SUMMARYThe paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis. Some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed. The numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive Gaussian quadrature and subdivision techniques.

SUMMARYThe work reported herein develops a generalized traction-BIE formulation which involves only weakly singular integrals (in the three-dimensional problem) or totally regular integrals (in the two-dimensional problem). The first step deals with the terms in the Somigliana displacement identity, and then the derivatives of these terms. The only conditions required for the existence of the traction-BIE and the related Somigliana stress identity are weak continuity of the in-plane derivatives of the surface displacements and of the surface tractions. It is shown that the Cauchy Principal Value (CPV) interpretations so commonly used in BIE developments are unnecessary. The formulation is established not only at a smooth boundary point, but also at a comer point. The extension of the non-singular formulation to discontinuous boundary tractions and tangential derivatives of the boundary displacements applicable to a generalized problem statement as well as the usual BEM implementations is also shown. In the demonstrated formulation, the source points are located directly at the boundary nodes and non-conformal elements are not needed.

The widely held notion that the use of standard conforming isoparametric boundary elements may not be used in the solution of hypersingular integral equations is investigated. It is demonstrated that for points on the boundary where the underlying ®eld is C 1Ya continuous, a class of rigorous nonsingular conforming BEM algorithms may be applied. The justi®cation for this class of algorithms is interpreted in terms of some recent criticism. It is shown that the numerical integration in these conforming BEM algorithms using relaxed regularization represents a ®nite approximation to the standard twosided Hadamard ®nite part interpretation of hypersingular integrals. It is also shown that the integration schemes in this class of algorithms are not based upon one-sided ®nite part interpretations. As a result, the attendant ambiguities associated with the incorrect use of the one-sided interpretations in boundary integral equations pose no problem for this class of algorithms. Additionally, the distinction is made between the analytic discontinuities in the ®eld which place limitations on the applicability of the conforming BEM and the discontinuities resulting from the use of piece-wise C 1Ya interpolations. IntroductionHypersingular integral equations are formed from differentiation of singular integral equations and as a result, the order of the singularities in the kernels is increased in these equations. The higher order singularities in the kernels requires more smoothness of the densities for the given integral to be ®nite. A suf®cient condition for the existence of hypersingular integrals is C 1Ya continuity of the density at the source point. This is a condition which is not met by the use of standard isoparametric boundary elements which only provide a piece-wise C 1Ya interpolation. For this reason, approximate solution techniques for solving hypersingular integral equations using the boundary element method (BEM) require special consideration.In general, this special consideration takes one of several forms. The hypersigularity may be reduced through integration by parts (Guidera and Lardner 1975;Giroire and Ne Âde Âlec 1995). In addition to being rather mathematically tedious, approaches of this form have yet to produce numerical results of the same accuracy as have been obtained with the more conventional approaches.Each of several remaining approaches seeks to impose C 1Ya continuity at the source point on the particular density in the hypersingular integral which is used in the numerical integration, as is required mathematically. The ®rst class of algorithms is based on interpolation schemes which are C 1Ya continuous. One way in which this is done is to introduce nodal displacement gradients in the interpolation scheme. Polch et al. (Polch et al. 1987) used a standard isoparametric representation for displacement gradients. This continuous displacement gradient ®eld was then coupled to the standard interpolation for displacements through a least-squares method. Young (Young 1996) has used a hybrid in...

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There has been increasing interest in evaluating the performance of existing reinforced concrete (RC) bridges just after natural disasters or man-made events especially when the defects are invisible, or in quantifying the improvement after rehabilitations. In order to obtain an accurate assessment of the reliability of a RC bridge, it is critical to incorporate information about its current structural properties, which reflects the possible aging and deterioration. This dissertation proposes to develop an adaptive reliability analysis of RC bridges incorporating the damage detection information obtained from nondestructive testing (NDT).In this study, seismic fragility is used to describe the reliability of a structure withstanding future seismic demand. It is defined as the conditional probability that a seismic demand quantity attains or exceeds a specified capacity level for given values of earthquake intensity. The dissertation first develops a probabilistic capacity model for RC columns and the capacity model can be used when the flexural stiffness decays nonuniformly over a column height. Then, a general methodology to construct probabilistic iv seismic demand models for RC highway bridges with one single-column bent is presented. Next, a combination of global and local NDT methods is proposed to identify in-place structural properties. The global NDT uses the dynamic responses of a structure to assess its global/equivalent structural properties and detect potential damage locations.The local NDT uses local measurements to identify the local characteristics of the structure. Measurement and modeling errors are considered in the application of the NDT methods and the analysis of the NDT data. Then, the information obtained from NDT is used in the probabilistic capacity and demand models to estimate the seismic fragility of the bridge. As an illustration, the proposed probabilistic framework is applied to a reinforced concrete bridge with a one-column bent. The result of the illustration shows that the proposed framework can successfully provide the up-to-date structural properties and accurate fragility estimates. v DEDICATION To my family and my fiancé, Dan Ocharzak vi ACKNOWLEDGEMENTS