Experimental and numerical investigation of PUR foam under dynamic loading

Various factors may subject buildings to shock which continues in their structure and is perceived by the people living in them as noticeable vibrations or noise. In this context, polyurethane (PUR) foams, which have been developed to isolate vibrations, have shown to be very effective in practical use. However, whereas static properties of open-cell structures have already been determined numerically in good agreement to experimental results, cf. [1], there are hardly any investigations on the dynamical properties characterizing acoustic damping. In order to validate experimental measurements of eigenfrequencies for different PUR foam specimen we present here a strategy to reproduce the foam behavior numerically. In doing so, PUR foams are modeled using a three dimensional Voronoi-tessellation technique. The resulting Voronoi cells correspond to open pores and are scaled in such a way that the volume ratio between the pores and material matches the given PUR foam. For finite element analysis the connections between the cells are modeled as beam elements, the beam shape follows Bezièr curves. The generated model is analyzed with a finite element software and the dynamical parameters are determined. The numerical results are compared to our experimental data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian planning of step‐stress accelerated degradation tests under various optimality criteria

Step‐stress accelerated degradation testing (SSADT) has become a common approach to predicting lifetime for highly reliable products that are unlikely to fail in a reasonable time under use conditions or even elevated stress conditions. In literature, the planning of SSADT has been widely investigated for stochastic degradation processes, such as Wiener processes and gamma processes. In this paper, we model the optimal SSADT planning problem from a Bayesian perspective and optimize test plans by determining both stress levels and the allocation of inspections. Large‐sample approximation is used to derive the asymptotic Bayesian utility functions under 3 planning criteria. A revisited LED lamp example is presented to illustrate our method. The comparison with optimal plans from previous studies demonstrates the necessity of considering the stress levels and inspection allocations simultaneously.     

The effect of various boundary conditions on the nonlinear dynamics of slightly curved pipes under thermal loading

Slightly curved pipes are prevalent in many industries including oil installations especially in the Delta regions of the world. The aim of this paper therefore is to investigate the nonlinear dynamics of these pipes conveying fluids under the influence of thermal loadings. These investigations are for three different boundary conditions, namely simply supported ends, clamped-clamped ends and clamped-simply supported ends respectively. To derive the governing equations, small strains of initial curvature, temperature, tension, pressure, longitudinal and transverse strains are considered. Furthermore, strains due to curvature change during bending which are hitherto neglected in most of the previous works on slightly curved pipes are added. The strain due to initial curvature accounts for the geometric imperfection. Two coupled nonlinear differential equations in both longitudinal and transverse directions are obtained and solved using eigenfunction expansion method, up to four modes. Linear natural frequencies were obtained, and is shown that for various boundary conditions, it increases as the initial curvature increases and decreases as thermal loading increases. The nonlinear results obtained show that the amplitude of the pipe motion becomes larger due to the obvious effect of thermal loading. Nonlinear results for both vanishing and non-vanishing longitudinal displacements are presented.     

Collapse of attractors for ODEs under small random perturbations

This paper concerns comparisons between attractors for random dynamical systems and their corresponding noiseless systems. It is shown that if a random dynamical system has negative time trajectories that are transient or explode with probability one, then the random attractor cannot contain any open set. The result applies to any Polish space and when applied to autonomous stochastic differential equations with additive noise requires only a mild dissipation of the drift. Additionally, following observations from numerical simulations in a previous paper, analytical results are presented proving that the random global attractors for a class of gradient-like stochastic differential equations consist of a single random point. Comparison with the noiseless system reveals that arbitrarily small non-degenerate additive white noise causes the deterministic global attractor, which may have non-zero dimension, to ‘collapse’. Unlike existing results of this type, no order preserving property is necessary.      

Deformation of polymers under friction loading

A study has been made of the laws of distribution of elastic and residual deformations in the surface layers of polymers subjected to friction. The dependence of these deformations on normal pressure, sliding velocity, and duration of loading has been determined. A relation between deformation and antifriction characteristics has been established, and the relative effect of normal and tangential loads on surface-layer deformation determined.Mekhanika Polimerov, Vol. 3, No. 3, pp. 539–543, 1967     

Optimal shape analysis of a column structure under various loading conditions by using differential transform method (DTM)

The effects of loading on the optimal shape of an Euler-Bernoulli column is investigated by considering four loading conditions which are mainly classified as eccentric compressive and follower type. The governing equations obtained from the structural stability condition of the column are used as a constraint to determine the minimum value of the volume by applying Hamilton principle. In the preceding task, the analysis is presented in step-by-step manner. The calculations are carried out by using differential transform method (DTM) which is a seminumerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the non-linear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The optimal distribution of cross-sectional area along column-length is obtained. Then, the volume of such column is calculated and compared to that of the uniform column which is also stable under given loading. The results obtained revealed out that DTM is a quite powerful solution technique for optimal shape analysis of a column structure.     

Controlled Markov set-chains under average criteria

In this paper, applying an interval arithmetic analysis, we consider the average case of controlled Markov set-chains, whose process allows for fluctuating transition matrices at each step in time. We introduce a v-step contractive property for the average case, under which a Pareto optimal periodic policy is characterized as a maximal solution of optimality equation. Also, in the class of stationary policies, the behavior of the expected reward over T-horizon as T approaches ∞ is investigated and the left- and right-hand side optimality equations are given, by which a Pareto optimal stationary policy is found. As a numerical example, the Taxicab problem is considered.     

Volume strains of polymers under short-time loading

The effect of the magnitude of the stress, the type of stress, and the previous loading history on the nonlinear deformation characteristics, the lateral strain coefficient, and the volume strains of two crystalline polymers has been investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 828–833, September–October, 1974.     

Experimental study of polyethylene under simple loading

The results are presented of experiments on thin-walled tubular samples of high pressure polyethylene with simple deformation at different strain rates. At constant strain rate intensity a unified curve was shown to exist for the stress intensity _I versus the strain intensity e_I.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 5, pp. 820–822, September–October, 1973.     

Lifetime of amorphous polymers under intermittent loading

The lifetimes of two types of amorphous polymers (polyvinyl chloride and plasticized epoxy resin) under intermittent loading have been investigated. It is established that the lifetime, determined without allowance for recovery time, is less than that under constant load. Under periodic loading at constant stress the lifetime varies with the loading regime. For each of the investigated polymers a lifetime minimum is observed at a certain duration of the loading and recovery periods.Higher Chemical Technology Institute, Sofia. Translated from Mikhanika Polimerov, No. 5, pp. 912–916, September–October, 1971.     

Strength of reinforced plastics under static loading

The question of the static fatigue of reinforced plastics is considered for plane stress. Relations that predict the static fatigue are given for very simple types of loading. Experimental data are presented for thin-walled tubes of SVAM (5:1) glass-reinforced plastic subjected to long-time tests at constant internal pressure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 265–273, March–April, 1969.     

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.     

Experimental study of polyethylene under complex loading

Experiments have been carried out on thin-walled tubular samples of high pressure polyethylene for strain paths having the form of a two-section broken line. The validity of the isotropy postulate is demonstrated and the vector and scalar properties of the material are studied qualitatively.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 10–17, January–February, 1974.     

External circular crack under arbitrary shear loading

An exact closed form solution in terms of elementary functions has been obtained to the governing integral equation of an external circular crack in a transversely isotropic elastic body. The crack is subjected to arbitrary tangential loading applied antisymmetrically to its faces. The recently discovered method of continuity solutions was used here. The solution to the governing integral equation gives the direct relationship between the tangential displacements of the crack faces and the applied loading. Now a complete solution to the problem, with formulae for the field of all stresses and displacements, is possible.     

Materials with graded coating under transverse loading

In the present paper 3-D elastic deformation of a material with functionally graded coating subjected to mechanical loading is investigated. Comparative study of graded versus homogeneous coating is conducted to examine the effect of the stiffness gradient in the coating on stress and displacement fields in the material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Viscoelastic-viscoplastic-damage modeling of thermoplastics under long-term cyclic loading

Thermoplastics tend to creep under mechanical loads and recover deformation during unloading. A viscoelastic-viscoplastic-damage model is presented to accommodate the behavior of a thermoplastic under cyclic loading-unloading. Finite element simulations may be computationally expensive in case of many loading cycles. A cycle jump method is proposed to mitigate parts of the cost. It can efficiently approximate large parts of the cyclic calculations by extrapolating internal variables over several cycles at once. Hence, only a fraction of the original computational effort remains. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)