In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles of the analytic continuation called resonances of the system, and a low frequency component associated to a branch point at frequency zero.We present the mathematical analysis of this method for the two-dimensional sea-keeping problem of a thin elastic plate (ice floe, floating runway, ...) and provide some numerical results to illustrate and discuss its efficiency.

We consider the question raised in [1] of whether relaxed energydensities involving both bulk and surface energiescan be written as a sum of two functions, one depending on the net gradientof admissible functions, and the other on netsingular part.We show that, in general, they cannot. In particular, if the bulk densityis quasiconvex but not convex, thereexists a convex and homogeneous of degree 1 function of the jump such thatthere is no such representation.