Кубанська музична фольклористика: етапи становлення

On the basis of materials related to the history of the Ukrainians in Kuban (of 1792) the author determines that priests, historians, ethnographers, students of local lore, regents, choirmasters, teachers and poets were at the beginnings of Kuban musical study of folklore. The formation of Kuban musical folklore had 3 stages: concert and representational stage (of 1818), stage of collection (of 1865), transcriptional and publishing stage. Bihday, Kontsevych, Zakharchenko and Koshyts made the most considerable contribution in development of this science. The author of the article gives detailed information about their biographies

Interfacing nonmatching FEM meshes: the zero moment rule

This is a tutorial paper that outlines, through a benchmark example, an efiective method for coupling nonmatched flnite element meshes. Coupling is done through a displacement frame interposed between the interface meshes. That frame is treated with a FEM discretization and \glued" to the meshes through localized Lagrange multipliers collocated at mesh-interface nodes. The approach can be used to couple meshes of arbitrary geometry, discretization type (e.g., FEM and BEM) and even meshes of difierent physics (e.g., structure and ∞uids). The example, however, focuses on a simplifled 2D case that can be explained within space constraints. The requirement for preservation of constant stress states leads to an easily visualized condition, called the zero-moment rule or ZMR, that can be used to locate frame nodes on frame geometry. The ZMR provides all possible consistent frame-node conflgurations. Generalizations of the 2D ZMR rule to 3D problems involve partitioning of the frame and are not reported here. Thus the ZMR is necessary but not su-cient. The constant stress consistency condition may be interpreted, according to the reader's taste, as either an interface patch test, a vanishing of the flrst variation of the interface potential under admissible kinematic modes, or a requirement for energy conservation across the interface

A simple algorithm for localized construction of non‐matching structural interfaces

A simple and effective algorithm for the modular construction of non-matched interfaces is presented for the partitioned solution of large-scale structural problems. The formulation is based on a recently developed four-field variational principle, which introduces a connection frame between the interfaced partitions. A key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori. The method is demonstrated with several 2D and 3D example problem

A contact formulation based on localized Lagrange multipliers: Formulation and application to two-dimensional problems

The non-penetration condition in contact problems is traditionally based on the classical Lagrange multiplier method. This method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non-matching. To deal with this problem we introduce a novel element in the Lagrange multiplier approach of contact modelling, namely, a contact frame placed in between contacting bodies. It acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models. Only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic. The contact frame has its own independent freedoms, which allows the formulation to pass contact patch tests by design