Axial tension of nonlinear elastic composite shells of zero Gaussian curvature with a rectangular hole

The formulation of physically nonlinear problems for composite shells of zero Gaussian curvature weakened by a rectangular hole under the action of axial loading is given. The initial equations are the equations of the theory of non-sloping shells, in which the Kirchhoff–Love hypotheses take place. Geometric relationships are written in vector form, and physical relationships are based on the deformation theory of plasticity for anisotropic materials. The system of resolving equations is obtained from the Lagrange variational principle. A technique has been developed for the numerical solution of two-dimensional physically nonlinear problems for orthotropic composite shells of this type, based on the use of the method of additional stresses and the method of finite elements. A variant of the finite element method is proposed, the peculiarity of which lies in the vector approximation of the sought values and the discrete execution of the geometric part of the Kirchhoff–Love hypotheses (at the nodes of finite elements). Using the developed technique, the nonlinear elastic state of an organoplastic conical shell with a rectangular hole, which at the ends is reinforced with frames and loaded with uniformly distributed tensile forces, has been investigated.

Local Shape of the Vapor–Liquid Critical Point on the Thermodynamic Surface and the van der Waals Equation of State

Differential geometry is a powerful tool to analyze the vapor–liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point (∂p/∂V)T=0 requires the isothermal process, but the universality of the critical point is its independence of whatever process is taken, and so we can assume (∂p/∂T)V=0. The distinction between the critical point and other points on the surface leads us to further assume that the critical point is geometrically represented by zero Gaussian curvature. A slight extension of the van der Waals equation of state is to letting the two parameters a and b in it vary with temperature, which then satisfies both assumptions and reproduces its usual form when the temperature is approximately the critical one.

Surfaces Modelling Using Isotropic Fractional-Rational Curves

The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.

Strain tolerance of two-dimensional crystal growth on curved surfaces

Two-dimensional (2D) crystal growth over substrate features is fundamentally guided by the Gauss-Bonnet theorem, which mandates that rigid, planar crystals cannot conform to surfaces with nonzero Gaussian curvature. Here, we reveal how topographic curvature of lithographically designed substrate features govern the strain and growth dynamics of triangular WS2 monolayer single crystals. Single crystals grow conformally without strain over deep trenches and other features with zero Gaussian curvature; however, features with nonzero Gaussian curvature can easily impart sufficient strain to initiate grain boundaries and fractured growth in different directions. Within a strain-tolerant regime, however, triangular single crystals can accommodate considerable (<1.1%) localized strain exerted by surface features that shift the bandgap up to 150 meV. Within this regime, the crystal growth accelerates in specific directions, which we describe using a growth model. These results present a previously unexplored strategy to strain-engineer the growth directions and optoelectronic properties of 2D crystals.

CONSTRUCTIVE SOLUTIONS OF VANT LOCATION IN CYLINDRO-PLATE-VANT (CPV) COATING OF BUILDING (CONSTRUCTION)

The article considers the calculation and spatial models of buildings with cylindrical-slab-guy covering and various constructive arrangement of the guy: radial, fan, parallel-transverse, parallel-longitudinal and longitudinal-transverse (cross). The calculations have been performed using the FEMAP / NX NASTRAN software package (PC), taking into account the geometric nonlinearity of the deformation. The novelty of the research is a combined design of cylindrical-slab-guy covering. This is a complex of different types of coverings, overlapping large spans of buildings: the cylindrical shell of zero Gaussian curvature and the flat slab are located in the middle part; symmetric guy coverings are located at the edges. The aim of the study is to assess the effect of guy system with various arrangement of guys on the stress-strain condition of cylindrical-slab-guy covering. The objective of the study is to provide a comparative analysis of the stress-strain condition of complex design of cylindrical-slab-guy covering and to select the optimal structural solution of the guy system under the same conditions (geometric parameters of the building, external loads and boundary fixings)

Twisted surfaces with vanishing curvature in Galilean 3-space

In this work, we define twisted surfaces in Galilean 3-space. In order to construct these surfaces, a planar curve is subjected to two simultaneous rotations, possibly with different rotation speeds. The existence of Euclidean rotations and isotropic rotations leads to three distinct types of twisted surfaces in Galilean 3-space. Then we classify twisted surfaces in Galilean 3-space with zero Gaussian curvature or zero mean curvature.