On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model

In this research, an elastic model based on the continuum mechanics is developed to study the static behaviors of functionally graded (FG) arbitrary straight-sided quadrilateral nanoplates. The model is constructed in the framework of Gurtin-Murdoch’s surface and Mindlin’s plate theories to account for the surface energy and shear deformation effects, simultaneously. The variational differential quadrature (VDQ) method is used along with a mapping technique to do the discretization process in a variational framework by means of differential and integral operators. Consequently, a weak form of governing equations is obtained from the energy quadratic representation of the problem. The solution method is of a distinguished feature as it involves just the first-order derivative of the field components in the mapping and discretization. After assuring the effectiveness of presented model by doing comparative studies, the critical buckling load and static deflection of the FG nanoplates with different shapes in geometry are investigated considering the surface effects. It is found that the surface energies effect on the static behavior of the rectangular nanoplates is more significant as compared to the non-rectangular nanoplates.

Computational methods of continuum mechanics for exaflop computer systems

Рассмотрены вопросы использования экзафлопсных вычислений для решения прикладных задач. На основе обзора работ в этой области выделены наиболее актуальные вопросы, связанные с экзафлопсными вычислениями. Особое внимание уделено особенностям программного обеспечения, алгоритмам и численным методам для экзафлопсных суперЭВМ. Приведены примеры разработки новых и адаптации существующих алгоритмов и численных методов для решения задач механики сплошной среды. Сделан анализ наиболее популярных приложений The article deals with applied issues which arise when exascale computing are used to solve applied problems. Based on the review of works in this area, the most pressing issues related to exascale calculations are highlighted. Particular attention is paid to software features, algorithms and numerical methods for exaflop supercomputers. The requirements for such programs and algorithms are formulated. Based on the review of existing approaches related to achieving high performance, the main fundamentally different and non-overlapping directions for improving the performance of calculations are highlighted. The question of the necessity for criteria of applicability for computational algorithms for exaflop supercomputers is raised. Currently, the only criterion which is used, demands the absence of a significant drop in efficiency in the transition from a petaflop calculation to a ten-petaflop calculation. In the absence of the possibility of such calculations, simulation modelling can be carried out. Examples of development for new and adaptation of existing algorithms and numerical methods for solving problems of continuum mechanics are given. The fundamental difference between algorithms specially designed for exascale machines and algorithms adapted for exaflops is shown. The analysis of publications has showed that in the field of solving problems of continuum mechanics, the approach not associated with the development of new, but rather with the adaptation of existing numerical methods and algorithms to the architecture of exaflop supercomputers prevails. The analysis of the most popular applications is made. The most relevant application of exaflop supercomputers in this area is computational fluid dynamics. This is because hydrodynamic applications are rich and diverse field. The number of publications indicates that the involvement of high-performance computing now is available and in demand

Application of vectorized algorithms for solving problems of continuum mechanics

The paper discusses the possibilities of constructing vectorized algorithms for solving problems of continuum mechanics, as well as the specialties of their software implementation in the MATLAB. These algorithms, on the one hand, widely use MATLAB functions designed to treat vectors and sparse matrixes, and on the other hand, are distinguished by high efficiency and counting speed.

Cosmic Geodesy Contribution to Geodynamics Monitoring

The cosmic geodesy provides methods and ways of various data acquisition. The collected data may be used for research, calculations and analysis in different fields of interest. According to the reliability and redundancy of data provided by cosmic geodesy methods, it is possible to contribute to the geodynamics monitoring. The geodynamics monitoring enables the tectonic plates movement tracking and predicts the movements which may result in disasters. Applying data provided by cosmic geodesy methods in the form of permanent observation station positions and their changes in time, in calculations, whose physical nature is based on the continuum mechanics, makes possible to monitor the direction, locality and size of visualised deformation tensors.

Developing a module to convert OpenFOAM computational meshes to the msh format

The paper reveals the features of developing an application for conversion of computational meshes built in OpenFOAM to the msh format applied for numerical simulation of continuum mechanics (CM) problems with the ANSYS FLUENT platform. Some companies apply this platform in parallel with OpenFOAM that requires a mesh conversion module. Although there are program tools capable to solve this problem, their application involves some difficulties, mainly the necessity to pay for a license, absence of complete documentation, paid technical support. Thus, the described problem is actual and its solution – developing a conversion module – is the study purpose. The article discloses features of the OpenFOAM utility for conversion, a list of technologies to develop a module, module action, results of its performance test using a CM problem. The study findings are statements of scientific novelty and expected practical significance.

Advancing a generalized method for solving problems of continuum mechanics as applied to the Cartesian coordinate system

Solving the problem of continuum mechanics has revealed the defining generalizations using the function argument method. The aim of this study was to devise new approaches to solving problems of continuum mechanics using defining generalizations in the Cartesian coordinate system. Additional functions, or the argument of the coordinates function of the deformation site, are introduced into consideration. The carriers of the proposed function arguments should be basic dependences that satisfy the boundary or edge conditions, as well as functions that simplify solving the problem in a general form. However, there are unresolved issues related to how not the solutions themselves should be determined but the conditions for their existence. Such generalized approaches make it possible to predict the result for new applied problems, expand the possibilities of solving them in order to meet a variety of boundary and edge conditions. The proposed approach makes it possible to define a series of function arguments, each of which can be a condition of uniqueness for a specific applied problem. Such generalizations concern determining not the specific functions but the conditions of their existence. From these positions, the flat problem was solved in the most detailed way, was tested, and compared with the studies reported by other authors. Based on the result obtained, a mathematical model of the flat applied problem of the theory of elasticity with complex boundary conditions was built. Expressions that are presented in coordinateless form are convenient for analysis while providing a computationally convenient context. The influence of the beam shape factor on the distribution of stresses in transition zones with different intensity of their attenuation has been shown. By bringing the solution to a particular result, the classical solutions have been obtained, which confirms its reliability. The mathematical substantiation of Saint-Venant's principle has been constructed in relation to the bending of a beam under variable asymmetric loading