scholarly journals BEM Solutions of Frequency Domain Gradient Elastodynamic 3-D Porblems

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
D. Polyzos ◽  
K. G. Tsepoura ◽  
D. E. Beskos
Keyword(s):  
Integral Representation ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Normal Derivative ◽  
Solution Procedure ◽  
Boundary Integral ◽  
Material Behavior ◽  
Linear Elastic ◽  
Microstructural Effects ◽  
Boundary Integral Representation

A boundary element methodology is presented for the frequency domain elastodynamic analysis of three-dimensional solids characterized by a linear elastic material behavior coupled with microstructural effects taken into account with the aid of the simple gradient elastic theory of Aifantis. A variational statement is established to determine all possible classical and non-classical (due to gradient terms) boundary conditions of the general boundary value problem. The gradient frequency domain elastodynamic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well posed problem. All the kernels in the integral equations are explicitly provided. Surface quadratic quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. The solution procedure is described in detail. A numerical example serves to illustrate the method and demonstrate its accuracy. The present version of the method does not provide explicit expressions for the computation of interior stresses.

Three-Dimensional LEFM Prediction of Fatigue Crack Propagation in a Gas Turbine Disk Material at Component Near Conditions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Christian Busse ◽  
David Gustafsson ◽  
Patrik Rasmusson ◽  
Björn Sjödin ◽  
Johan J. Moverare ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Crack Propagation ◽  
Gas Turbine ◽  
Plastic Flow ◽  
Fatigue Crack Propagation ◽  
Three Dimensional ◽  
Turbine Disk ◽  
Material Behavior ◽  
Linear Elastic ◽  
Disk Material

In this paper, the possibility to use linear elastic fracture mechanics (LEFM), with and without a superimposed residual stress field, to predict fatigue crack propagation in the gas turbine disk material Inconel 718 has been studied. A temperature of 400 °C and applied strain ranges corresponding to component near conditions have been considered. A three-dimensional crack propagation software was used for determining the stress intensity factors (SIFs) along the crack path. In the first approach, a linear elastic material behavior was used when analyzing the material response. The second approach extracts the residual stresses from an uncracked model with perfectly plastic material behavior after one loading cycle. As a benchmark, the investigated methods are compared to experimental tests, where the cyclic lifetimes were calculated by an integration of Paris' law. When comparing the results, it can be concluded that the investigated approaches give good results, at least for longer cracks, even though plastic flow was taking place in the specimen. The pure linear elastic simulation overestimates the crack growth for all crack lengths and gives conservative results over all considered crack lengths. Noteworthy with this work is that the 3D-crack propagation could be predicted with the two considered methods in an LEFM context, although plastic flow was present in the specimens during the experiments.

Alternative Boundary-Integral Representations of Ship Waves

2002 ◽  
Author(s):  
Francis Noblesse ◽  
Chi Yang ◽  
Dane Hendrix ◽  
Rainald Lo¨hner
Keyword(s):  
Integral Representation ◽  
Fundamental Problem ◽  
Boundary Integral ◽  
Ship Hull ◽  
Integral Representations ◽  
Singular Boundary ◽  
Ship Waves ◽  
Classical Boundary ◽  
The Green Function ◽  
Boundary Integral Representation

The fundamental problem of determining the free-surface potential flow that corresponds to a given flow at a ship hull surface is reconsidered. Stokes’ theorem is used to transform the dipole distribution over the ship hull surface in the classical boundary-integral representation of the velocity potential. This Stokes’ transformation yields a weakly-singular boundary-integral representation that defines the potential in terms of the Green function G and related functions that are no more singular than G. Accordingly, the velocity representation only involves functions that are no more singular than ∇G.

COMPUTATIONAL HOMOGENIZATION OF POLYCRYSTALLINE MATERIALS WITH PORES: A THREE-DIMENSIONAL GRAIN BOUNDARY FORMULATION

2012 ◽  
Vol 04 (03) ◽  
pp. 1250012 ◽  
Author(s):  
F. TRENTACOSTE ◽  
I. BENEDETTI ◽  
M. H. ALIABADI
Keyword(s):  
Grain Boundary ◽  
Mechanical Model ◽  
Volume Fraction ◽  
Effective Properties ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Elastic Problem ◽  
Polycrystalline Materials ◽  
Effective Material Properties ◽  
Boundary Integral Representation

In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a 3D grain boundary micro mechanical model. The volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The formulation is built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi Tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are obtained through material homogenization, computing the volume averages of micro-strains and stresses and taking the ensemble average over a certain number of microstructural samples. The obtained results show the capability of the model to assess the macroscopic effects of porosity.

Some boundary integral equation solutions for three-dimensional stress concentration problems

1983 ◽  
Vol 18 (4) ◽  
pp. 207-215 ◽  
Author(s):  
M J Abdul-Mihsein ◽  
R T Fenner
Keyword(s):  
Integral Equation ◽  
Stress Concentration ◽  
Stress Analysis ◽  
Boundary Integral Equation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Circular Cylinders ◽  
Linear Elastic ◽  
Circular Holes ◽  
Stress Concentration Factors

The boundary integral equation (BIE) method for three-dimensional linear, elastic stress analysis is applied to some stress concentration problems associated with transverse circular holes in either hollow or solid circular cylinders subject to axial tension or torsion, also offset-oblique holes in cylinders subject to internal pressure. Satisfactory agreement is obtained with some previously published experimental results, although computed maximum stress concentration factors are generally higher than those obtained experimentally. The BIE method is shown to be a very useful tool for solving three-dimensional problems of engineering stress analysis.

An Integral Formulation for Dynamic Poroelasticity

1991 ◽  
Vol 58 (2) ◽  
pp. 588-591 ◽  
Author(s):  
Jose´ Dominguez
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Integral Representation ◽  
Frequency Domain ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Integral Formulation ◽  
Equation Formulation ◽  
Independent Variables ◽  
Integral Equation Formulation

A boundary integral equation formulation for dynamic poroelasticity in the frequency domain is presented. The formulation is accomplished using the solid displacements and the fluid stress as independent variables. The integral representation of the fluid stress is obtained using a fundamental solution corresponding to a combination of body forces applied in the solid and in the fluid.

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