Asymptotic research of deformations of elliptic bottom and conic shell

In the paper, for the set of two homogeneous differential equations (in Novozhilov sense) that describes non-axial-symmetric deformation of rotation hull, which is under arbitrary edge load, we obtain by elliptic method the approximate solutions for elliptic and conic shells. We find expressions for transitions.

A study of buckling phenomenon in dielectric elastomeric actuator with different potential energy functions

The present study deals with the buckling phenomenon modeling in a dome-shaped dielectric elastomeric (DE) actuator used in different aerodynamic and fluid power system applications. The DE actuator is a circular membrane type of actuator, which shows a large out-of-plane axial-symmetric deformation with an electrically induced loading condition. A classical continuum mechanics-based analytical model is developed to predict the electrically induced buckling deformation in the actuator. A detailed parametric study has been performed to see the influence of standard Neo-Hookean and Mooney-Rivlin types of potential energies on the geometrical and physical parameters. The findings show that the present model successfully links the sensitivity of different potential energies concerning the actuator’s initial dome height and radius.

Indentation and bifurcation of inflated membranes

We study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a two-dimensional membrane with either a line or plane indenter for which the stable deformation path is determined by computing the total system potential energy of different configurations. An axisymmetric membrane with indenters of different shapes and sizes is further investigated numerically. In this case, a cylindrical indenter can always trigger bifurcation while a small spherical indenter tends to be encapsulated rather than induce an asymmetric deformation mode. This result suggests that the observed bifurcation behaviour can be actively tuned and even triggered selectively by tuning indenter shape and size. We also demonstrate the effects of friction and biased bifurcation analytically through the example of a two-dimensional membrane with a line indenter.

Tall von-Mises trusses' skew-symmetric deformation

The work’s aim is to investigate the tall two-rods three-hinged von-Mises trusses' deformation regularities at the sloped load that applied to the ridge joint.The horizontal elastic support influence in the ridge joint when changing the force's inclination angle in a wide range is also investigated Particular attention is paid to the tall two-rod trusses' skew-symmetric stability loss possibility. The possibility of the skew-symmetric shape of а loss of stability of high trusses with at a very small angle of inclination of the force from the vertical axis was confirmed. The horizontal elastic support's influence on increasing the stability against skew-symmetric deformation was shown.It was found that skew-symmetry deformation is essentially non-linear, but under certain conditions it is not catastrophic.It is also noticed that asymmetric deformation depends on vertical deformation.Scientific novelty lies in a detailed study of the tall two-rod three-hinged trusses' deformation, and the establishment of the tendency of such structures to skew-symmetric buckling.The tall von-Mises trusses' new detailed deformation regularities character at skew-symmetric deformation at small inclination angles of force that applied in the ridge joint has been established. Also, the two-rod structures' new deformation regularities has been revealed with a wide inclination angles range of the concentrated force applied in the ridge joint. It is shown that on increasing the loading's inclination angles, which coincide with the rod's inclination angles, the stability loss of the individual rods is possible, since there is a significant increase in the truss' carrying capacity. The research results can be used in the structure design of large general dimensions, modeling of which gives the real structure work under various loads.

The Tension-Twist Coupling Mechanism in Flexible Composites: A Systematic Study Based on Tailored Laminate Structures Using a Novel Test Device

The focus of this research is to quantify the effect of load-coupling mechanisms in anisotropic composites with distinct flexibility. In this context, the study aims to realize a novel testing device to investigate tension-twist coupling effects. This test setup includes a modified gripping system to handle composites with stiff fibers but hyperelastic elastomeric matrices. The verification was done with a special test plan considering a glass textile as reinforcing with different lay-ups to analyze the number of layers and the influence of various fiber orientations onto the load-coupled properties. The results demonstrated that the tension-twist coupling effect strongly depends on both the fiber orientation and the considered reinforcing structure. This enables twisting angles up to 25° with corresponding torque of about 82.3 Nmm, which is even achievable for small lay-ups with 30°/60° oriented composites with distinct asymmetric deformation. For lay-ups with ±45° oriented composites revealing a symmetric deformation lead, as expected, no tension-twist coupling effect was seen. Overall, these findings reveal that the described novel test device provides the basis for an adequate and reliable determination of the load-coupled material properties between stiff fibers and hyperelastic matrices.

POLAR-SYMMETRIC DEFORMATION OF AN ELASTIC CYLINDER UNDER TEMPERATURE-HUMIDITY EXPOSURE

The actual scientific and technical problem of polar-symmetric deformation of an elastic cylinder under conditions of temperature and humidity influences is considered. An exact analytical solution to this problem is obtained with the determination of unambiguous expressions for stresses, deformations and radial displacement. The obtained solution allows solving this problem for an incompressible material with μ = 1/2 as a special case.

Stress Amplification/Shielding Phenomena of Spherically Anisotropic and Radially Inhomogeneous Linear Elastic Hollow Spheres

Summary Exact solutions of radially symmetric deformation of a spherically anisotropic and radially inhomogeneous linear elastic hollow sphere subjected to uniform radial tractions on the surfaces are derived. The power-law function is assumed to represent the radially inhomogeneity. Stress amplification/shielding phenomena are fully investigated and the benefits of using functionally graded materials are indicated. For a solid sphere under external uniform loadings, the conditions in which infinite stresses occur at the centre of the sphere regardless of applied traction magnitudes are specified. Also, circumferential stresses might have opposite sign of the applied loadings. Cavitation and blackhole phenomena at the centre of the sphere are also discussed.

The spacetime metric of a spherically symmetric deformation of space derived from the cosmic fabric model of gravity

The Cosmic Fabric model of gravity that was previously introduced by Tenev and Horstemeyer [T. G. Tenev and M. F. Horstemeyer, Int. J. Mod. Phys. D 27 (2018) 1850083; Rep. Adv. Phys. Sci. 2 (2018) 1850011] is further developed to provide a method for deriving the spacetime metric of the fabric's deformation due to a spherically symmetric gravitating body. We show that the derived metric is equivalent to the Schwarzschild metric up to a rescaling factor. From analyzing the membrane portion of the elastic energy due to an inclusion, we conclude that matter cannot be continuous at arbitrary sizes but must comprise discrete particles. Therefore, we show that the Cosmic Fabric model leads to results consistent with accepted theories at both continuum as well as sub-continuum length scales.

An analytical solution for the stress distribution within a spherically isotropic hollow sphere under diametrical compression

An analytical solution for the stress distributions within a spherically isotropic hollow sphere under diametrical compression is derived. The deformation of the spherically isotropic hollow sphere is divided into axis-symmetric deformation and non-symmetric deformation. The analytical solution for the axis-symmetric deformation is obtained by following the displacement method, while that for non-symmetric deformation of the spherically isotropic hollow sphere is obtained by employing the displacement function method. When the isotropic limit is considered, the analytical solution for isotropic hollow spheres is recovered identically. Numerical results show that tensile stress concentrations are usually developed both at the inner surface and near r/ R = 0.85 within a hollow sphere along the axis of loading. A small value of the anisotropy in Young’s modulus or Poisson’s ratio usually leads to a large value of the maximum tensile stress at the inner surface. While a smaller value of the anisotropy in Poisson’s ratio or a large value of the anisotropy in the shear modulus may lead to a large value of the maximum tensile stress near r/ R = 0.85 for a thick and anisotropic hollow sphere. In addition, it is found that the anisotropy in the shear modulus has drastic influence on the tensile stress distributions within a thin hollow sphere, and a particular value of the anisotropy in the shear modulus may reduce greatly the tensile stress concentrations both at inner surface and near r/ R = 0.85 of a thin hollow sphere. This result may provide us a very attractive method to optimize the elastic constants of anisotropic hollow spheres by synthesis process technique so as to improve the load capacity of a hollow sphere, and extend the fatigue life of composite material made of thin hollow spheres.