An improved local radial basis function method for solving small-strain elasto-plasticity

Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be elusive because of often non-smooth constitutive relations between stress and strain. The novelty in tackling them is the introduction of virtual finite difference stencils to formulate a hybrid radial basis function generated finite difference (RBF-FD) method, which is used to solve smallstrain von Mises elasto-plasticity for the first time by this original approach. The paper further contrasts the new method to two alternative legacy RBF-FD approaches, which fail when applied to this class of problems. The three approaches differ in the discretization of the divergence operator found in the balance equation that acts on the non-smooth stress field. Additionally, an innovative stabilization technique is employed to stabilize boundary conditions and is shown to be essential for any of the approaches to converge successfully. Approaches are assessed on elastic and elasto-plastic benchmarks where admissible ranges of newly introduced free parameters are studied regarding stability, accuracy, and convergence rate

Применение программного продукта «Яндекс.Сервер» для организации поиска в электронном каталоге библиотеки

The huge amounts of information accumulated by libraries in recent years put before developers a problem of the organization of fast and qualitative search which decision is possible with the use of modern search tools of Web-technology. The author examines one of these tools the software product “Yandex. Server”, allowing to organize optimum search in the electronic library catalog. The software product “Yandex. Server” gives a chance to carry out optimum search taking into account morphology of Russian and English languages, as well as the various logical conditions that provides effective and flexible search in the electronic library catalog.Накопленные библиотеками за последние годы огромные массивы информации ставят перед разработчиками задачу организации быстрого и качественного поиска, решение которой возможно с использованием современных поисковых инструментов веб-технологии. Автор рассматривает один из таких инструментов - программный продукт «Яндекс. Сервер», позволяющий организовать оптимальный поиск в электронном каталоге библиотеки с учетом морфологии русского и английского языков, а также различных логических условий

Non-singular method of fundamental solutions for biomedical Stokes flow problems

2siopenopenSincich, Eva; Sarler, BozidarSincich, Eva; Sarler, Bozida

The method of fundamental solutions for the Stokes flow with the subdomain technique

The collocation version of the Method of Fundamental Solutions (MFS) with subdomains is introduced in the present work for the solution of the 2D Stokes flow in backward-facing-step geometry, including Dirichlet and Neumann boundary conditions. The motivation for the present work is the inability of the MFS to solve such problems and the problems with slits and cracks due to the discretization of a single domain. The inability stems from the artificial boundary that is difficult or impossible to properly geometrically set in such cases. The solution for such problems is found by splitting such domains into subdomains. The MFS equations for the equilibrium conditions at the collocation points on the interface between the adjacent subdomains are derived for the Stokes equation. A matrix that simultaneously solves the collocation problem on all the subdomains is formed and solved. A sensitivity study of the MFS results is performed by comparing the relative root mean square error with the reference solution obtained by the classical mesh-based finite volume method on a very fine mesh. The subdomain technique is verified by dividing the domain into 2, 3 and 5 subdomains. The velocity, vorticity and pressure compare very well with the reference solution in all three cases while the solution for the single domain approach is outstandingly poor and inappropriate. The paper shows that the proposed subdomain technique maintains the simplicity, true meshless character and accuracy of the MFS for the Stokes flow in cases where the domain topology requires the use of the subdomain technique

Large scale multiphysics and multiscale simulations based on meshless methods

Structure of a novel meshless solution procedure for calculation of solid and fluid mechanics problems, coupled with the electromagnetic fields, is presented. The discretisation of the governing coupled set of partial differential equations is defined on a set of nodes which can be non-uniformly distributed. The domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented with radial basis functions collocation on a subset of nodes, present in the influence area. The micro-scale problems are tackled through transition rules between the nodes. All governing equations are solved in their strong form. The polygonisation is not present. The large deformation and growth problems are handled by node redistribution and activation of additional nodes. The solution procedure can be adapted in node redistribution and/or refinement sense, which is of utmost importance when coping with the fields exhibiting sharp gradients. The method is extremely simple to code and accurate, allowing straightforward parallelisation. Besides this, the inclusion of complicated physics is transparent, reducing the development time. The coding in 2D or 3D is almost identical. Applications to several large-scale industrial problems are shown, particularly in the field of thermomechanical processing of steel and aluminium alloys