Boundary-based finite element method for two-dimensional anisotropic elastic solids with multiple holes and cracks

Published on Jun 1, 2017in Engineering Analysis With Boundary Elements2.964
路 DOI :10.1016/J.ENGANABOUND.2017.03.003
Chyanbin Hwu25
Estimated H-index: 25
(NCKU: National Cheng Kung University),
Shao Tzu Huang1
Estimated H-index: 1
(NCKU: National Cheng Kung University),
Chung Chaio Li1
Estimated H-index: 1
(NCKU: National Cheng Kung University)
Sources
Abstract
Abstract A special boundary element for the two-dimensional anisotropic elastic solids containing a single elliptical hole or crack is applied. The main feature of this special boundary element is that no meshes are needed along the hole or crack boundary. Take this special boundary element as a base, in this paper a new method called boundary-based finite element method is developed to deal with the problems of two-dimensional anisotropic elastic solids containing multiple holes and cracks. This method is established by using the relation between nodal force of finite element and surface traction of boundary element. With the aid of this relation, a combination of boundary elements can be transformed into a single finite element. By purposely arranging each subregion with a single hole or crack and assembling the entire region according to the rule of finite element method, the problems with multiple holes and cracks can be solved. Furthermore, simple formulae to evaluate the stress concentration factor of hole and the stress intensity factors of crack are derived, by which these factors can be evaluated by using only the remote boundary displacements and tractions. Accuracy and efficiency are illustrated by comparison with analytical solutions, conventional boundary element, and finite element method.
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Abstract In order to solve the three-dimensional problem of crack initiation in a cavity and propagation in an elastic medium under the effect of pumping a viscous liquid inside the cavity, a modification of the boundary element method is used for determining the strain鈥搒tress state in vicinity of the cavity with the crack connected to it, loaded with the pumped-in viscous liquid. The foundation of the method is equations of elastic equilibrium written in the form of boundary integral equations....
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#1I. A. Alatawi (Durham University)H-Index: 2
#2Jon Trevelyan (Durham University)H-Index: 19
We introduce an alternative method in computational fracture mechanics to evaluate Stress Intensity Factors (SIFs) directly using the Extended Dual Boundary Element Method (XBEM) for 2D problems. Like other enrichment approaches, the new approach is able to yield accurate results on coarse discretisations, and the enrichment increases the problem size by only two degrees of freedom per crack tip. The BEM equations formed by collocation at nodes are augmented by two additional equations that enfo...
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#1Y.C. ChenH-Index: 4
#2Chyanbin Hwu (NCKU: National Cheng Kung University)H-Index: 25
Abstract By using the anisotropic elastostatic fundamental solutions and employing the dual reciprocity method, a special boundary element method (BEM) was developed in this paper to perform elastodynamic analysis of anisotropic elastic plates containing holes, cracks or interfaces. The system of ordinary differential equations obtained for the vibration transient analysis was solved using the Houlbolt's algorithm and modal superposition method. These equations were reduced to the standard eigen...
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#1Qing-Hua Qin (Henan University of Technology)H-Index: 58
#2Hui Wang (Henan University of Technology)H-Index: 23
In this paper, a three-dimensional material point human head model is constructed from the computed tomography (CT) scanned images of an adult male volunteer, and used to study the dynamic response of human head under the impact of a three-dimensional cylindrical lead projectile with a speed of 6.4 m/s. The model consists of skull bone, brain tissue and membrane of human head, which is close to the real one. The skull and membrane are modeled by an elastic constitutive model, and the brain tissu...
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#1Chyanbin HwuH-Index: 25
Linear Anisotropic Elastic Materials.- Lekhnitskii Formalism.- Stroh Formalism.- Infinite Space, Half-Space, and Bimaterials.- Wedges and Interface Corners.- Holes.- Cracks.- Inclusions.- Contact Problems.- Thermoelastic Problems.- Piezoelectric Materials.- Plate Bending Analysis.- Coupled Stretching-Bending Analysis.- Holes/Cracks/Inclusions in Laminates.- Boundary Element Analysis.
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The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the stati...
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#1Chyanbin Hwu (NCKU: National Cheng Kung University)H-Index: 25
#2Y.C. Liang (NCKU: National Cheng Kung University)H-Index: 2
Abstract Usually, the stress concentration factors (SCFs) for holes and the stress intensity factors (SIFs) for cracks are evaluated by using the data near holes or cracks. However, the abrupt change of the stresses near holes, especially near crack tips, may lead to an unavoidable error. Thus, it is always interesting to find an equivalent formulation for SCF and SIF by using only remote boundary responses (displacements, stresses and strains) cooperating with the necessary geometric data. Thro...
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#2H.-K. Hong (NTU: National Taiwan University)H-Index: 1
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This paper presents a boundary element method (BEM) analysis of linear elastic fracture mechanics in two-dimensional solids. The most outstanding feature of this new analysis is that it is a single-domain method, and yet it is very accurate, efficient and versatile: Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched, internal or edged type with a straight or curved shape. Loading ...
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#1Chongmin Song (EPFL: 脡cole Polytechnique F茅d茅rale de Lausanne)H-Index: 52
#2John P. Wolf (EPFL: 脡cole Polytechnique F茅d茅rale de Lausanne)H-Index: 35
The scaled boundary finite-element method, alias the consistent infinitesimal finite-element cell method, is developed starting from the governing equations of linear elastodynamics. Only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals must be evaluated. General anisotropic material is analysed without any increase in computational effort. Boundary con...
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Abstract null null Recently, we corrected the Green's functions for holes/cracks in composite laminates under coupled stretching-bending deformation. Through these corrected Green's functions, the fundamental solutions required for the special boundary element of holes/cracks in composite laminates are derived. By the use of dual coordinates, the derived fundamental solutions can be further applied to the cases of inclined holes and cracks. Moreover, a formula evaluating the stress intensity fac...
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Abstract null null In this study the time-stepping method, which can convert the problem of anisotropic viscoelasticity into two sets of elastic-like system, is employed for both analytical solutions and boundary element method (BEM) to solve the two-dimensional problems of holes and cracks in anisotropic viscoelastic solids. Based upon this method and the available solutions for the corresponding elastic problems, some analytical solutions for the two-dimensional problems of holes and cracks in...
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A new approach of multi-scale simulation via coupling of boundary element and finite element is proposed to predict fracture toughness and crack propagation of a single layer graphene sheet. In this simulation a molecular dynamics-based nonlinear beam element is developed for the atomistic model near the crack tip, whereas a special two-dimensional boundary element is employed for the continuum model in the remaining field of the cracked specimen. The material and section properties required in ...
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