In this paper, the modelling and design of a multivariable controller for a smart thick composite cantilever beam with embedded shear sensors and actuators is investigated. The first 3 dominant vibratory modes are retained in the modelling of the composite beam. The beam is divided into 8 finite elements and shear piezoelectric patches are embedded into the master structure. These shear piezoel...

In standard deformable object simulation in computer animation, all the mesh elements or vertices are timestepped synchronously, i.e., under the same timestep. Previous asynchronous methods have been largely limited to explicit integration. We demonstrate how to perform spatially-varying timesteps for the widely popular implicit backward Euler integrator. Spatiallyvarying timesteps are useful w...

‎in this paper‎, ‎we investigate a damped korteweg-de‎ ‎vries equation with forcing on a periodic domain‎ ‎$mathbb{t}=mathbb{r}/(2pimathbb{z})$‎. ‎we can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

Koren, B. and P.W. Hemker, Damped, direction-dependent multigrid for hypersonic flow computations, Applied Numerical Mathematics 7 (1991) 309-328. A nonlinear multigrid technique with improved robustness is developed for the solution of the steady Euler equations. The system of nonlinear equations is discretized by an upwind finite volume method. Collective symmetric point Gauss-Seidel relaxati...

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representation...