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Advances in Boundary Element and Meshless Techniques XVIII
Abstract
PREFACE
The Conferences on Boundary Element and Meshless Techniques are devoted to
fostering the continued involvement of the research community in identifying new problem
areas, mathematical procedures, innovative applications, and novel solution techniques in
both boundary element methods (BEM) and boundary integral equation methods (BIEM).
Previous successful conferences devoted to Boundary Element Techniques were held in
London, UK (1999), New Jersey, USA (2001), Beijing, China (2002), Granada, Spain
(2003), Lisbon, Portugal (2004), Montreal, Canada (2005), Paris, France (2006), Naples,
Italy (2007), Seville, Spain (2008), Athens, Greece (2009), Berlin, Germany (2010),
Brasilia, Brazil (2011), Prague, Czech Republic (2012), Paris, France (2013), Florence,
Italy (2014), Valencia, Spain (2015) and Ankara, Turkey (2016).
The present volume is a collection of edited papers that were accepted for presentation
at the Boundary Element Techniques Conference held at the Radisson Blu Hotel,
Bucharest, Romaina during 11-13th July 2017. Research papers received from 18 countries
formed the basis for the Technical Program. The themes considered for the technical
program included solid mechanics, fluid mechanics, potential theory, composite materials,
fracture mechanics, damage mechanics, contact and wear, optimization, heat transfer,
dynamics and vibrations, acoustics and geomechanics.
The conference organizers would also like to express their appreciation to the
International Scientific Advisory Board for their assistance in supporting and promoting the
objectives of the meeting and for their assistance in the form of reviews of the submitted
papers.
Editors
The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration.
In this thesis, several numerical approaches for the development of structural health monitoring (SHM) methodologies for engineering structures are described. In particular, the first boundary element models of three-dimensional piezoelectric smart structures are introduced. Comparing to the finite element method (FEM), the boundary element method (BEM) demonstrates higher numerical stability and requires less computational resources. Also, the dual boundary integral formulation provides a natural and efficient approach for replicating the targets of SHM techniques – material discontinuities.
A boundary element formulation for the ultrasonic guided wave based damage detection strategy is firstly presented. The semi-analytical finite element model of piezoelectric patches is coupled with the boundary element model of substrates via the variables of the BEM. The first systematic approach for determining the number of Laplace terms to be used for an elastodynamic boundary element analysis is also introduced.
The above-mentioned formulation is then transformed to the Fourier domain for simulating the electro-mechanical impedance (EMI) based damage detection strategy. The key to attaining accurate EMI signatures is the inclusion of appropriate damping effects. In addition to the detection of the damages in substrates, a partially debonded coupling condition between substrates and piezoelectric patches is derived for modelling the diagnosis of faulty transducers.
The computational efficiency of the BEM is further enhanced by the implementation of high-order spectral elements. The difficulties associated with the applications of these elements in the BEM are among the key emphases. The accelerated BEM is used to reformat the models of the two damage detection strategies. The performances of the two strategies are more deeply investigated and understood.
At the end of this thesis, a technique for the characterisation of cracks in plate structures is established. By utilising a two-stage approach, the long-existed difficulty of the simultaneous localisation and sizing of arbitrary cracks can be overcome. The technique is developed mathematically using analytic models and the FEM, and is extensively assessed by numerically simulated extreme scenarios.
Throughout this thesis, physical experiments are heavily relied on for validation studies. A summary of the skills and the experiences, which the author has gained on experimental testing, is reported in this thesis for further reference.
We employ the method of fundamental solutions (MFS) for detecting a sound-soft scatterer surrounding a host acoustic homogeneous medium due to a given point source inside it. The measurements are taken inside the medium and, in addition, are contaminated with noise. The MFS discretization yields a nonlinear constrained regularized minimization problem which is solved using standard software. The results of several numerical experiments are presented and discussed.
We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining, accessible and known part of the boundary of a two-dimensional domain, for problems governed by Helmholtz-type equations. This inverse geometric problem is solved using the plane waves method (PWM) in conjunction with the Tikhonov regularization method. The value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples.
In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi-region boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter- or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. This is the first time inter- and trans-granular fracture are being modelled together by BEM, and DBEM is being extended to include cohesive approach for anisotropic materials. Finally numerical simulations are presented to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.
This book constitutes the edited proceedings of the Advanced Studies Institute on Boundary Element Techniques in Computer Aided Engineering held at The Institute of Computational Mechanics, Ashurst Lodge, Southampton, England, from September 19 to 30, 1984. The Institute was held under the auspices of the newly launched "Double Jump Programme" which aims to bring together academics and industrial scientists. Consequently the programme was more industr ially based than other NATO ASI meetings, achieving an excellent combination of theoretical and practical aspects of the newly developed Boundary Element Method. In recent years engineers have become increasingly interested in the application of boundary element techniques for'the solution of continuum mechanics problems. The importance of boundary elements is that it combines the advantages of boundary integral equations (i.e. reduction of dimensionality of the problems, possibility of modelling domains extending to infinity, numerical accura'cy) with the versatility of finite elements (i.e. modelling of arbitrary curved surfaces). Because of this the technique has been well received by the engineering and scientific communities. Another important advantage of boundary elements stems from its reduction of dimensionality, that is that the technique requires much less data input than classical finite elements. This makes the method very well suited for Computer Aided Design and in great part explains the interest of the engineering profession in the new technique.
This work determines the three-dimensional (3D) fundamental MHD creeping flow and associated electric potential produced by a concentrated source point, with given unit strength (Formula presented.), located in a conducting Newtonian liquid bounded by a plane solid and motionless wall and subject to a given uniform magnetic field normal to the wall. The wall is no-slip but may be either perfectly conducting or insulating. By linearity, the analysis is confined to the cases of (Formula presented.) either normal or parallel to the wall. Such different wall natures and force orientations result in different flows and electric potential functions which are obtained using direct and inverse two-dimensional Fourier transforms. As a result, it has been possible to analytically express in closed-form each resulting fundamental flow and potential.
The computational efficiency of the boundary element method in elastodynamic analysis can be significantly improved by employing high-order spectral elements for boundary discretisation. In this work, for the first time, the so-called boundary spectral element method is utilised to formulate the piezoelectric smart structures that are widely used in structural health monitoring (SHM) applications. The resultant boundary spectral element formulation has been validated by the finite element method (FEM) and physical experiments. The new formulation has demonstrated a lower demand on computational resources and a higher numerical stability than commercial FEM packages. Comparing to the conventional boundary element formulation, a significant reduction in computational expenses has been achieved. In summary, the boundary spectral element formulation presented in this paper provides a highly efficient and stable mathematical tool for the development of SHM applications.
