Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 363–370, May–June, 1998.     

Thermal-field propagation in an exocontact zone of a magmatic body and its impact on radiogenic isotope concentrations in minerals

In application of radioactive isotope systems (K-Ar, Rb-Sr etc.) during the last decades, experience was gained not only on their geochronometrical uses, but also on estimations of some important parameters of geological processes, especially temperatures and durations of superimposed thermal events. In this paper, the formation of an exocontact thermal field of a magmatic intrusion is considered as a spreading of a thermal source delta-function. Appropriate solutions of the heat-transfer equation are deduced and correlated with diffusion parameters of the radiogenic argon, coupling radioactive, thermal and kinetic parameters in an exocontant zone of a magmatic body. These solutions were used for quantitative reinterpretations of data taken from Hart's classical paper [The petrology and isotopic mineral age relations of a contact zone in the Front Range, Colorado. J. Geol., 1964, v. 72, pp. 493-525]. Theoretic and measured radiogenic argon and strontium concentrations within exocontact aureoles are found to be in good concordance.     

Evolution of the Theory of Laminated Plates and Shells

The theory of laminated plates and shells is considered. Three-dimensional models of layered systems and methods of reducing them to two-dimensional models are elucidated. An analysis is made of how two-dimensional models are constructed by the method of hypotheses. Two basic approaches to the construction are presented: one leads to the discrete structural theory of laminated systems and the other to continuous structural theory. Attention is drawn to transverse shear and reduction in nonclassical theories of high approximation. The finite-element implementation of the theory is described. Examples of analysis by various models are given. Results of an applicability analysis of various theories and experimental data supporting them are presented. New research areas for the theory of laminated structures are pointed out.     

Parametric Vibrations of a Three-Layer Conical Piezoshell

Based on the Kirchhoff-Love hypotheses and adequate supplementary hypotheses for the distribution of electric field quantities, a model for parametric vibrations of composite shells of revolution made of a passive (without a piezoeffect) middle layer and two active (with a piezoeffect) surface layers under the action of harmonic mechanical and electric loads is developed. The dissipative material properties are taken into account by linear viscoelastic models. Since the vibrations on the boundary of the main domain of dynamic instability (MDDI) are harmonic, the investigation of this domain, in a first approximation, is reduced to generalized eigenvalue problems, which are solved by the finite-element method. The problem on parametric vibrations of a three-layer conical shell under harmonic mechanical loading is considered. The influence of the shell thickness, dissipation, and electric boundary conditions on the MDDI is investigated. Two limiting cases of electric boundary conditions are considered, where the electrodes are short-circuited or not. The curves presented show a considerable influence of the electric boundary conditions on the characteristics of the MDDI, namely on its width and position on the frequency axis and on the critical parameter of excitation.     

Calculation of the stress-strain state and stability of laminated shells with allowance for the actual properties of the materials of the layers

Kiev Automobile-Transportation Institute. Translated from Prikladnaya Mekhanika, Vol. 28, No. 2, pp. 38–46, February, 1992.     

Simulation of conditions for fabrication of optical nanowaveguides in the form of chains of spherical metal nanoparticles by electrostatic functionalization of the process substrate

A method is proposed for electrostatic functionalization of substrates used to prepare ordered structures composed of closely spaced plasmon-resonant nanoparticles. The method ensures selective deposition of nanoparticles from the bulk of a colloidal system onto the substrates. This method is based on placing a metal nanotemplate of a required configuration at the opposite side of a substrate, with an electric potential being applied to the template. A mathematical model is developed to ensure that the system parameters responsible for the deposition of metal nanoparticles into ordered single-domain structures on the substrate from a bulk sol in a nonuniform electric field generated by the nanotemplate correspond to the real experimental conditions. Since the degree of imperfection of the synthesized chains governs the applicability of these structures to transmission of the optical excitation at the frequency of the surface plasmon of the particles, the dependence of the degree of imperfection on the physicochemical and electrical parameters of the system is studied using the Brownian-dynamics model. The calculations of the spectral and transmission properties of nanowaveguides of this type are exemplified.     

Nonaxisymmetric oscillations of shells of revolution induced by nonstationary thermal effects

The finite-element method of solving the dynamic behavior of shells of revolution under nonstationary thermal effects, which is the basis of a precise theory of shells (a quadratic change of lateral shear strain in thickness is hypothesized), is investigated. Ukrainian Transportation University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 69–76, July, 1999.