We present an adaptive spacetime discontinuous Galerkin (SDG) method for linearized elastodynamics. The SDG method uses a simple Bubnov-Galerkin projection that delivers stable and oscillation–free solutions, with O (N) complexity and exact momentum balance on every spacetime element. An extended version of the Tent Pitcher algorithm generates unstructured spacetime grids that support simultane...

For nearly incompressible elasticity, volumetric locking is a well-known phenomenon with low-order (cubic or lower) fi nite element method methods, of which continuous extended fi nite element methods (XFEMs) are no exception. We will present an XFEM that is simultaneously lock-free and optimally convergent. Based on our earlier work of an optimally convergent discontinuous-Galerkin-based XFEM,...

free vibration of sandwich plates with temperature dependent functionally graded (fg) face sheets in various thermal environments is investigated. the material properties of fg face sheets are assumed to be temperature-dependent and vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. also, the material properties of...

We show that three well-known \variational crimes" in nite elements { upwinding, mass lumping and selective reduced integration { may be derived from the Galerkin method employing the standard polynomial-based nite element spaces enriched with residual-free bubbles.

The application of finite element methods to problems in structural acoustics ( the vibration of an elastic body coupled to an acoustic fluid medium) is considered. New stabilized methods based on the Hellinger-Reissner variational principle with a generalized least-squares modification are developed which yield improvement in accuracy over the standard Galerkin finite element method for both i...