scholarly journals Dynamic Response of a Cracked Viscoelastic Anisotropic Plane Using Boundary Elements and Fractional Derivatives

2018 ◽  
Vol 48 (2) ◽  
pp. 24-49 ◽  
Author(s):  
Tsviatko V. Rangelov ◽  
Petia S. Dineva ◽  
George D. Manolis
Keyword(s):  
Wave Propagation ◽  
Bulk Material ◽  
Numerical Technique ◽  
Surface Elasticity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Nano Scale ◽  
Viscoelastic Wave Propagation ◽  
Macro Scale ◽  
Modelling Effort

Abstract The aim of this study is to develop an efficient numerical technique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed approach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equation derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary conditions at the nano-scale. Conditions of plane strain are assumed to hold. Following verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress intensity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the presence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material.

scholarly journals Wave Scattering by Cracks at Macro- and Nano-Scale in Anisotropic Plane by Boundary Integral Equation Method

2016 ◽  
Vol 46 (4) ◽  
pp. 19-35 ◽  
Author(s):  
Petia Dineva ◽  
Tsviatko Rangelov
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Wave Scattering ◽  
Surface Elasticity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Boundary Integral Equation Method ◽  
Equation Method ◽  
Nano Scale ◽  
Subsequent Step

AbstractElastic wave scattering by cracks at macro- and nano-scale in anisotropic plane under conditions of plane strain is studied in this work. Furthermore, time-harmonic loads due to incident plane longitudinal P- or shear SV- wave are assumed to hold. In a subsequent step, the elastodynamic fundamental solution for general anisotropic continua derived in closed-form via the Radon transform is implemented in a numerical scheme based on the traction boundary integral equation method (BIEM). The surface elasticity effect in the case of nano-crack is taken into consideration via non-classical boundary condition along the crack surface proposed by Gurtin and Murdoch [1]. The numerical results obtained herein reveal substantial differences between anisotropic materials containing a macro- and a nano-crack in terms of their dynamic stress response, where the latter case demonstrates clearly the strong influence of the size-effects. Finally, these types of examples serve to illustrate the present approach and to show its potential for evaluating the stress concentration fields (SCF) inside cracked nanocomposites. The obtained results concern the reliability and safety of the advancing nanomaterials.

Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 765-771 ◽  
Author(s):  
B. Kummer ◽  
A. Behle ◽  
F. Dorau
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Hybrid Scheme ◽  
Finite Difference Techniques

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.

Analysis of Clamped Plates on Elastic Foundation by the Boundary Integral Equation Method

1984 ◽  
Vol 51 (3) ◽  
pp. 574-580 ◽  
Author(s):  
J. T. Katsikadelis ◽  
A. E. Armena`kas
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Elastic Foundation ◽  
Boundary Integral Equation ◽  
Numerical Evaluation ◽  
Boundary Integral Equations ◽  
Numerical Technique ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Plates On Elastic Foundation

In this investigation the boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is developed for analyzing clamped plates of any shape resting on an elastic foundation. A numerical technique for the solution to the boundary integral equations is presented and numerical results are obtained and compared with those existing from analytical solutions. The effectiveness of the BIE method is demonstrated.

A Submerged Compliant Breakwater

1992 ◽  
Vol 114 (2) ◽  
pp. 83-90 ◽  
Author(s):  
A. N. Williams ◽  
P. T. Geiger ◽  
W. G. McDougal
Keyword(s):  
Flexural Rigidity ◽  
Numerical Technique ◽  
Structural Parameters ◽  
Unit Length ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Numerical Results ◽  
Small Scale

A numerical technique is utilized to investigate the dynamics of a submerged compliant breakwater consisting of a flexible, beamlike structure anchored to the seabed and kept under tension by a small buoyancy chamber at the tip. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a one-dimensional beam of uniform flexural rigidity and mass per unit length subjected to a constant axial force. The boundary integral equation method is applied to the fluid domain, modifications are made to the basic formulation to account for the zero thickness of the idealized structure and the singularity in the fluid velocity which occurs at the breakwater tip. The dynamic behavior of the breakwater is described through an appropriate Green function. Numerical results are presented which illustrate the global influence of the tip singularity on the solution and the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. Small-scale physical model tests were also carried out to validate the foregoing theory. In general, the agreement between experimental and numerical results was reasonable, but with considerable scatter.

scholarly journals DYNAMICS OF POROVISCOELASTIC PRISMATIC SOLID FOR VARIOUS VALUES OF MATERIAL PERMEABILITY

2019 ◽  
Vol 81 (4) ◽  
pp. 416-428
Author(s):  
A.A. Ipatov ◽  
F. dell'Isola ◽  
I. Giorgio ◽  
I. Rahali ◽  
S.R. Eugster ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Boundary Element ◽  
Mixed Boundary ◽  
Viscoelastic Behavior ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Dynamic Responses ◽  
Element Discretization ◽  
Engineering Sciences ◽  
Element Approach

In present paper wave propagation poroviscoelastic solids is studied. Study of wave propagation in saturated porous media is an important issue of engineering sciences. The poroelasticity theory was developed and nowadays is an important to engineering applications. Also research is dedicated to modeling of a slow compressional wave in poroviscoelastic media by means of boundary-element method. Poroviscoelastic formulation is based on Biot's model of fully saturated poroelastic media with a correspondence principal usage. Standard linear solid model is employed in order to describe viscoelastic behavior of the skeleton in porous medium. The boundary-value problem of the three-dimensional dynamic poroviscoelasticity is written in terms of Laplace transforms. Direct approach of the boundary integral equation method is employed. The boundary-element approach is based on the mixed boundary-element discretization of surface with generalized quadrangular elements. Subsequent application of collocation method leads to the system of linear equations, and then to the solution in Laplace domain. Numerical inversion of Laplace transform is used to obtain time-domain solution. The problem of the load acting on a poroelastic prismatic solid is solved by means of developed software based on boundary element approach. An influence of permeability of porous material on dynamic responses is studied. Slow wave phenomena appearance is demonstrated. Viscosity parameter influence on dynamic responses of displacements and pore pressure is studied.

Analysis of Cracked Body Strengthened by Adhesively Bonded Patches by BEM-FEM Coupling

2020 ◽  
pp. 2041013
Author(s):  
Binh V. Pham ◽  
Thai Binh Nguyen ◽  
Jaroon Rungamornrat
Keyword(s):  
Numerical Technique ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Singular Boundary ◽  
Adhesively Bonded ◽  
Crack Face ◽  
Finite Element Procedure ◽  
The Right

This paper presents an efficient numerical technique capable of handling the stress analysis of three-dimensional cracked bodies strengthened by adhesively bonded patches. The proposed technique is implemented within the framework of the coupling of the weakly singular boundary integral equation method and the standard finite element procedure. The former is applied to efficiently treat the elastic body containing cracks, whereas the latter is adopted to handle both the adhesive layers and patches. The approximation of the near-front relative crack-face displacement is enhanced by using local interpolation functions that can capture the right asymptotic behavior. This also offers the direct calculation of the stress intensity factors along the crack front. A selected set of results is reported to demonstrate the capability of the proposed technique and the influence of various parameters on the performance of the strengthening.

Anisotropic stress analysis of inclusion problems using the boundary integral equation method

1992 ◽  
Vol 27 (2) ◽  
pp. 67-76 ◽  
Author(s):  
C L Tan ◽  
Y L Gao ◽  
F F Afagh
Keyword(s):  
Integral Equation ◽  
Stress Analysis ◽  
Boundary Integral Equation ◽  
Numerical Technique ◽  
Integral Equation Method ◽  
Anisotropic Elasticity ◽  
Boundary Integral ◽  
Element Formulation ◽  
Inclusion Problems ◽  
Structural Applications

Numerical methods for stress analysis are increasingly being employed in the micromechanics of solids. In this paper, the boundary integral equation (BIE) method for two-dimensional general anisotropic elasticity, based on the quadratic isoparametric element formulation, is extended to treating some inclusion problems. All the cases analysed involved an elliptical zirconia inclusion in an alumina matrix, noting that ZrO2–Al2O3 is an advanced ceramic increasingly used in structural applications. The BIE results are compared with those calculated using Eshelby's equivalent inclusion approach where possible, and excellent agreements between them are obtained. The present work demonstrates the suitability of using this numerical technique for analysing such problems and, in particular, the ease with which it may be used even in the case of general anisotropy.

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