By now it is well known that reliable numerical modeling of shells by traditional low-order finite element formulations is not an easy task. The most dramatic failure occurs when approximating nearly inextensional (or bending-dominated) deformations by standard low-order elements. In this case an asymptotic approximation failure, known as shear-membrane locking, occurs at the limit of zero shel...

A finite-dimensional global attractor A can be embedded, using some linear map L, into a Euclidean space R k of sufficiently high dimension. The Holder exponent ̈ y1 Ž . of L depends upon k and upon t A , the ‘‘thickness exponent’’ of A. We show that global attractors which are uniformly bounded in the Sobolev spaces H s for Ž . all s ) 0 have t A s 0. It follows, using a result of B. R. Hunt an...

In this paper, we present a method for estimating local thickness distribution in finite element models, applied to injection molded and cast engineering parts. This method features considerable improved performance compared to two previously proposed approaches, and has been validated against thickness measured by different human operators. We also demonstrate that the use of this method for a...

We propose and analyze an hp finite element method for the Nagdhi shell model, based on rectangular elements. We show that for the bending-dominated case, assuming sufficient smoothness on the solution, the method is locking free in terms of both h and p, as the thickness of the shell tends to zero. Our results are established under the assumption that the geometrical coefficients appearing in ...

Reliable and efficient residual-based a posteriori error estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The error is estimated by a computable error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate’s thickness and are uniform for a wide range of stabilisa...

The suppression of photon bremsstrahlung due to a variety of in-medium effects is discussed. Different electrodynamic suppression effects are discussed, and compared with the related color analogs. Higher order effects are considered, and found to be important. Data from SLAC E-146 is discussed, and compared with theory. The effect of finite thickness targets is emphasized, since nuclear size i...

A three-dimensional finite element implementation of a simple nonassociative Drucker-Prager plasticity model with strong discontinuity mode of localized deformation is formulated for small deformations. A strong discontinuity mode of localized deformation represents slip along a surface of zero measure, whereas a weak discontinuity mode of localized deformation represents shear within a band of...

A strategy is proposed to reduce surface tensile stresses that develop in ceramic microlaminate structures. As a specific example, surface stresses, which can lead to unwanted edge cracking, appear within a thin alumina/mullite layer bounded by thicker alumina layers after fabrication at some elevated temperature and subsequent cooling. A stress analysis is performed using the finite element me...

Thickness optimization can be considered as a case of sizing optimization for plane structures. It can also be used as an intermediate step for topology problems, i.e. we can eliminate the parts where the thickness tends to be zero. This paper is concerned with the case of plane stress structures coupled with the finite element method. The aim is to present a formulation of this problem as a ca...