Boundary Integral Operators for Plate Bending in Domains with Corners
نویسنده
چکیده
The paper studies boundary integral operators of the bi{Laplacian on piecewise smooth curves with corners and describes their mapping properties in the trace spaces of variational solutions of the biharmonic equation. We formulate a direct integral equation method for solving mixed boundary value problems for the biharmonic equation on a nonsmooth plane domain, analyse the solvability of the corresponding systems of integral equations and prove their strong ellipticity.
منابع مشابه
Well conditioned boundary integral equations for two-dimensional sound-hard scattering problems in domains with corners
We present several well-posed, well-conditioned integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We call these integral equations Direct Regularized Combined Field Integral Equations (DCFIE-R) formulations because (1) they consist of combinations of direct boundary integral equations of the ...
متن کاملIdentities for the fundamental solution of thin plate bending problems and the nonuniqueness of the hypersingular BIE solution for multi-connected domains
Four integral identities for the fundamental solution of thin plate bending problems are presented in this paper. These identities can be derived by imposing rigid-body translation and rotation solutions to the two direct boundary integral equations (BIEs) for plate bending problems, or by integrating directly the governing equation for the fundamental solution. These integral identities can be...
متن کاملWaveguide mode solver based on Neumann-to-Dirichlet operators and boundary integral equations
For optical waveguides with high index-contrast and sharp corners, existing full-vectorial mode solvers including those based on boundary integral equations typically have only second or third order of accuracy. In this paper, a new full-vectorial waveguide mode solver is developed based on a new formulation of boundary integral equations and the so-called Neumann-to-Dirichlet operators for sub...
متن کاملAnalysis of the Bending of a Uniformly Loaded Rectangular Plate with Variable Width Corner Supports
The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy-Na'dai approach and the mixed boundary equation at the...
متن کاملBending Solution for Simply Supported Annular Plates Using the Indirect Trefftz Boundary Method
This paper presents the bending analysis of annular plates by the indirect Trefftz boundary approach. The formulation for thin and thick plates is based on the Kirchhoff plate theory and the Reissner plate theory. The governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. The Trefftz method employs the complete set of solu...
متن کامل