A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

A Kinematic Theory for Planar Hoberman and Other Novel Foldable Mechanisms

In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.

Multi-UAV Task Allocation using Team Theory

A multiple UAV search and attack mission in a battlefield involves allocating UAVs to different target tasks efficiently. This task allocation becomes difficult when there is no communication among the UAVs and the UAVs sensors have limited range to detect the targets and neighbouring UAVs, and assess target status. In this paper, we propose a team theoretic approach to efficiently allocate UAVs to the targets with the constraint that UAVs do not communicate among themselves and have limited sensor range. We study the performance of team theoretic approach for task allocation on a battle field scenario. The performance obtained through team theory is compared with two other methods, namely, limited sensor range but with communication among all the UAVs, and greedy strategy with limited sensor range and no communication. It is found that the team theoretic strategy performs the best even though it assumes limited sensor range and no communication.

Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

Average variation L2-stability criteria for time-varying feedback systems-A unified approach

The problem of developing L2-stability criteria for feedback systems with a single time-varying gain, which impose average variation constraints on the gain is treated. A unified approach is presented which facilitates the development of such average variation criteria for both linear and nonlinear systems. The stability criteria derived here are shown to be more general than the existing results.

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Unified Spectral Efficiency Analysis of Cellular Systems with Channel-Aware Schedulers

Spectral efficiency is a key characteristic of cellular communications systems, as it quantifies how well the scarce spectrum resource is utilized. It is influenced by the scheduling algorithm as well as the signal and interference statistics, which, in turn, depend on the propagation characteristics. In this paper we derive analytical expressions for the short-term and long-term channel-averaged spectral efficiencies of the round robin, greedy Max-SINR, and proportional fair schedulers, which are popular and cover a wide range of system performance and fairness trade-offs. A unified spectral efficiency analysis is developed to highlight the differences among these schedulers. The analysis is different from previous work in the literature in the following aspects: (i) it does not assume the co-channel interferers to be identically distributed, as is typical in realistic cellular layouts, (ii) it avoids the loose spectral efficiency bounds used in the literature, which only considered the worst case and best case locations of identical co-channel interferers, (iii) it explicitly includes the effect of multi-tier interferers in the cellular layout and uses a more accurate model for handling the total co-channel interference, and (iv) it captures the impact of using small modulation constellation sizes, which are typical of cellular standards. The analytical results are verified using extensive Monte Carlo simulations.

Group Actions and Elementary Number Theory

Abstract | In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.

Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory

The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.

Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory

This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier's method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations theta(x) and theta(y) are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.