Numerical solution to the linearized model of a clamped-free plate using nonconforming finite elements

Abstract

In the paper, the numerical solution to the linearized problem of a partially clamped, partially free rectangular plate is considered in order to model and simulate the unstable end behavior. Such a problem is modeled by a nonlinear plate evolution equation with stretching effects in the span-wise direction and wind-flow in the chord-wise direction. The motivation is to model a cantilever bridge in order to consider the long-time behavior of a nonlinear elastic structure forced by external/internal inputs. The non-conservative force acting upon the system and the resulting loss of dissipativity of the system are the major features. The dependence of the structure of stationary states on the values of the gas velocity will be analyzed. A numerical approximation with a Morley finite element is adapted to the plate with clamped-free edges, and corresponding numerical computations are provided.