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The plane-wave pseudo-potential method, which is based on density functional theory, is used to determine the structure, elastic constants and phase transition properties of transition metal nitride (TMN; TM = Ti, Zr, Hf, V, Nb and Ta) nanocomposite films under external pressures. Enthalpy–pressure and volume–energy relations of TMNs with different structures are calculated, and their relative stability is discussed. Mechanical stability of external pressure is calculated, and changes in elastic constants with external pressure are analyzed. The present study obtains influence of external pressure on the mechanical properties of material. By analyzing total energy–volume relation, enthalpy–pressure relation and mechanical stability, phase transition law of TMNs under external pressure is obtained.

The elastic properties and electronic structure of tetragonal Potassium dihydrogen phosphate (KDP) under polishing pressures were investigated using the plane-wave pseudopotential method based on density functional theory. The results show that the calculated lattice constant, elastic constants and bandgap agreed well with the results of the experiments and the other calculations at ambient pressure. The elastic constants and the elastic moduli of KDP increase with increasing pressure, but Vickers hardness of KDP decreases. KDP crystal changes from brittleness to ductility beyond the pressure of 3 GPa. The anisotropy of KDP increases and the ratio of $E_{[100]}$/$E_{[110]}$ increases with the increase of pressure. When the pressure reaches 4.5 GPa, the tetragonal KDP will undergo structural phase transition. As pressure increases, the bandgap between and O-2$p$ and P-3$s$ states increases. The interatomic distances were shortened under external pressure, and the interaction between K${}^{+}$ and the neighboring H₂PO${}_4^{-}$ was enhanced, which leads to the increase of elastic mechanical properties.

This paper summarizes the results of numerical studies into the effects of initial geometric imperfections on the elastic buckling behaviour of steel circular and elliptic toroidal shells subjected to follower-type external pressure. The types of initial imperfection studied are (a) axisymmetric localized ones and (b) sinusoidal buckling modes. The principal localized imperfections studied are (i) circular increased-radius "flat spots" and (ii) smooth dimples. The buckling pressures p_cr of circular toroidal shells were not very sensitive to initial imperfections. With elliptic toroids, whether the shell was sensitive to initial imperfections or not depended on the ratio k(≡ a/b) of major to minor radii of the section. The shells on the ascending part of the p_cr versus k curve behaved like circular toroidal shells, i.e. they were not sensitive to initial imperfections. However, the behaviour of elliptic toroids on the descending part of the versus k curve was very different. The numerical results quoted in the paper are for limited ranges of the geometric parameters. It would be useful to extend these ranges, to explore the effects of plasticity and to conduct model tests on imperfect steel models to verify the conclusions of the numerical studies.

The buckling of isotropic rings under external pressure has attracted the interest of researchers since late 1950s. The formula for critical fluid buckling pressure of thin rings is very well known. This formula was directly extended to account for homogeneous orthotropic rings as well. The buckling of orthotropic cylindrical shells was also a subject of interest since the 1960s. However, the formulations developed, to date, require numerical solutions to obtain the critical pressure. In this work, a generalized closed form analytical formula for the buckling of thin orthotropic multi-angle laminated rings/long cylinders is developed. Standard energy based formulation is used to express the kinematics and equilibrium equations. Classical lamination theory is implemented to introduce the constitutive equations of thin shells. These equations are statically condensed, in terms of the ring's boundary conditions, to produce effective axial, coupling and flexural rigidities for the cases of rings and long cylinders. The critical buckling pressure may be calculated by hand using the derived equation in terms of these effective elastic rigidities. Comparisons are made with some existing results. Parametric studies are conducted to compare the present results with those of the buckling equations implemented by design standards. Various fiber orientations and stacking sequences are considered.

The paper reports on the buckling of a ring-stiffened hemi-ellipsoidal prolate dome under external hydrostatic pressure. The study was partly theoretical and partly experimental, where in the case of the latter, the finite element method was used. Comparison between experiment and theory was good. The effect of ring stiffening the dome was to increase its buckling resistance by a factor of 2.05.

Post-buckling and collapse phenomenon of a thick closed ring subjected to external pressure on its outer surface is analyzed in this research. Ring is made of a linearly elastic polar orthotropic material. Constitutive law of linear elasticity under plane stress conditions is used. Virtual work principle is implemented to obtain the governing equations. Unlike the available noncompressible ring theories, a two-dimensional elasticity solution including the complete nonlinear Green strain field is used. The finite element method is used to solve the highly nonlinear coupled equilibrium equations. The well-known Newton–Raphson iterative technique is applied to the matrix representation of the equilibrium equations to trace the post-buckling response of the ring up to the collapse point where two antipodal points on the interior side of the ring are collided with each other. It is shown that, including the complete Green strain field is necessary in accurate estimation of the post-buckling path, especially for higher load levels and collapse load. Furthermore, orthotropic rings under external pressure load follow the bifurcation type of buckling accompanied with a stable post-buckling path.

Nonlinear buckling analysis for honeycomb auxetic-core sandwich toroidal shell segments with CNT-reinforced face sheets surrounded by elastic foundations under the radial pressure is presented in this study. The basic equation system of shells is established based on the von Kármán–Donnell nonlinear shell theory, combined with Stein and McElman approximation. Meanwhile, the foundation-shell elastic interaction is simulated by the foundation model based on the Pasternak assumption. The Galerkin procedure is utilized to achieve the pre-buckling and post-buckling responses for the shell, from which the radially critical buckling load is determined. Numerical analysis shows the various influences of auxetic-core layer, CNT-reinforced face sheets, and elastic foundation on the pre-buckling and postbuckling behavior of sandwich shells with CNT reinforced face sheets.

We develop and test a theoretically-based integrative framework of key proximal factors (orientation, pressure, and control) that helps to explain the effects of more general factors (the organisation's strategy, structure, and environment) on intentions to adopt an innovation one year later. Senior managers from 134 organizations were surveyed and confirmatory factor analyses showed that these hypothesized core factors provided a good fit to the data, indicating that our framework can provide a theoretical base to the previous, largely atheoretical, literature. Moreover, in a subgroup of 63 organizations, control mediated the effects of organizational strategy and centralisation on organizational innovation adoption intentions one year later. We suggest this model of core factors enables researchers to understand why certain variables are important to organisational innovation adoption and promotes identification of fertile research areas around orientation, pressure and control, and it enables managers to focus on the most proximal triggers for increasing innovation adoption.

A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners subjected to external pressure is presented in this paper. By employing the Donnell shell theory, the geometrical nonlinearity in Von Kármán sense and developed Lekhnitskii’s smeared stiffener technique, the governing equations of sandwich functionally graded circular cylindrical shells are derived. Resulting equations are solved by applying the Galerkin method to obtain the explicit expression of critical buckling external pressure load and postbuckling load–deflection curve. Effects of spiral stiffeners, thermal environment, external pressure, and geometrical parameters on nonlinear buckling behavior of sandwich functionally graded circular cylindrical shells are shown in numerical results.

The collapse of cylindrical shells under external fluid pressure is generally controlled by elastic buckling, material failure or a combination thereof. Composites like other laminated materials suffer from layer separation or delamination, which may affect the stiffness and stability of the structural component. Deep delaminations, near cylinder mid surface, are expected to reduce the effective flexural stiffness of the shell wall and lead to possible premature collapse. This problem is treated numerically and studied parametrically. A Fourier series-based 2-D shell finite element is formulated for delaminated composite long cylinders. The compatibility of deformation at the delamination tip is maintained by means of Lagrange multipliers. Contact between the separated layers is taken into account through a penalty formulation. A parametric study is conducted to assess the influence of delamination length, depth, and orientation on the reduction in collapse pressure of imperfect cylindrical shells.