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.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

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.

scholarly journals NUMERICAL ANALYSIS OF THE DYNAMICS OF THREE-DIMENSIONAL ANISOTROPIC BODIES BASED ON NON-CLASSICAL BOUNDARY INTEGRAL EQUATIONS

2021 ◽  
Vol 83 (1) ◽  
pp. 76-86
Author(s):  
A.A. Belov ◽  
A.N. Petrov
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Classical Approach ◽  
Classical Boundary ◽  
Nonclassical Formulation

The application of non-classical approach of the boundary integral equation method in combination with the integral Laplace transform in time to anisotropic elastic wave modeling is considered. In contrast to the classical approach of the boundary integral equation method which is successfully implemented for solving three-dimensional isotropic problems of the dynamic theory of elasticity, viscoelasticity and poroelasticity, the alternative nonclassical formulation of the boundary integral equations method is presented that employs regular Fredholm integral equations of the first kind (integral equations on a plane wave). The construction of such boundary integral equations is based on the structure of the dynamic fundamental solution. The approach employs the explicit boundary integral equations. The inverse Laplace transform is constructed numerically by the Durbin method. A numerical solution of the dynamic problem of anisotropic elasticity theory based on the boundary integral equations method in a nonclassical formulation is presented. The boundary element scheme of the boundary integral equations method is built on the basis of a regular integral equation of the first kind. The problem is solved in anisotropic formulation for the load acting along the normal in the form of the Heaviside function on the cube face weakened by a cubic cavity. The obtained boundary element solutions are compared with finite element solutions. Numerical results prove the efficiency of using boundary integral equations on a single plane wave in solving three-dimensional anisotropic dynamic problems of elasticity theory. The convergence of boundary element solutions is studied on three schemes of surface discretization. The achieved calculation accuracy is not inferior to the accuracy of boundary element schemes for classical boundary integral equations. Boundary element analysis of solutions for a cube with and without a cavity is carried out.

On mixed boundary value problems for the Helmholtz equation

1977 ◽  
Vol 77 (1-2) ◽  
pp. 65-77 ◽  
Author(s):  
R. Kress ◽  
G. F. Roach
Keyword(s):  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Theoretic Approach ◽  
Mixed Boundary Value Problems

SynopsisExistence and uniqueness theorems are obtained for a class of mixed boundary value problems associated with the three-dimensional Helmholtz equation. In this context the boundary of the region of interest is assumed to consist of the union of a finite number of disjoint, closed, bounded Lyapunov surfaces on some of which are imposed Dirichlet conditions whilst Neumann conditions are imposed on the remainder. An integral equation method is adopted throughout. The required boundary integral equations are generated by a modified layer theoretic approach which extends the work of Brakhage and Werner [1] and Leis [2, 3].

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