An analytic solution to the mild slope wave equation is derived for long waves propagating over a circular, bowl-shaped pit located in an otherwise constant depth region. The analytic solution is shown to reduce to a previously derived analytic solution for the case of a bowl-shaped enclosed basin and to agree well with a numerical solution of the hyperbolic mild-slope equations. The effects of...

This paper presents a test case to help validate simulation codes for contact problems involving beams. A closed form solution is derived and the comparison made with finite element (FE) implementation that uses mortar method enforcing constraints. The consists of semi-infinite cantilever beam subjected constant distributed load experiencing frictionless straight rigid substrate. Both an Euler-...