The stability of geometrically nonlinear plate systems under the action of dynamic loads

Relevance. Single-connected and multi-connected plate systems are widely used in construction, aircraft, shipbuilding, mechanical engineering, instrument making. As a result, the study of the stability of geometrically nonlinear plate systems is an urgent topic. But, despite significant achievements in this area, there are still many unsolved problems. Thus, the requests of the above-mentioned areas of application of thin-walled spatial systems require further study of the issue of static and dynamic stability. The aim of the work - development of a method of the dynamic stability analysis of geometrically nonlinear plate systems such as prismatic shells under the action of dynamic compression loads. Methods. A plate system, which is subject to dynamic compression loads in the longitudinal direction, is considered. Kirchhoff - Love hypotheses are taken into account. The material stress-deformation diagram is linear. The displacement of points in the normal direction to the median plane of the plates is determined in the form of the Vlasov expansion. To derive the basic differential equations of stability, the energy method and the variational Vlasov method are used. The extreme value of the total energy is determined using the Euler - Lagrange equation. As a result, a set of basic nonlinear differential equations for studying the buckling of the plate system under the action of dynamic compression loads is obtained. Results. The developed method is used to stability analysis of a geometrically nonlinear prismatic shell with a closed contour of the cross section, under central compression under the action of dynamic loading. The edges of the shell rest on the diaphragm. The buckling of the prismatic shell in the longitudinal direction along one and two half-waves of a sinusoid is studied. The numerical integration of nonlinear differential equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the dependence of the relative deflection on the dynamic coefficient are constructed. The influence of the rate of change of compression stress, the initial imperfection of the system, and other parameters on the criteria for the dynamic stability of the plate system is investigated.

Biomineral Reactivity: The Kinetics of the Replacement Reaction of Biological Aragonite to Apatite

We present results of bioaragonite to apatite conversion in bivalve, coral and cuttlebone skeletons, biological hard materials distinguished by specific microstructures, skeletal densities, original porosities and biopolymer contents. The most profound conversion occurs in the cuttlebone of the cephalopod Sepia officinalis, the least effect is observed for the nacreous shell portion of the bivalve Hyriopsis cumingii. The shell of the bivalve Arctica islandica consists of cross-lamellar aragonite, is dense at its innermost and porous at the seaward pointing shell layers. Increased porosity facilitates infiltration of the reaction fluid and renders large surface areas for the dissolution of aragonite and conversion to apatite. Skeletal microstructures of the coral Porites sp. and prismatic H. cumingii allow considerable conversion to apatite. Even though the surface area in Porites sp. is significantly larger in comparison to that of prismatic H. cumingii, the coral skeleton consists of clusters of dense, acicular aragonite. Conversion in the latter is sluggish at first as most apatite precipitates only onto its surface area. However, the process is accelerated when, in addition, fluids enter the hard tissue at centers of calcification. The prismatic shell portion of H. cumingii is readily transformed to apatite as we find here an increased porosity between prisms as well as within the membranes encasing the prisms. In conclusion, we observe distinct differences in bioaragonite to apatite conversion rates and kinetics depending on the feasibility of the reaction fluid to access aragonite crystallites. The latter is dependent on the content of biopolymers within the hard tissue, their feasibility to be decomposed, the extent of newly formed mineral surface area and the specific biogenic ultra- and microstructures.