells and the numerical methods of linearized nonsteady aerodynamics. The displacements are determined by a finite-difference method and the aerodynamic load intensity by means of a model of a thin lifting surface. The numerical results are presented in the form of graphs reflecting the laws of deformation of the middle surface of the panel and pressure distribution and their development with time. Curves characterizing the motion of individual points in relation to the parameters reflecting the anisotropic properties of the panel are also constructed.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 662–669, July–August, 1974.     

Dispersion of the mechanical characteristics of plastics at various temperatures

The results of an investigation of the dispersion (standard deviation s and coefficient of variation V) of the static and dynamic strengths of plastics are described. The effect of temperature, state of stress, and type of plastic on the dispersion characteristics is considered.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 29–34, January–February, 1970.     

Reasons for the lowering of the lifetime of polymers under cyclic loading

A model is proposed which explains the lowering of the lifetime of polymers on transition from static to cyclic loading by the interaction of local stresses from an external load with residual stresses which arose after preceding loading cycles. The results predicted on the basis of the model have been checked experimentally on polymethyl methacrylate, and a good agreement has been shown.M. I. Kalinin Leningrad Polytechnic Institute. Translated from Mekhanika Polimerov, No. 2, pp. 279–283, March–April, 1976.     

An experimental study of the deformation of multilayer cylindrical shells

Experimental results are presented on the deformation of two-layer and four-layer reinforced shells subject to static loading. The strains on the outside and inside surfaces are unequal at points remote from the region of the edge effect when the shell is subject to an internal pressure and an axial force.P. I. Baranov Central Institute for Aviation Engine Design. Translated from Mekhanika Polimerov, No. 5, pp. 943–944, September–October, 1973.     

Numerical Analysis of the Synchronization of Coupled Chemical Oscillators

A reaction–diffusion model describing a system of coupled oscillators is constructed and investigated. The oscillators in this study are chemical oscillators that represent an oscillatory heterogeneous catalytic reaction in a granular catalyst layer. The oscillators are arranged serially in the reagent stream and are coupled through the gaseous phase. The dynamic behavior of the system is investigated as a function of the main external parameter — the partial pressure of one of the reagents in the gaseous phase. Existence regions of regular and chaotic oscillations are identified. Synchronization conditions are established for the oscillations in such a chain of coupled chemical oscillators.     

Optimal winding of filament-wound reinforced plastic shells designed to resist buckling under external pressure or axial compression

The optimal method of winding the reinforcement of thin cylindrical shells subjected to external pressure or axial loading is investigated. Various types of winding — normal, simple oblique, crossed, and isotropic — are considered. An approximate formula is obtained for the critical external pressure. This formula is used to analyze the possibility of raising the critical load by adopting oblique winding. In the case of axial compression different buckling modes are examined and the optimal winding determined.Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 864–875, September–October, 1968.