The effects of selected membrane, plate and flat shell finite element formulations on optimal topologies are numerically investigated. Two different membrane components are considered. The first is a standard 4-node bilinear quadrilateral, and the other is a 4-node element accounting for in-plane (drilling) rotations. Plate elements selected for evaluation include discrete Kirchhoff quadrilater...

Efficient finite element (FE) analyses of Reissner-Mindlin (RM) plate bending problems require a combination of high-order polynomial trial functions (p-extension) and locally refined meshes, or, in short, an hp-extension of the FE method. In the optimal case, exponential rates in the convergence of the error in energy norm can be obtained by such a discretization. This contribution discusses s...

The Reissner-Mindlin plate models thin plates. The condition numbers of finite element approximations of these plate models increase very rapidly as the thickness of the plate goes to 0. A Balancing Domain Decomposition by Constraints (BDDC) Deluxe method is developed for these plate problems discretized by Falk-Tu finite elements. In this new algorithm, subdomain Schur complements restricted t...

Experimentally determined natural frequencies and modes shapes are presented for an elastically point-supported isotropic plate with attached masses under impulsive loading. These results are compared to frequencies and to modes shapes determined from the Rayleigh–Ritz method and a finite element analysis using COMSOL. Accelerometers mounted at three locations on the plate, provide input for ME...

In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory have been used, respectively, with the stiffness matrices of the plate and the beams obtained separately. The stiffness matric...

The nite element method with rectangular meshes for the Reissner-Mindlin plate is analyzed. For a plate with thickness bounded below by a positive constant (moderately thick plate), derivative superconvergence of the nite element solution at the Gaussian points is justiied and optimal error estimates for both rotation and displacement are established.

Surface acoustic waves (Rayleigh waves) are analyzed for semi-infinite anisotropic solids only for essential propagation characteristics like the velocity and decaying parameters, which are important in engineering applications. The limitations of these results are obvious because devices are usually built on a finite piezoelectric substrate with propagation properties different from the analyt...

In a previous paper from the authors, the bounds from Kelsey et al. (1958) were applied to a sandwich panel including a folded core in order to estimate its shear forces stiffness (Lebée and Sab, 2010b). The main outcome was the large discrepancy of the bounds. Recently, Lebée and Sab (2011a) suggested a new plate theory for thick plates –the Bending-Gradient plate theory– which is the extensio...

This paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the Reissner-Mindlin equations. These coefficients are related with the eigenvalues of a non-compact operator. We give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues. Then we consider the numer...