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.     

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.     

A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing – both dynamic and static – is beneficial and assess the value of the dynamic policy.     

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.     

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.     

Static and dynamic elasticity of some thermotropic liquid-crystalline copolyesters

Two series of thermotropic liquid crystalline copolyesters were studied in static and dynamic tensile deformation. Static loading generally does not lead to any peculiar phenomena: the stress-strain diagrams are linear or convex, except one copolyester fibre, the stress-strain diagram of which is concave at high temperatures. On the contrary, in dynamic loading the elasticity modulus increased during deformation for all the samples investigated. So it can be assumed that formation of a more rigid and stable structure takes place due to the dynamic deformation.Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 704–709, September–October, 1997.     

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.     

Evolution of the Stress–Strain State of a Three-Dimensional Plate Weakened by a Central Crack under Impulsive Tension

A method is developed to describe the formation of the stress–strain state in the vicinity of the tip of a stationary crack in a three-dimensional plate under dynamic loading. The energy model used to describe the formation of the stress concentration zone around the crack tip is modified to take into account the transient character of the loading process and the influence of the free surfaces of the plate on the stress–strain state of the central part of the sample. The method is useful for describing static and dynamic brittle fracture from a unified point of view.     

Acoustic creep of glass-fiber-reinforced plastic

A method of investigating acoustic creep of polymer composites developing under the effect of static tensile forces and small amplitudes of dynamic stresses with a frequency of 20 kHz acting coaxially with the static loads is considered. Results of investigating acoustic creep of glass-fabric-reinforced plastic are presented. It is shown that the presence of a high-frequency stress component regularly accelerates relaxation processes and reduces considerably the deformation resistance of the material. Generalized curves simulating the long-time static creep of reinforced plastic are constructed by the method of temperature-time, stress-time, and vibration-time analogies. The results of prediction are compared with the control experiment.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 397–404, May–June, 1973.     

Mechanical behavior of cylindrical laminated plastic shells

The static and dynamic behavior of a cylindrical glass-reinforced plastic shell with an open cross section under long-term loading and unloading has been experimentally and theoretically investigated. The experimental results are compared with the theoretical data obtained using a geometrically nonlinear theory based on the Kirchhoff hypothesis. For calculation purposes the glass-reinforced plastic is assumed to be a homogeneous orthotropic linearly elastic material.Building Research Institute, Prague. Translated from Mekhanika Polimerov, No. 1, pp. 110–115, January–February, 1976.     

Nonlinear parametric vibrations of cylindrical shells made from composite materials

The dynamic properties of a hinged shell made from a composite material and subjected to combined loads are investigated by means of an orthotropic model. The problem is solved by means of the geometrically nonlinear dynamic equations of the theory of sloping shells, set up on the basis of the Kirchhoff-Love hypothesis. Various cases of loading are considered, i.e., the combined action of a longitudinal pulsating load and an external static pressure and also of a pulsating external pressure and a static axial compression. The wave processes at the middle surface are not taken into account. The system of resolvents is obtained by consecutive application of the variation and averaging methods. The results of the calculations are presented graphically and are analyzed in detail.Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 531–539, May–June, 1973.     

Vibrocreep of polymeric materials

Experimental data on the static and vibrational creep of rigid porous polyurethane are used in an analysis of the time dependence of the vibrocreep coefficient and its dependence on the derivative of the stresses created by the incremental vibrational load and the static stress level. It is shown that at a constant value of the static stresses and the incremental vibrational load the vibrocreep coefficient decreases with time and in long-time vibrocreep tends to unity. As the parameter characterizing the vibrocreep coefficient for a given moment of time it is possible to employ the amplitude of the dynamic stress rate. The dependence proposed for describing the vibrocreep coefficient curves satisfactorily describes the experimental data. It is shown that the value of the vibrocreep coefficient does not depend on the static stress level (up to 0.5 of the short-time strength).For Communication 5, see [9].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 643–647, July–August, 1970.     

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.     

Static and dynamic properties of glass-reinforced plastics

The effect of the number of reinforcing layers in glass-reinforced plastics on the static and dynamic E-and G-moduli is analyzed. The experimentally obtained data are compared with theoretical calculations.Mekhanika Polimerov, Vol. 1, No. 3, pp. 87–92, 1965     

Analogies and the modeling of composites

On the basis of the solution of a series of problems of the distribution of static and dynamic fields of various physical kinds in the microstructure of composite materials reinforced with dispersed particles or fibers analogies are established between the stress, displacement, temperature, electromagnetic, and other fields subject to certain similarity criteria imposed on the properties of the components.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1028–1037, November–December, 1969.     

Dynamic properties of certain unvulcanized rubbers in the high-elastic and fluid states

The dynamic properties of a series of unvulcanized rubbers (cis-polybutadienes, Na-polybutadiene, cis-polyisoprene, butyl rubber, polyisobutylene, and ethylene-propylene copolymer) have been investigated in a low-frequency dynamic testing machine and a frequency rheometer on the frequency range from 5 · 10^–2 to 4.5 · 10³ Hz at temperatures of 25 and 60°C. At these temperatures the mechanical loss factor is the most sensitive criterion of transitions from one physical state of the polymer to another. For all the specimens investigated on the experimental range of angular frequencies the modulus of the complex dynamic viscosity and the effective viscosity determined under static conditions coincide, assuming the equivalence of angular frequencies and shear rates.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 698–703, July–August, 1969.     

Investigation of the mechanical properties of acrylics under conditions of creep,stress relaxation,and harmonic vibration

The dynamic and static (creep, stress relaxation) mechanical properties of various acrylics have been investigated. A relation is established between the structure and the macroscopic mechanical properties. The previous thermal history and the characteristics of the state of stress are shown to affect the nature of the relaxation processes and the mechanical properties of the acrylics. Generalized stress relaxation curves are constructed. The mechanical glass transition temperatures of the acrylics investigated are determined.Lenin Moscow State Pedagogic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 157–159, January–February, 1973.     

Comparative performance of living and dead bony tissue under static and dynamic loading

The dependence of the mechanical properties of bony tissue on different conditions of storing the samples has been studied. As the performance characteristic under static loading we used the ultimate compressive strength of the bony tissue, and under dynamic loading we used the specific impact strength.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.I. M. Sechenov First Moscow Medical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 647–649, July–August, 1975.     

Investigation of the dynamic behavior of optically active polymer materials

In view of the importance of the dynamic behavior of optically active plastics in connection with their use in model studies of the earthquake resistance of hydraulic engineering structures by the photoelastic method, the static and dynamic characteristics of the commonest types of photoelastic plastics are presented using published data and measurements made in the Photoelasticity Laboratory of the Vedeneev All-Union Scientific Research Institute of Hydroengineering, Leningrad.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1117–1124, 1967     

Behavior of rigid plastics under cyclic loading

Research progress on the dynamic fatigue of plastics is briefly reviewed. Attention is concentrated on the problems of damage accumulation and self-heating. The effect of various factors on the fatigue of plastics is considered. The possibility of predicting the cyclic life-time from the results of long-time static strength tests is examined. The prospects for the construction of a theory of fatigue strength in complex states of stress are weighed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 97–107, January–February, 1969.