A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numeric...

The Layerwise Shell Theory is used to model discretely stiffened laminated composite plates and cylindrical shells for stress, vibration, pre-buckling and post-buckling analyses. The layerwise theory reduces a 3-D problem to a 2-D problem by expanding the 3-D displacement field as a function of a surface-wise 2-D displacement field and a 1-D interpolation polynomial through the shell thickness....

A recent line of work has studied the statistical properties of neural networks to great success from a mean field theory perspective, making and verifying very precise predictions of neural network behavior and test time performance. In this paper, we build upon these works to explore two methods for taming the behaviors of random residual networks (with only fully connected layers and no batc...

In this paper we provide a framework for computable analysis of measure, probability and integration theories. We work on computable metric spaces with computable Borel probability measures. We introduce and study the framework of layerwise computability which lies on Martin-Löf randomness and the existence of a universal randomness test. We then prove characterizations of effective notions of ...

in this paper, a closed form solution for bending and free vibration analyses of simply supported rectangular laminated composite plates is presented. the static and free vibration behavior of symmetric and antisymmetric laminates is investigated using a refined first-order shear deformation theory. the winkler–pasternak two-parameter model is employed to express the interaction between the lam...

Layerwise computability is an effective counterpart to continuous functions that are almosteverywhere defined. This notion was introduced by Hoyrup and Rojas [17]. A function defined on Martin-Löf random inputs is called layerwise computable, if it becomes computable if each input is equipped with some bound on the layer where it passes a fixed universal Martin-Löf test. Interesting examples of...

In this paper, a closed form solution for bending and free vibration analyses of simply supported rectangular laminated composite plates is presented. The static and free vibration behavior of symmetric and antisymmetric laminates is investigated using a refined first-order shear deformation theory. The Winkler–Pasternak two-parameter model is employed to express the interaction between the lam...

In this paper we propose a uniform description of basic BDD theory and algorithms by means of term rewriting. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develop appropriate theory. A rewriting system is presented by which canonical forms can be obtained. Various reduction strategies give rise to di erent algorithms. A layerwise strategy is proposed having th...

We present a confocal microscopy study of 1.55 microm monodisperse silica hard spheres as they sediment and crystallize at the bottom wall of a container. If the particles sediment onto a feature less flat wall, the two bottom layers crystallize simultaneously and layerwise growth follows. If the wall is replaced by a hexagonal template, only layerwise growth occurs. Our results complement earl...