Modification of boundary integral equation method for investigation of dynamic stresses for couple stress elasticity

Mikulich, Olena; Shvabyuk, V. I.; Pasternak, Iaroslav; Andriichuk, Oleksandr

doi:10.1016/j.mechrescom.2018.06.004

Cited by 14 publications

(8 citation statements)

References 9 publications

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“…The paper examines the problems associated with production of high-strength concretes by using a general purpose blended Portland cement which is to be mechanically activated and modified with an organomineral additive, and with optimization of concrete mixes taking into account cost-effective use of resources. The research and application of highstrength concrete is an urgent task, especially in road construction [4,[12][13]. Plan of the experiment and concrete compressive strength value (in the 28 days' age) are summarized in Table 2.…”

Section: Resultsmentioning

confidence: 99%

Investigation of the structure of cement stone, obtaining and optimization of high-strength concrete on mechanically activated binder

et al. 2018

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Physico-chemical methods of the study of hydrated cement by mechanically activated binding substance with organo-mineral additive (microsilica + C-3) were presented. It was explored the influence of the additive into the kinetics of formation lowly-basic calcium hydrosilicate. The experiment conducted in accordance with a three-factorial D-optimum plan enabled to establish an influence of blending and technological factors (x1 – content of microsilica in the binder - 5±5%; x2 – binder consumption in concrete - 450±100 kg/m3; x3 – specific area (Ssp) of Portland cement 400±100 m2/kg) on physical and mechanical properties of concrete (compression strength, water absorption). It was established that the use of the mechanically activated blended Portland cement of general purpose with an organomineral additive (microsilica+C-3) makes it possible to obtain high-strength concretes which compression strength on the 28th day reaches 120 MPa. Optimization of concrete mixes was achieved on the basis of obtained mathematical models that reflect the influence of blending and technological factors on physical and mechanical properties of a high-strength concrete.

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Section: Resultsmentioning

confidence: 99%

Investigation of the structure of cement stone, obtaining and optimization of high-strength concrete on mechanically activated binder

et al. 2018

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“…The boundary integral formulations and boundary element developments based on C-CST clearly demonstrate the consistency and practicality of this theory (Hadjesfandiari and Dargush, 2012;Hadjesfandiari et al, 2013;Hajesfandiari et al, 2016Hajesfandiari et al, , 2017Mikulich et al, 2018).…”

Section: Discussionmentioning

confidence: 62%

An Assessment of Couple Stress Theories

Hadjesfandiari¹,

Dargush²

2018

Preprint

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In this paper, we examine the mathematical and physical consistencies of the three primary couple stress theories: original Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), modified couple stress theory (M-CST) and consistent couple stress theory (C-CST).  As has been known for many years, MTK-CST suffers from some fundamental inconsistencies, such as the indeterminacy of the couple-stress tensor.  Therefore, despite the fact that MTK-CST has a fundamental position in the evolution of size-dependent continuum mechanics, it is not a reliable theory within continuum mechanics, for example, in developing new size-dependent multi-physics formulations.  We also observe that M-CST not only inherits all inconsistences from the original MTK-CST, but also suffers from new additional inconsistencies, such as the introduction of a new non-physical governing equation.  These inconsistencies refute the claim of those who state that the couple-stress tensor may be chosen symmetric.  Therefore, the apparent success of MTK-CST and M-CST in describing a size-effect for some problems, such as two-dimensional plate and beam bending, is not enough to justify these theories as suitable for general cases.  In fact, the symmetric couple-stresses in M-CST create torsional or anticlastic deformation, not bending.  On the other hand, C-CST, with a skew-symmetric couple-stress tensor, is the consistent continuum mechanics suitable for solving different size-dependent solid, fluid and multi-physics problems. 

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“…A curve 1 is plotted without accounting for the effect of shear-rotation deformations (basic on motion equations of classical elasticity) by the method [14]. Curve 2 is plotted for Cosserat elasticity with constrained microrotations (couple stress elasticity) by the method [18]. Curve 3 is plotted by the modified in this work method.…”

Section: Numerical Examplementioning

confidence: 99%

Ivestigation of the Dynamic Stress State of Foam Media in Cosserat Elasticity

Sulym

Mikulich

Shvabyuk

2018

Mechanics and Mechanical Engineering

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The paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements and microrotations are written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum are built. Thus, the fundamental functions of displacement for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature is applied for numerical calculations. Numerical example shows the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse load accounting for the shear-rotation deformations effect and without accounting for this effect.

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Modification of boundary integral equation method for investigation of dynamic stresses for couple stress elasticity

Cited by 14 publications

References 9 publications

Investigation of the structure of cement stone, obtaining and optimization of high-strength concrete on mechanically activated binder

Investigation of the structure of cement stone, obtaining and optimization of high-strength concrete on mechanically activated binder

An Assessment of Couple Stress Theories

Ivestigation of the Dynamic Stress State of Foam Media in Cosserat Elasticity

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