Boundary Element Methods

The desire to establish a three-dimensional framework for use in analyzing problems of stable mixed-mode crack propagation has received lately a considerable attention. The study of predicting crack paths under the most general possible hypotheses (three dimensions, arbitrary geometry of the body and of the crack, arbitrary loading) is an ambitious objective. Recently, Leblond [1] and Leblond et al. [2] established formulae which specify the general functional form of the successive terms of the expansions of the SIFs along the front of the extended crack and, as they underline, the formulation of the propagation criterion is an open problem only in the presence of mode III. Therefore, in a mode I+II situation, the widely accepted “principle of local symmetry” of Goldstein and Salganik [3] receives a general recognition. In numerical experiments the FRANC3D code uses new concepts with a model that allows for the implementation of 3D crack growth mechanics [4] with the support of both finite and boundary elements. Keeping in mind such beneficial developments, one should emphasize that for a specific geometry and loading we may obtain various experimental crack paths which are dependent on the local position of the initial crack, as any deviation from “symmetry” influences the future crack trajector

... Reina Mercedes, Seville 41012, Spain (Received 23 January 1995; revised version received 13 February 1995; accepted 2 March 1995) A method to calculate the ... 1, we can express the kth layer as: ak(Zk) = Tk(Zk)hk(O) + Rk(Zk) (10) where matrix T and vector R are given in ...

In this presentation the general motion of an asymmetrical homogeneous rigid body in a fluid environment is studied. By means of a defined new theorem – The Theorem for changing the rigid body general impulse and new form of Lagrange equations, called Lagrange condensed equations, the differential equations describing the three-dimensional motion of the body in a matrix form is obtained. With a new theorem for the fluid flow of an asymmetrical rigid body, the presence of a destabilizing aerodynamic moment is proved. A new complete matrix of aerodynamic forces is defined. The spherical component of body general motion is counted with Cardan corners. The paper is entirely theoretical. It is the basis on which a second paper on the motion of an ideal rigid ellipsoid in a fluid environment is developed.

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace's equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller's equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

Computational methods for the acoustic modal analysis of an enclosed fluid are considered. The finite element method is outlined and methods based on the boundary integral equations are reviewed.

The discretization of the boundary integral equation results in a non-linear eigenvalue problem. However, through a polynomial approximation with respect to the wavenumber, the non-linear eigenvalue problem is reduced to a standard generalized eigenvalue problem. Methods based on this are applied to the test problems of the axisymmetric three-dimensional cases of a sphere and a cylinder.

The physical importance of the interior acoustic resonances of a loudspeaker is discussed. An acoustic modal analysis of an axisymmetric loudspeaker interior is carried out using this method and the results are compared with results from the finite element method and experimental results.

In this paper the extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. In order to avoid collocation at crack tips, crack kinks and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elastoplastic behaviour is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This formulation was implemented for two-dimensional domains only, although there is no theoretical or numerical limitation to its application to three-dimensional ones. A centre-cracked plate and a slant edge-cracked plate subjected to tensile load are analysed and the results are compared with others available in the literature. J-type integrals are calculated.

The possibility to excite and detect acoustic waves in fluids using capacitive transducers built on silicon using surface micromachining offers attractive opportunities in the manufacturing of high quality low cost imaging probes. As in the case of standard probe transducers, simulation codes are required to accurately design such devices. The periodic structures extensively used for these capacitive transducers has to

Classical analysis of seismic soil-structure interaction phenomena for the design of civil engineering structures and lifelines are based on two simplifying assumptions~: lateral homogeneity of the soil underneath the foundation and representation of the ground motion (free field) as a pulse train of vertically or obliquely incident plane waves. For large structures founded on flexible spread footings, these hypotheses are not valid any longer. Furthermore, data recorded after the installation of dense seismograph arrays have shown that seismic ground motions can have a strong spatial variability, even over short distances and irrespective of deterministic wave passage effects. We develop in this thesis some theoretical tools for the modelization and numerical analysis of the influence of the free field and soil spatial varibilities on the structural response. A probabilistic approach is chosen, and the structural response of interest is given by an integral formulation which considers these two aspects simultaneously. Relevancy of numerical implementations are enhanced by introducing a spectral reduction of the random dimension of the fluctuating part - large or small - of the uncertain soil mechanical parameters through its Karhunen-Loeve expansion. This technique is applied to the free field as well. The numerical results obtained for various realistic cases display some specific features whose consideration seems essential in the process of industrial design. Notably, some usefull trends and sensitivity of the structural response with the free field and soil spatial variabilities are derived.

Companies have learned that radical innovations (RIs) are a prerequisite to grow organically. However, companies struggle to identify and introduce RIs, as their inherent high uncertainties and novelty challenge established organisations and management routines. To address the first challenge, companies need to take a holistic approach and design a trans-boundary environment of creativity, trans-disciplinary and entrepreneurial spirit. This environment attracts and retains visionary people, fosters generation of new opportunities and cultivates adaptability. By adapting evaluation metrics for RI, setting up flexible processes, and promoting trans-disciplinary exchange, the second challenge can be addressed. Increased research has concentrated on several aspects of RI lately, but so far a combining framework is missing.Our paper bridges this gap by developing an improved theoretical framework, enhancing the existing literature and introducing art as a method to advance trans-disciplinary interchange. In a case-study approach, we have applied our framework to the research and development department of Vodafone Research and Development, Germany, as they integrate art methodically in their research and development process. Analysing their RI capabilities, we identify the trans-disciplinary exchange with artists as a novel initiator and driver of RI, which has not yet been adequately considered.

Cavitation is one of the most important problems in hydrodynamic
applications which causes a noticeable deterioration of the machine
performance. Thus, accurate prediction of cavitation is very important in
estimating the hydrodynamic performance of pumps, marine propellers
and high speed hydrofoils. For this reason, substantial efforts have been
taken by many researchers to develop capabilities to predict the extent of
cavitation for various types of geometries.
Several researchers have successfully analyzed the cavitation
phenomenon and its application. They used different analytical and
numerical methods to determine the shape and the size of the cavity and
to know the velocities and/ or pressure along the boundaries. Due to the
complexity of the cavitation problem and due to the difficulty to obtain
analytical solutions many researchers prefer numerical methods.
The most popular numerical technique for analyzing cavitation
problems is the boundary element method (BEM). Boundary element
method has gained its popularity from its simplified nature and many
other reasons that will be encountered through the thesis.
The boundary element method was used herein as a mathematical
tool to solve the cavity flow around hydrofoils. Two major difficulties
meet the researcher in this field of study. These difficulties are the
determination of the cavity free surface and the potential at the leading
point.
In the present thesis, these difficulties are solved by a new
suggested technique and it gives excellent results. Also, the new
technique saves the time and effort needed by previous techniques. The
algorithm is applied to solve the different symmetric hydrofoil NACA
sections with studying the effect of three different parameters. Excellent
agreement was obtained with the available existing results.

Featured Application: An analysis method has been developed to study single piles under horizontal loading. The proposed method is innovative because it considers the highly non-linear response of circular reinforced concrete pile sections, taking also into account the influence of tension stiffening, and considers suction for partially saturated soil conditions. Abstract: A hybrid BEM-p-y curves approach was developed for the single pile analysis with free/fixed head restraint conditions. The method considers the soil non-linear behaviour by means of p-y curves in series to a multi-layered elastic half-space. The non-linearity of reinforced concrete pile sections, also considering the influence of tension-stiffening, has been considered. The model reproduces the influence of suction by increasing the stress state and hence the stiffness of shallow soil-layers. Suction is modeled using the Modified-Kovacs model. The hybrid BEM-py curves method was validated by comparing results from data of 22 load tests on single piles. In addition, a detailed comparison is presented between measured and computed data on a large-diameter reinforced concrete bored single pile.

BOUNDARY ELEMENT PROGRAMMING IN MECHANICS Nonlinear stress analysis is an essential feature in the design of such diverse structures as aircraft, bridges, machines, and dams. Computational techniques have become vital tools in dealing with the complex, time-consuming ...

As the power required to run micro-electronics
circuitry is decreasing these days, an untiring attempt of the
contemporary researchers has been to find new environmental
energy sources that may have the potential to replace the battery
usage in wearable subsystems. In this paper the study of an
unobtrusive piezoelectric device has been presented that can be
integrated within human shoe-sole, thereby converting a part of
the mechanical energy originated from human locomotion into
electrical energy for running such low power portable devices
and wireless sensors, without affecting the user's gait. To serve
the desired purpose, a PZT bimorph and a flexible PVDF stave
have been used to harness the heel strike energy and sole bending
energy respectively. The proposed system has been
mathematically modeled, simulated in COMSOL environment
and the results have also been compared with the experimental
values. The power output was found to be much lower than the
desired one and hence an attempt was made for the enhancement
of charge accumulation by parasitic harvesting technique using
soft sneakers and an innovative charge extraction circuitry. This
provided a considerable amount of power gain, sufficient to run a low-power electronics device.