Sensitivity analysis of multi-storey building due to blast loading

In this paper the vibration problems of multi-storey column-slab buildings are considered. Vibrations are caused by the explosion in the building and destruction of some construction elements. The influence of sudden loss of these elements as well as the explosion pressure are taken into account. In particular, the influence of destruction location on the building vibrations is examined. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Longitudinal track-structure interaction on railway bridges

In this paper, a computational model for the correct simulation of an arbitrary sequence of longitudinal loading cases on coupled track-bridge systems is proposed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wave propagation in finite structures due to transient loading with application to pyroshock simulation

Pyroshocks are transient motions of a structure caused by e.g. explosion of ordnance devices. Prior to their launching space modules have to be tested for fulfillment of strict requirements concerning the expected acceleration during a space mission. Since, in practical applications, this is still based on empirical knowledge and time consuming testing procedures, an analytical way to face this problem is the modelling of a pyroshock test device for the simulation of mechanical impacts on plates carrying the module to be tested. From the mechanical point of view, the problem is described by the wave propagation in a disk or a plate carrying a point mass and being exposed to a punctual load caused by the impact of a sphere. The displacement field is calculated semi-analytically by the use of a modal approach, HERTZian contact theory as well as the GALERKIN procedure. In order to systematically determine the optimum setup leading to a desired acceleration signal an evolution strategy is used as well as comparisons with experimental and FEM results have been made. The present procedure allows for a better and faster simulation and predictability of pyroshock tests. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Concentration of deformations around openings in a glass-fiber plastic due to pulse loading

Conclusions The data on the deformation concentrations around circular and elliptic openings in fabric glass-fiber plastic in the case of pulse loading, presented in the article, show that K is a function of the ratio between pulse length and opening dimensions, as well as of the orientation of the material structure with respect to the direction of the load. The results obtained correspond to the commensurability between pulse length and opening dimensions. Experiments on cylindrical panels made of wound glass-fiber plastic have resulted in a test procedure for curvilinear surfaces. The values of K presented indicate an additional effect of the surface curvature on the deformation concentration.B. E. Bedeneev All-Union Scientific-Research Institute of Hydrotechnology, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 1088–1092, November–December, 1976.     

Transient response of a transversely isotropic multilayered half-space due to a vertical loading

This paper investigates the transient response of a transversely isotropic multilayered half-space under vertical loadings. With the aid of a Laplace–Hankel transform, the global stiffness matrix for a multilayered half-space is acquired by assembling the analytical layer-element of each layer medium. The solutions for the displacements in the time domain are obtained by using the global stiffness matrix equations and a numerical inversion procedure. The accuracy of the proposed method is verified through comparisons with existing solutions for displacements induced by a step and rectangular pulse loading. In addition, selected numerical results for displacements induced by the buried loading are presented to illustrate the effect of transient loading type and material anisotropy on the transient response.     

On a generalized thermoelastic interaction in an unbounded body due to a line heat source

In this paper, we study the problem of interactions in an unbounded body due to a prescribed line heat source. Applying the Laplace transform technique, the algebraic eigenvalue approach solutions for displacement, temperature and stress are deduced. Exact discontinuities at the wave fronts are obtained and analysed in some detail and compared with corresponding results obtained in earlier works. Numerical results for gold are presented.     

Singularities of the thermodynamic potential under second-order phase transitions due to the interband electron-phonon interaction

We consider phase transitions in crystals with a strong interband electron-phonon interaction. We investigate the thermodynamic potential of the system using the method of temperature Green’s functions, which takes quantum and thermal fluctuations into account. We show that in the absence of striction, these phase transitions are realized as a sequence of second-order phase transitions in each of which the thermodynamic potential has a logarithmic singularity, as in the Onsager model. This suggests that this singularity is characteristic of all second-order phase transitions. We show that the energy preference of the transition to the ordered phase is ensured by the electron coupling to coherent displacements of ions along normal coordinates of the phonon modes. We calculate the limit value of the energy decrease in the ordered phase compared with the symmetric phase as T → 0 K. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 273–285, November, 2008.     

Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field, where deformations are relatively small, a linear elastic constitutive behavior is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model using a subdomain formulation. The results show that, in the near field, the response of the soil is dominated by a vertically polarized shear wave, whereas in the far field, Rayleigh waves dominate the ground vibration and body waves are importantly attenuated. Finally, the computed ground vibrations are compared with the results of field measurements reported in the literature.     

Analytical and numerical solutions of the expected number of occurrences for combinations of event sequences due to variability

This paper investigates variability in the occurrence of different event sequences on an annual basis during the operation of a proposed nuclear facility. During the operational period of a nuclear facility, the annual radiological dose received by workers or members of the public depends on the number of event sequence occurrences. Based on the facility design, some combinations of event sequences will be expected to occur at least once during the operational period, and some combinations will not. This paper provides analytical solutions for calculating the expected number of combinations of independent event sequences. These analytical solutions agree with numerical solutions for an example problem. Although uncertainties can be incorporated into the method, only point-estimate parameter values are used in the example problem presented. The main objectives of this paper are to present calculational approaches to (i) identify which combinations of event sequences within the same year are expected to occur at least once during the operational life of a proposed facility and (ii) determine the annual doses from those identified combinations. Facility performance based on some proposed design is evaluated against the operational dose limits. Because the operational dose limits tend to be annual quantities that may not be exceeded in any year of operation, calculation of the doses resulting from combinations of event sequences that are expected to occur at least once can provide insight on the maximum annual dose expected during the operation of a proposed facility.     

New approach to nonrepetitive sequences

A sequence is nonrepetitive if it does not contain two adjacent identical blocks. The remarkable construction of Thue asserts that three symbols are enough to build an arbitrarily long nonrepetitive sequence. It is still not settled whether the following extension holds: for every sequence of three‐element sets L₁,…,L_n there exists a nonrepetitive sequence s₁,…,s_n with s_i∈L_i. We propose a new non‐constructive way to build long nonrepetitive sequences and provide an elementary proof that sets of size 4 suffice confirming the best known bound. The simple double counting in the heart of the argument is inspired by the recent algorithmic proof of the Lovász local lemma due to Moser and Tardos. Furthermore we apply this approach and present game‐theoretic type results on nonrepetitive sequences. Nonrepetitive game is played by two players who pick, one by one, consecutive terms of a sequence over a given set of symbols. The first player tries to avoid repetitions, while the second player, in contrast, wants to create them. Of course, by simple imitation, the second player can force lots of repetitions of size 1. However, as proved by Pegden, there is a strategy for the first player to build an arbitrarily long sequence over 37 symbols with no repetitions of size greater than 1. Our techniques allow to reduce 37–6. Another game we consider is the erase‐repetition game. Here, whenever a repetition occurs, the repeated block is immediately erased and the next player to move continues the play. We prove that there is a strategy for the first player to build an arbitrarily long nonrepetitive sequence over 8 symbols. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Modeling the depletion of dissolved oxygen due to algal bloom in a lake by taking Holling type-III interaction

In this paper a non-linear mathematical model for depletion of dissolved oxygen due to algal bloom in a lake is proposed and analyzed. The model is formulated by considering four variables namely, cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen. In the modeling process it is assumed that nutrients are continuously coming with a constant rate to the lake through water runoff from agricultural fields and domestic drainage. The Holling type-III interaction between nutrients and algal population is considered. Equilibrium values have been obtained and their stability analysis has also been performed. Numerical simulations are carried out to explain the mathematical results.     

Relaxation techniques applied to some loading problems

In this paper a two-stage loading problem, dealing with allocation of jobs to machines, is studied. The outer problem is to choose a subset among a number of available machines such that a feasible assigment exists and the total cost price is minimized. The inner problem, is then to find the optimal allocation, given the subset of machines and some assigment criterion at this lower level. It is shown that the choice of problem formulation can be crucial for the strength of the continuous relaxation. Computational results are also presented     

Axisymmetric elastic membranes subjected to fluid loading

We consider axisymmetric isotropic elastic membranes that areloaded by an incompressible liquid. The resulting deformationwhich contains the liquid is assumed to be axisymmetric. Weconsider undeformed plane disks of varying thickness and alsohemispherical cups. We show how the resulting deformation canbe controlled by the initial thickness variation of the disk.In all cases there is a critical loading where the membraneundergoes a very rapid change of shape, from being almost concaveto having an hourglass shape. For a hemispherical cup, the deformationproduces a wrinkled region which diminishes with increased loadingbut briefly reappears as the membrane traverses the unstableregion. The onset of instability appears to be governed by theequibiaxial deformation at the apex of the deformed container.Instability is initiated when the deformation reaches the correspondingvalue of the first bifurcation point for a spherical membrane.     

The effect of crack faces contact interaction on the critical strain in composites under compressive loading

Aviation and aerospace structural components made of composite laminates due to their internal structure and manufacturing methods often contain a number of inter- and intra-component defects which size, dispersion and interaction alter significantly the critical compression strain level [1]. The current study investigates the effect of the cracks interaction and crack faces contact interaction on the critical strain in laminar transversally isotropic material (cross-ply) compressed in a static manner along interlaminar defects. The frictionless Hertzian contact and the shear and extensional mode of stability loss are considered for the interacting crack faces. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium and the 3-D stability theory [2]. The moment of stability loss in the microstructure of material is treated as the onset of the fracture process. The complex non-classical fracture mechanics problem is solved utilizing the finite elements analysis. The results are obtained for the typical dispositions of cracks. It was found that the crack faces contact interaction alter significantly the critical strain level of the composite. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extension of Henrici's method to matrix sequences

In this paper we generalize the definition of linear convergence to matrix sequences. This new definition is used to establish some new results useful to study the new extension of Henrici's method. A convergence theorem, an algorithm for implementation of this method and some numerical examples are given.     

Almost-convergent sequences with respect to polynomial hypergroups

Each polynomial hypergroup on ?₀ generates a family of generalized translation operators?T _m on sequence spaces. We introduce the concept of almost convergence for polynomial hypergroups (determined by the operators?T _m ), extending the notion of almost convergence introduced by Lorentz. Our investigations lead to two theorems characterizing almost convergent sequences on polynomial hypergroups.     

The convergence to zero of Gaussian sequences

Conditions for Gaussian sequences to converge to zero with unit probability are examined. A comparison theorem is proved, on the basis of which sufficient conditions are derived for the convergence to zero of Gaussian sequences, including, in particular, the previously known ones.Translated from Matematicheskie Zametki, Vol. 21, No. 4, pp. 531–538, April, 1977.