PIMS-SFU CSC Seminar: Travis Askham

In the Kirchoff-Love theory, the vertical displacement of a homogeneous, thin clamped plate under pure bending satisfies the biharmonic equation in a two dimensional domain with Dirichlet boundary conditions (the value and normal derivative are specified along the boundary). Because the boundary conditions are of a different order (one is a derivative of the solution and the other is not), it is difficult to derive integral representations of the solution which result in a second kind integral equation for the unknowns. We show that existing integral representations for the related Stokes equation can be bootstrapped to provide a representation for this problem which is well behaved, even on domains with high curvature and on multiply connected domains. The eigenvalues and eigenmodes of the differential equation are also of interest, as they correspond to vibrating modes of the elastic plate. We present some preliminary results on extending these techniques to the eigenvalue problem.