Structural Mechanical Model Research Articles

Structural–mechanical model of filled rubber: Influence of filler arrangement

Filled rubber is modelled as a volume filled with hard spherical inclusions (filler) connected to each other via hyperelastic links (polymer in gaps). These inclusions are arranged into a network of fractal clusters, which are observed in real filled rubbers. The force response of links to external loads is calculated by the finite element method applied to solve the problem of pair interaction of inclusions in the polymer matrix. The obtained dependencies are used then in a structural–mechanical model of the deformation of a representative volume of inclusions. At a certain elongation of the link the volume is broken and in consequence the Mullins softening effect is modeled at the macroscopic level. Therefore, the model explicitly takes into account the specific features of the microstructure and allows one to establish a direct relation between the micro and macro properties of the material. In addition to the clustered structure, the stress–strain behavior of the material with periodic and random arrangements of inclusions (filler volume fraction: 0.13 and 0.20) is simulated. It is shown that the structure with a regular arrangement of filler particles is less resistant to large deformations than the structure in which filler particles are arranged in a disordered manner. It was found that during deformation the initially close inclusions of clustered or random structures move in groups, maintaining their relative position. The largest local deformations of material in the gaps occur between inclusions where the initial gap is at least equal to size of inclusion.

Pressure relief and structure stability mechanism of hard roof for gob-side entry retaining

In order to explore the pressure relief and structure stability mechanism of lateral cantilever structure in the stope under the direct coverage of thick hard roof and its impact on the gob-side entry retaining, a lateral cantilever fractured structural mechanical model was established on the basis of clarification for the stress environment of gob-side entry retaining, and the equation of roof given deformation and the balance judgment for fracture block were obtained. The optimal cantilever length was proposed based on the comparison of roof structural characteristics and the stress, deformation law of surrounding rocks under six different cantilever lengths by numerical simulation method. Double stress peaks exist on the sides of gob-side entry retaining and the entry located in the low stress area. The pressure of gob-side entry retaining can be relieved by reducing the cantilever length. However, due to the impact of arch structure of rock beam, unduly short cantilever would result in insufficient pressure relief and unduly long cantilever would bring larger roof stress which results in intense deformation. Therefore, there is optimal cantilever length, which was 7-8 m in this project that enables to achieve the minimum deformation and the most stabilized rock structure of entry retaining. An engineering case of gob-side entry retaining with the direct coverage of 10 m thick hard limestone roof was put forward, and the measured data verified the reasonability of conclusion.

The Vibrational Behavior of Coupled Bladed Disks with Variable Rotational Speed

AbstractLow pressure steam turbine blades are subjected to high static and dynamic loads during operation. These loads strongly depend on the turbine's rotational speed, leading to entirely new load conditions. To avoid high dynamic stresses due to the forced vibrations, a coupling of the blades, such as shrouds or snubber coupling, is applied to reinforce the structure. In this work the influence of the rotational speed on the vibration behavior of shrouded blades is investigated. Two fundamental phenomena are considered: the stress stiffening and the spin softening effect. Both effects are caused by centrifugal forces and affect the structural mechanical properties, i.e. the stiffness matrix K, of the rotating system. Since the rotational speed Ω appears quadratically, it is possible to derive the stiffness matrix as a second order matrix polynomial in Ω2 [3].In the case of shrouded blades, contact forces between neighboring blades must be taken into account. The contact status and the pressure distribution in particular is strongly influenced by the rotational speed, respectively, centrifugal forces, caused by the untwisting and radial deformation of the blades. For the calculation, a three dimensional structural mechanical model including a spatial contact model is considered. The solution of the nonlinear equations of motion is based on the well known Multiharmonic Balance Method [2]. Here, the nonlinear forces are computed in the time domain and transferred in the frequency domain by the use of the Fast Fourier Transformation (FFT), also known as the Alternating Frequency Time method (AFT) [1]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Research on modelling of spatial dynamic structural mechanics and spatio-temporal evolution of coal mine stopes

Original scientific paper Major hazardous accidents in coal mines are basically attributable to a lack of understanding of or the failure to establish a complete spatial structural mechanical model of the stope during the course of exploitation, as well as of the spatial movement over time caused by the mining itself, mining at the wrong time, as well as improper roadway maintenance and advance of the work face. To efficiently study and analyze the mechanism behind major stope disasters, a method based on monitoring the stress and displacement of stopes was adopted to deduce the process whereby the overlying strata fracture, and a method of ascertaining stope stability based on qualitative identification of the dynamics was further proposed. The study found that the stability of stopes during the process of mining the face can be divided into two stages: (1) Unstable stage: i.e. the distance the work face has advanced Lx width of work face L0. These research results provide a basis for reasonable determination of a space-time relationship for the mining process.

Key technologies and equipment for a fully mechanized top-coal caving operation with a large mining height at ultra-thick coal seams

Key technologies and equipment for a fully mechanized top-coal caving operation with a large mining height at ultra-thick coal seams

Modeling and Analysing the Tensile Behavior of Fabric Samples

This paper presents a structural-mechanical model for describing the tensile behavior of textile fabrics in main directions based on the fiber-bundle-cells modeling theory and method. The applicability of this model, created by a variable transformed E- bundle shifted along the deformation axis, was demonstrated by analyzing the tensile load- deformation behavior and the breaking process including some size effects of a plain woven fabric made of OE rotor cotton yarns.

Numerical simulation of the end-winding deformations in the synchronous machine under symmetrical short-circuit conditions using FEM*

In this paper the numerical simulation of the end-winding deformations in a synchronous machine under symmetrical short circuit conditions is presented. A sequentially coupled numerical simulation between an electromagnetic and a structural mechanical problem has been carried out. Owing to the short-circuit conditions, both problems are to be computed in the time-domain. Analysis of the time-variant magnetic field has been performed using the T, Φ – Φ formulation for the finite element method (FEM). This way, the influence of the induced eddy currents in the clamping-plates and in the housing of the machine on the magnetic field in the end-region of the generator has been taken into the account. In order to reduce the computational time, the non-conforming finite element (FE) mesh approach has been used to solve the electromagnetic problem. In each time-step the Lorentz forces in the end-winding have been calculated and carried over to the structural-mechanical model. These forces have been applied in the centre of the end-winding bars in order to provoke the transient excitation for the mechanical structure. A time-stepping scheme has been applied to calculate end-winding deformations in each time-step.

Frequency analysis of perfect and defective SWCNTs

This paper develops a structural mechanical model that analyzes the natural frequency of single-walled carbon nanotubes (SWCNTs) subjected to fixed–fixed and free–fixed boundary conditions. A Morse potential is employed for stretching and bending potentials, and a periodic type of bond torsion is used for torsion interactions. The natural frequencies for various aspect ratios are predicted by this structural model. The effect of different vacancy and Stone–Wales defects on the natural frequency of zigzag and armchair nanotubes is also investigated. Finally, the results of the present structural model are compared with those from other numerical methods.

The Modernisation of Manipulative Therapy

Research indicates that, despite physiotherapists’ comprehensive training in the basic sciences, manipulative (currently “musculoskeletal”) therapy is still dominated in the clinical setting by its original, now obsolete, structure-based “biomedical” model. This is further inexplicable in the light of evidence that not only the underlying “philosophy” but also several of the fundamental requirements of the clinical process itself which has the structural-mechanical model as its basis, have been shown to be flawed or at least irrelevant. The apparent inability of the profession to fully abandon outmoded “concepts” (and embrace the acknowledged science-based “best practice” biopsychosocial model) may have potentially undesirable consequences for both patients and therapists engaged in the management of (chronic) musculoskeletal pain and disability.

Design of a modular feeder for optimal operating performance

Flexible feeding technology is one of the main challenges in modern assembly systems. A promising approach is a new modular feeding system, which was developed at the iwb. This paper presents a method to ensure an optimal operating performance of the new feeder at single or double line frequency. Hereby, the modular system's natural frequencies are adjusted adequately during the development phase by adapting the masses and inertias of the relevant components. This is done with the aid of a structural mechanical model of the modular feeding system, which is derived and verified on a product-neutral basic set-up. Finally, the application of the model during the development phase of the modular feeder is presented.

On the modeling of confined buckling of force chains

Buckling of force chains, laterally confined by weak network particles, has long been held as the underpinning mechanism for key instabilities arising in dense, cohesionless granular assemblies, e.g. shear banding and slip-stick phenomena. Despite the demonstrated significance of this mechanism from numerous experimental and discrete element studies, there is as yet no model for the confined buckling of force chains. We present herein the first structural mechanical model of this mechanism. Good agreement is found between model predictions and confined force chain buckling events in discrete element simulations. A complete parametric analysis is undertaken to determine the effect of various particle-scale properties on the stability and failure of force chains. Transparency across scales is achieved, as the mechanisms on the microscopic and mesoscopic domains, which drive well-known macroscopic trends in biaxial compression tests, are elucidated.

Sur une théorie des méconnaissances en calcul des structures

The quantification of the quality of a structural mechanical model remains a major issue today, with the use of an increasing number of methods in order to validate a model in comparison with an experimental reference. This paper presents a new theory based on the concept of Lack of Knowledge combining convex uncertainty models with probabilistic features by introducing for each substructure two bounds of the strain energy as stochastic variables. A general strategy of reduction of the lack of knowledge is discussed and applied to academic as well as industrial cases.

Assessment of intrinsic creep resistance evolution based on the results of constant load creep tests

In the present study a method to assess the intrinsic creep resistance evolution by using data of constant load creep tests is proposed. The investigation has been performed on the austenitic steels X6 CrNi 18 11 and X8 CrNiMoNb 16 16. To develop the constitutive equation describing the intrinsic creep resistance evolution a simple structural mechanical model has been used. The applied model is based on a modification of the Levy‐Mises equation for plasticity to consider creep time effects. The proposed model has been verified experimentally. The experimental creep resistance evolution curves have been derived with the aid of strain transient dip test performed in transient, steady state and accelerated creep stage.

Thermal expansion, Debye temperature and Gr�neisen parameter of synthetic (Fe, Mg)SiO3 orthopyroxenes

Thermal expansion properties of synthetic orthopyroxenes (Fe0.20Mg0.80)SiO3, (Fe0.40Mg0.60)SiO3, (Fe0.50Mg0.50)SiO3, (Fe0.75Mg0.25)SiO3 and (Fe0.83Mg0.17)SiO3 were systematically studied by means of single-crystal x-ray diffraction in the temperature range from 296 to 1300 K. The measurements of unit cell dimensions as a function of temperature reveal that the a and c dimensions and the unit cell volume V increase nonlinearly with a positive curvature with rising temperature, whereas the b dimension behaves differently, depending on the total Fe content. For Mg-rich orthopyroxenes (Fe/(Fe+Mg) 30%. Together with the high temperature neutron diffraction data on enstatite (MgSiO3) (McMullan, Haga and Ghose, unpublished) and x-ray diffraction data on ferrosilite (FeSiO3) (Sueno et al. 1976), the measured unit cell dimensions were analyzed in terms of the Gruneisen theory of thermal expansion. The linear thermal expansion coefficients α a and α c both increase as temperature is elevated, with α c increasing faster, while α b changes gradually from increasing for Mg-rich orthopyroxenes to decreasing for Fe-rich orthopyroxenes. The relative magnitudes of linear thermal expansion coefficients are always in the order α b >α c >α a between 300 and 500 K, but at higher temperatures, the order changes to α c >α b >α a for Mg-rich orthopyroxenes and α c >α a >α b for Fe-rich ones. The linear thermal expansion behavior is interpreted on the basis of the structural mechanical model of Weidner and Vaughan (1982). The anomalous behavior of α b is mainly attributed to the changes in the Fe2+ population at the M2 site and the relative stiffness of the M2(Fe2+)-O bonds compared to the M2(Mg2+)-O bonds. The volume thermal expansion coefficients are nonlinear functions of temperature and lie between 23 and 49×10−6/K. The previously reported results of mean volume thermal expansion coefficients appear to represent the α V values characteristic of higher temperatures compared to our results. The thermal Debye temperatures are composition-dependent, decreasing linearly from 812 (MgSiO3) to 561 K (FeSiO3), and are systematically higher than the corresponding acoustic Debye temperatures. The Gruneisen parameters range from 0.85 to 0.89 and do not seem to vary with composition. The linear compressibilities derived from thermal expansion and elastic moduli data agree very well. The pressure derivatives of the isothermal bulk modulus (dK0/dP) are also composition-dependent and decrease from 11.2 (MgSiO3) to 8.77 (FeSiO3). Such large values indicate possible anomalous elastic behavior of orthopyroxenes at high pressures in the Earth's upper mantle.

Elasticity of MgSiO 3 in the ilmenite phase

The single-crystal elastic moduli of the ilmenite phase of MgSiO 3 have been determined from Brillouin spectroscopy. They are: C 11 = 472, C 12 = 168, C 33 = 382, C 13 = 70, C 44 = 106, C 14 = −27, C 66 = 152 and C 25 = −24 in GPa. These elastic properties are consistent with a structural mechanical model where the silicon octahedra are very stiff under compression and shear. This latter property yields an unexpectedly high shear modulus for the magnesium silicate ilmenite as compared with analogue compounds. The further transformation to perovskite will probably be associated with a significant increase in elastic properties since the strong silicon polyhedra form a structural network in this phase. The transformation of spinel and stishovite to ilmenite is associated with a slight density increase and a slight decrease in acoustic velocities. This transformation will probably not produce a seismic discontinuity even if it does occur in the Earth's mantle.

A structural mechanical model for tendon crimping

For tendon collagen, an explanation is proposed for the “toe” region of the stress-strain curve. We ascribe the “toe” effect to the fascicle as a whole. Studies of tendon morphology have shown a distribution of crimp angles. In our model, restoring force arises from the elasticity of those fibrils which are already straightened. Resistance of a crimped fibril is assumed to be negligible. The model was found to fit experimental mechanical data for all ages and over the entire “toe” region.