Comparative analysis of the use of the defining equations of plasticity theories obtained at the loading step in three ways is performed. In the first method, the relations between strains increments ...and stresses increments are obtained by differentiating the governing equations of the small elastic-plastic deformations theory between full stresses and strains. In the second method, the authors based on the proportionality hypothesis between the component deviators of strains increments and the component deviators of stresses increments without separating the incremental strain into elastic and plastic parts obtain the determining equations at the loading step. In the third method, the relations between the incremental strain and the stresses increment of the plastic flow theory are used on the basis of the hypothesis about the proportionality of the plastic deformations increments to the components of the stress deviator. Based on the analysis of algorithms for obtaining the constitutive relations and the analysis of the numerical results of the calculation example, preference is given to the second method of obtaining expressions between stress increments and strain increments without separating the latter into elastic and plastic parts.
The displacement vector components vector (invariant) approximation implementation and the initial inclination angles by the hypothesis of S. P. Tymoshenko in obtaining the thin shell quadrangular ...finite element nodal forces stiffness matrix and the column is shown.
This article discusses the algorithm for calculating the shell structure of arbitrary shape, taking into account the physical nonlinearity of the material used. In determining the parameters of the ...stress-strain state, a step loading procedure was used. Algorithm for calculating the shell structure of arbitrary shape, taking into account the physical nonlinearity of the used material is discussed in this article. In determining the parameters of the stress-strain state, a step loading procedure was used.
The purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment ...of the middle surface as a discretization element. Nodal axial forces and moments, as well as components of the nodal displacement vector were selected as unknown variables. The number of unknowns in each node of the four-node discretization element reaches nine: six force variables and three kinematic variables. To obtain the flexibility matrix and the nodal forces vector, a modified Reissner functional was used, in which the total specific work of stresses is represented by the specific work of membrane forces and bending moments of the middle surface on its membrane and bending strains, and the specific additional work is determined by the specific work of membrane forces and bending moments of the middle surface. Bilinear shape functions of local coordinates were used as approximating expressions for both force and displacement unknowns. The dimensions of the flexibility matrix of the four-node discretization element were found to be 36×36. The solution of benchmark problem of analyzing a truncated ellipsoid of revolution loaded with internal pressure showed sufficient accuracy in calculating the strength parameters of the studied shell.
Nanotechniques Inactivate Cancer Stem Cells Goltsev, Anatoliy N.; Babenko, Natalya N.; Gaevskaya, Yulia A. ...
Nanoscale research letters,
06/2017, Volume:
12, Issue:
1
Journal Article
Peer reviewed
Open access
One of the tasks of current oncology is identification of cancer stem cells and search of therapeutic means capable of their specific inhibition. The paper presents the data on phenotype ...characteristics of Ehrlich carcinoma cells as convenient and easy-to-follow model of tumor growth. The evidence of cancer stem cells as a part of Ehrlich carcinoma and significance of CD44
+
and CD44
–
subpopulations in maintaining the growth of this type of tumor were demonstrated. A high (tenfold) tumorigenic activity of the Ehrlich carcinoma CD44
+
cells if compared to CD44
–
cells was proven. In this pair of comparison, the CD44
+
cells had a higher potential of generating in peritoneal cavity of CD44
high
, CD44
+
CD24
–
, CD44
+
CD24
+
cell subpopulations, highlighting the presence of cancer stem cells in a pool of CD44
+
cells.
In this study, the ability of synthesized hybrid nanocomplexes, comprising the nanoparticles of rare earth orthovanadates GdYVO
4
:Eu
3+
and cholesterol to inhibit the tumor growth and to increase the survival of the animals with tumors was established. A special contribution into tumor-inhibiting effect is made by each of its components. Treatment of Ehrlich carcinoma cells with two-component hybrid complex resulted in maximum reduction in the concentration of the most tumorigenic CD44
high
cells with simultaneous rise in the number of CD117
+
cells that decreased an intensity of tumor growth by 74.70 ± 4.38% if compared with the control.
For describing elastoplastic deformation, three versions of constitutive equations are used. The first version employs the governing equations of the flow theory. In the second version, elastic ...strain increments are defined the same way as in the flow theory, and the plastic strain increments are expressed in terms of stress increments using the condition of their proportionality to the components of the incremental stress deviator tensor. In the third version, the constitutive equations for a load step were obtained without using the hypothesis of separating strains into the elastic and plastic parts. To obtain them, the condition of proportionality of the components of the incremental strain deviator tensor to the components of the incremental stress deviator tensor was applied. The equations are implemented using a hybrid prismatic finite element with a triangular base. A sample calculation shows the advantage of the third version of the constitutive equations.
Relevance. The problems of decline of resource-demanding of objects of building and engineer dictate the necessity of consideration of processes of deformation of constructions at the ...resiliently-plastic state. The widely in-use theory of account of practical properties of material is a deformation theory of plasticity. The aim of the research is development of variants of receipt of determining correlations on the step of ladening at deformation of material outside a resiliency. Methods. Algorithms over of receipt of determining correlations of theory of small resiliently-plastic deformations are brought on the step of ladening in two variants. In the first they turn out differentiation of expressions of tensions as functions of deformations on the basis of deformation theory of plasticity; in the second determining correlations turn out on the basis of hypothesis about the proportion of components of deviators increases of tensions to components of deviators increases of deformations. Results. On the test example of calculation of the jammed cylindrical shell realization of the got determining correlations is presented.
Relevance. Currently, in connection with the wider spread of large-span thinwalled structures such as shells, an urgent issue is the development of computational algorithms for the strength ...calculation of such objects in a geometrically nonlinear formulation. Despite a significant number of publications on this issue, a rather important aspect remains the need to improve finite element models of such shells that would combine the relative simplicity of the resolving equations, allowance for shear deformations, compactness of the stiffness matrix being formed, the facilitated possibility of modeling and changing boundary conditions and etc. The aim of the work is to develop a finite element algorithm for calculating a thin shell with allowance for shear deformations in a geometrically nonlinear formulation using a finite element with a limited number of variable nodal parameters. Methods. As research tools, the numerical finite element method was chosen. The basic geometric relations between the increment of deformations and the increment of the components of the displacement vector and the increment of the components of the normal vector angle are obtained in two versions of the normal angle of the reference. The stiffness matrix and the column of nodal forces of the quadrangular finite element at the loading step were obtained by minimizing the Lagrange functional. Results. On the example of calculating a cylindrical panel rigidly clamped at the edges under the action of a concentrated force, the efficiency of the developed algorithm was shown in a geometrically nonlinear setting, taking into account the transverse shear strain.
The usage of traditional approximating functions directly to the desired displacement vector of the internal point of a finite element to determine it through nodal unknowns in the form of ...displacement vectors and their derivatives is described. To analyze the stress state of a geometrically non-linearly deformable shell of rotation at the loading step, the developed algorithm for forming the stiffness matrix of a hexagonal finite element with nodal values in the form of displacement increments and their derivatives was used. To obtain the desired approximating expressions, the traditional interpolation theory is used, which, when calculated in a curved coordinate system, is applied to the displacement vector of the internal point of a finite element for its approximation of class C(1) through nodal displacement vectors and their derivatives. For the coordinate transformation, expressions of the bases of nodal points are obtained in terms of the basis vectors of the inner point of the finite element. After the coordinate transformations, approximating expressions of class C(1) are found for the components of the displacement vector of the internal point of the finite element, leading in a curved coordinate system to implicitly account for the displacement of the finite element as a rigid whole. Using calculation examples, the results of the developed method of approximation of the required values of the FEM with significant displacements of the structure as an absolute solid are obtained.
Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite ...elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.
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