Application of boundary integral method to elastoplastic analysis of V-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problem. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single-edge notch and subjected to pure bending. The boundary integral equation method reduced the inhomogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with a method of successive elastic solutions

Parallel efficiency of a boundary integral equation method for nonlinear water waves

We describe the application of domain decomposition on a boundary integral method for the study of nonlinear surface waves on water in a test case for which the domain decomposition approach is an important tool to reduce the computational effort. An important aspect is the determination of the optimum number of domains for a given parallel architecture. Previous work on hetero- geneous clusters of workstations is extended to (dedicated) parallel platforms. For these systems a better indication of the parallel performance of the domain decomposition method is obtained because of the absence of varying speed of the processing elements

A numerical boundary integral equation method for elastodynamics. I

The boundary initial value problems of elastodynamics are formulated as boundary integral equations. It is shown that these integral equations may be solved by time-stepping numerical methods for the unknown boundary values. A specific numerical scheme is presented for antiplane strain problems and a numerical example is given

Analytical results regarding electrostatic resonances of surface phonon/plasmon polaritons: separation of variables with a twist

The boundary integral equation method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies but also offer the opportunity to expand the study of phenomena like cloaking by anomalous localized resonance. For that reason we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the boundary integral equation method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nano-disks. Finally, symmetry-based operator analysis can be extended from electrostatic to full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.Comment: 25 pages, 3 figures, to be published Proc. Royal Soc.

Boundary integral equation method for electromagnetic and elastic waves

In this thesis, the boundary integral equation method (BIEM) is studied and applied to electromagnetic and elastic wave problems. First of all, a spectral domain BIEM called the spectral domain approach is employed for full wave analysis of metal strip grating on grounded dielectric slab (MSG-GDS) and microstrips shielded with either perfect electric conductor (PEC) or perfect magnetic conductor (PMC) walls. The modal relations between these structures are revealed by exploring their symmetries. It is derived analytically and validated numerically that all the even and odd modes of the latter two (when they are mirror symmetric) find their correspondence in the modes of metal strip grating on grounded dielectric slab when the phase shift between adjacent two unit cells is $0$ or $\pi$. Extension to non-symmetric case is also made. Several factors, including frequency, grating period, slab thickness and strip width, are further investigated for their impacts on the effective permittivity of the dominant mode of PEC/PMC shielded microstrips. It is found that the PMC shielded microstrip generally has a larger wave number than the PEC shielded microstrip. Secondly, computational aspects of the layered medim doubly periodic Green\u27s function (LMDPGF) in matrix-friendly formulation (MFF) are investigated. The MFF for doubly periodic structures in layered medium is derived, and the singularity of the periodic Green\u27s function when the transverse wave number equals zero in this formulation is analytically extracted. A novel approach is proposed to calculate the LMDPGF, which makes delicate use of several techniques including factorization of the Green\u27s function, generalized pencil of function (GPOF) method and high order Taylor expansion to derive the high order asymptotic expressions, which are then evaluated by newly derived fast convergent series. This approach exhibits robustness, high accuracy and fast and high order convergence; it also allows fast frequency sweep for calculating Brillouin diagram in eigenvalue problem and for normal incidence in scattering problem. Thirdly, a high order Nystr\ {o}m method is developed for elastodynamic scattering that features a simple local correction scheme due to a careful choice of basis functions. A novel simple and efficient singularity subtraction scheme and a new effective near singularity subtraction scheme are proposed for performing singular and nearly singular integrals on curvilinear triangular elements. The robustness, high accuracy and high order convergence of the proposed approached are demonstrated by numerical results. Finally, the multilevel fast multipole algorithm (MLFMA) is applied to accelerate the proposed Nystr\ {o}m method for solving large scale problems. A Formulation that can significantly reduce the memory requirements in MLFMA is come up with. Numerical examples in frequency domain are first given to show the accuracy and efficiency of the algorithm. By solving at multiple frequencies and performing the inverse Fourier transform, time domain results are also presented that are of interest to ultrasonic non-destructive evaluation

A boundary integral equation method in the frequency domain for cracks under transient loading

Acknowledgments The financial support of the German Academic Exchange Service (DAAD), Engineering and Physical Sciences Research Council (EPSRC) and Advanced Research Collaboration (ARC) Programme (funded by the British Council and DAAD) is gratefully acknowledged.Peer reviewedPublisher PD

Conformal mapping of unbounded multiply connected regions onto canonical slit regions

We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unboundedmultiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels