Wyniki wyszukiwania - BazTech

1

The effect of model size and boundary conditions on the representativeness of digital material representation simulations of ferritic-pearlitic sample compression

Perzyński Konrad

Computer Methods in Materials Science

|

2022

|

Vol. 22, No. 2

59--66

EN

The main objective of this work is to investigate the representativeness of the digital material representation (DMR) models of ferritic-pearlitic steel generated by the hybrid cellular automata (CA) / Monte Carlo (MC) algorithm. Particular attention is focused on determining the effect of the size of the digital representation model on its representativeness under deformation conditions simulated with the finite element (FE) framework. In addition, the effect of periodic and non-periodic boundary conditions on the deformation behaviour of DMR models is analysed. A dedicated buffer zone approach applied the periodic boundary conditions on non-periodic finite element models. The results of equivalent stresses and strains and their average values are used to evaluate the differences between the models’ predictions.

2

Statistical analysis of mechanical damage in arrays of mixed nanopillars

Derda T.

Journal of Applied Mathematics and Computational Mechanics

|

2015

|

Vol. 14, nr 1

43--53

EN

We apply the Fibre Bundle Model to study critical loads and catastrophic avalanches in arrays of axially loaded nanopillars under so-called local load sharing. Nanopillars with assigned random strength-thresholds are located in the nodes of the supporting square lattice. We analyzed different mixtures of weak and strong pillars, i.e. we use distributions of strength-thresholds drawn from two different uniform distributions.

3

Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method

Łoś M., Paszyński M, Dalcin L., Calo V.

Computer Methods in Materials Science

|

2015

|

Vol. 15, No.1

213--218

EN

In this paper we analyze the problem of implementing periodic boundary conditions in the isogeomotric finite element method (ISO-FEM). The ISO-FEM method uses the B-spline-based basis functions, which facilitates usage of the same basis functions for approximation of the geometry as well as for the numerical solution of the modeled physical phenomena. The usage of the B-spline based basis functions results in CA(p-l) global continuity of the solution. The drawback is a difficulty in implementing the periodic boundary conditions, and special dedicated methods are necessary. In this paper we present two algorithms implementing the periodic boundary conditions. The first one is an iterative algorithm that utilizes widely available block-diagonal LAPACK solver. The second one is a modification of the multi-frontal solver algorithm itself, and it requires a dedicated solver with its source code modified accordingly. The presented methods can be applied in one, two or three-dimensional isogeometric finite element method.

PL

W artykule analizujemy sposób implementacji periodycznych warunków brzegowych w izogeometrycznej metodzie elementów skończonych (ISO-FEM). Metoda ISO-FEM cechuje się użyciem B-spline'ów jako funkcji bazowych, co pozwala na zastosowanie takiej samej bazy wielomianów do odwzorowania geometrii jak również do rozwiązania modelowanego zagadnienia fizycznego. Baza zbudowana z B-spline'ów stopnia p posiada globalną ciągłość C۸(p-l). Z tego też powodu sposób wymuszania periodycznych warunków brzegowych nie jest oczywisty, i konieczne jest zastosowanie specjalnych technik. W artykule tym prezentujemy dwa algorytmy wymuszające periodyczne warunki brzegowe. Pierwszy algorytm iteracyjny umożliwia wykorzystanie powszechnie dostępnych solwerów (takich jak LAPACK) dla macierzy blokowo-diagonalnych, drugi algorytm polega na modyfikacji kodu solwera wielofrontalnego, i z tego względu wymaga dedykowanej implementacji algorytmu solwera. Przedstawione sposoby implementacji periodycznych warunków brzegowych można zastosować w jedno, dwu i trójwymiarowej isogeometrycznej metodzie elementów skończonych.

4

2D FE Micromechanics Modelling of Honeycomb Core Sandwich Panels

Betts Ch., Lin J., Balint D., Atkins A.

Engineering Transactions

|

2012

|

Vol. 60, iss. 3

187-187

EN

A repeating unit cell 2D ?nite element modelling procedure has been established to model the mechanical behaviour of honeycomb core sandwich panels (e.g. Young’s modulus, energy absorbed, etc.). Periodic boundary conditions have been implemented within the model to simulate an in?nitely long sandwich panel. An analytical solution using Timoshenko beam theory has been developed to predict the Young’s modulus of the honeycomb core, and this has been compared with the FE model results; it is found that there is good agreement between the two values. The FE model can shed light on the mechanics of more complex 3D metal foams.

5

Application of Boundary Element Method to Solution of Transient Heat Conduction

Werner-Juszczuk A. A., Sorko S. A.

Acta Mechanica et Automatica

|

2012

|

Vol. 6, no. 4

67-74

EN

The object of this paper is the implementation of boundary element method to solving the transient heat transfer problem with nonzero boundary condition and particularly with periodic boundary condition. The new mathematical BEM algorithm for two dimensional transient heat conduction problem with periodic boundary condition is developed and verified. The results of numerical simulation of transient heat conduction in two dimensional flat plate under non zero initial condition are compared with results obtained with analytical method. Then the practical application of developed algorithm is presented, that is the solution of ground temperature distribution problem with oscillating temperature of ambient. All results were obtained with a new authoring computer program for solving transient heat conduction problem, written in Fortran.

6

A Contribution to the Nature of Periodic Boundary Conditions

Müller M., Ostermeyer G.-P.

Machine Dynamics Problems

|

2009

|

Vol. 33, No. 2

74-78

EN

Many dynamical systems are characterized by the property that the system-determining processes may occur on different scales. Not seldom the model then contains very different dynamical processes, each of them formulated on another length- or timescale. In order to keep the numerical effort small, for those systems the implementation of periodic boundary conditions is a common approach. Some of those systems are additionally determined by anisotropy or preferred directions. For such problems a modified structure of periodic boundary conditions can be helpful to preserve the representational character the system area is bound to. This paper firstly dedicates to the problem of preferred directions. This is followed by the explanation of certain modified periodic boundary conditions and a discussion of their respective manifolds' properties.

7

Solutions for the higher-grade hybrid model of layered superconductors

Sztyren M.

Journal of Technical Physics

|

2006

|

Vol. 47, no 3

149-157

EN

A class of basic solutions for a model of layered superconductors is constructed. The considerations are based on the higher-grade hybrid model, constructed in the previous paper. In particular, for any range K of the Josephson interlayer couplings, we determine the spectrum of excited states with respect to all types of ground states calculated there for an infinite uniform superconductor. We discuss also solutions for a finite number of layers with periodic boundary conditions. In this way, instances of the amplitude-modulated solutions for the infinite stack of layers are found.