scholarly journals Application of Trefftz method for the solution of two-dimensional Poisson’s problem taking into account material properties

2018 ◽  
Vol 19 (6) ◽  
pp. 363-367
Author(s):  
Dorota Borkowska
Keyword(s):  
Material Properties ◽  
Domain Boundary ◽  
Two Dimensional ◽  
Weighted Residual Method ◽  
Boundary Equation ◽  
Weighting Functions ◽  
Trefftz Method ◽  
Classical Formulation ◽  
Dimensional Boundary ◽  
Theoretical And Numerical Analysis

The aim of this paper is theoretical and numerical analysis of one of the nonsingular Trefftz method. Two-dimensional boundary value problem governed by Poisson’s equation is taken as the example. Domain boundary equation is obtained by transformation of classical formulation of the boundary problem with the use of weighted residual method. In this paper the original variation formulation is considered. The solution of the problem is assumed as the superposition of Trefftz functions, which satisfy Laplace’s equation. Taking the same functions as the weighting functions one obtains equations of the Galerkin version of the Trefftz method with symbolic name OS;TT. The paper contains the theoretical analysis of the OS;TT method which is confirmed with numerical example. .

scholarly journals Theoretical and numerical analysis of selected hybrid Trefftz method with the use of method of subdomains coupling based on “frame” concept

2018 ◽  
Vol 19 (12) ◽  
pp. 323-330
Author(s):  
Dorota Borkowska
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Hybrid Method ◽  
Numerical Experiments ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Problem Domain ◽  
Trefftz Method ◽  
Theoretical And Numerical Analysis

The aim of this paper is theoretical and numerical analysis of Trefftz method in Galerkin version, which symbol is O-S;T-T.The analysis was conducted on the example of two-dimensional Poisson’s problem. Domain of interest was divided into homogeneous subdomains. In this way hybrid method was obtained, that is a combination of the boundary method with conventional finite element known from the Finite Element Method. The method based on idea of “frames” was used to couple subdomains. Finally, the results of numerical experiments obtained for two boundary value problems were presented. The accuracy of the method was analyzed depending on the number of Trefftz coefficients.

On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain

2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Boundary

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

Investigation of Contact Conditions During Stamping of a Thin Plate

2020 ◽  
Author(s):  
Harshal Y. Shahare ◽  
Rohan Rajput ◽  
Puneet Tandon
Keyword(s):  
Wave Propagation ◽  
Material Properties ◽  
High Speed ◽  
Fdtd Method ◽  
Propagation Model ◽  
Transmitted Wave ◽  
Two Dimensional ◽  
Contact Conditions ◽  
Simulation Based ◽  
Difference Time

Abstract Stamping is one of the most used manufacturing processes, where real-time monitoring is quite difficult due to high speed of the mechanical press, which leads to deterioration of the accuracy of the products In the present work, a method is developed to model elastic waves propagation in solids to measure contact conditions between die and workpiece during stamping. A two-dimensional model is developed that reduces the wave propagation equations to two-dimensional equations. To simulate the wave propagation inside the die-workpiece model, the finite difference time domain (FDTD) method and modified Yee algorithm has been employed. The numerical stability of the wave propagation model is achieved through courant stability condition, i.e., Courant-Friedrichs-Lewy (CFL) number. Two cases, i.e., flat die-workpiece interface and inclined die-workpiece interface, are investigated in the present work. The elastic wave propagation is simulated with a two-dimension (2D) model of the die and workpiece using reflecting boundary conditions for different material properties. The experimental and simulation-based results of reflected and transmitted wave characteristics are compared for different materials in terms of reflected and transmitted wave height ratio and material properties such as acoustic impedance. It is found that the numerical simulation results are in good agreement with the experimental results.

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