Conventional First-order Theory Research Articles

Bending, free vibration and impact response of thick laminated composite plates

In the present paper, the higher-order shear deformation theories (HST6, HST9, HST11, HST12) and the conventional first-order theory (FST) are employed to develop finite element analysis methods using eight-noded isoparametric elements to study the bending, free vibration and impact behaviour of laminated composite plates. The present results, based on higher-order theories, compare well with those existing in the literature. The effects of various parameters, such as span to thickness ratios, support conditions and stacking sequences on the laminate response are investigated. It is revealed that the first-order theory provides reasonably dependable results for natural frequencies, contact force, impact response and velocity profile of impactor for both thin and thick laminates. However, the higher-order theories are needed to compute stresses accurately in thick laminates.

Impact Behavior of Thick Laminated Composite Beams

In the present investigation a higher-order shear deformation theory (HST) and the conventional first-order theory (FST) are used to develop a finite element method to analyze the impact behavior of laminated composite beams. The higher-order theory assumes all the displacement components u, v, w that contain variation up to cubic power of z. The effects of various parameters, such as span to thickness ratios, support conditions and stacking sequence on the impact behavior of laminated composite beams are studied. Both eight-noded and nine-noded isoparametric elements are employed to compare the computational efficiency. However, to save computational time, numerical results are generated using only eight-noded isoparametric elements. The present results compare well with those of W. Goldsmith. It is observed that stresses computed using HST and FST exhibit wide variations.

Bending and free vibration analysis of shear deformable laminated composite beams by finite element method

In the present investigation a higher-order shear deformation theory and the conventional first-order theory are used to develop a finite element method to analyse accurately the bending and free vibration behaviour of laminated composite beams, using nine-noded isoparametric elements. The higher-order theory assumes all the displacement components, u, v and w, which contain variation up to a cubic power of z. The effects of various parameters such as fibre orientation, stacking sequence, span-to-thickness ratio and support condition on the non-dimensionalised deflections, stresses and fundamental frequencies are investigated. Cases where only the higher-order theory is likely to yield accurate results are highlighted.

Improved coupled-mode theory for parallel electron waveguides

A coupled-mode theory for parallel electron waveguide structures is developed and presented. This theory takes the nonorthogonality between the modes belonging to different electron waveguides, which is neglected in the first-order theory, into consideration and reflects this fact by including the modal overlap integral terms in the resultant coupled-mode equations. Various numerical examples are presented, using this improved theory and the first-order theory, and are compared with those of the exact calculations. It is shown that the improved theory can give more accurate results than the conventional first-order theory. Therefore, it is very useful for analyzing the quantum field-effect directional couplers and similar quantum interference devices.

Spin-wave renormalization in the Heisenberg ferromagnet. II. Consistent linearized Green's-function theory forS=12

In an earlier paper (referred to as I), the general structure of first-order Green's-function theories of the Heisenberg ferromagnet was analyzed, with particular emphasis on the spin-wave energy renormalization factor $R$. Spectral theorems and Dyson's rigorous low-temperature results were used to derive certain necessary conditions on $R$, and a critique of the standard first-order theories was also given. The special difficulties that occur in the case $S=\frac{1}{2}$ were brought out, and the impossibility of obtaining the correct low-$T$ results for both the spontaneous magnetization $\ensuremath{\sigma}$ and the specific heat $\ensuremath{\gamma}$ in a conventional first-order theory was established. In this paper, we present the theory promised in I: a completely consistent first-order Green's-function theory for $S=\frac{1}{2}$ that yields the correct low-$T$ results for both $\ensuremath{\sigma}$ and $\ensuremath{\gamma}$, and incorporates all the other constraints derived in I, among which are: the incorporation of all the extra spin-operator identities specific to $S=\frac{1}{2}$; the conservation of the zeroth and first moments of the spectral function; the determination of a unique expression for the longitudinal spin-spin correlation (in terms of $\ensuremath{\sigma}$ and the transverse correlation) from which various limits and special cases are recovered correctly; the inclusion of the leading effects of multiple spin-wave states via a dispersive part even in the lowest-order Green's function, following the derivation of an integral equation in the momentum variable for the latter quantity. It is emphasized that what follows is not just the application of yet another decoupling prescription to a well-known problem and the working out of its consequences. The problem of linearization is carefully scrutinized and a systematic derivation of the optimal result in this regard is given. The key ingredients are the retention of all possible two-spin correlations and the evaluation of the longitudinal spin-spin correlation in a manner free of arbitrary parameters. Finally, we show also that, as $\ensuremath{\sigma}\ensuremath{\rightarrow}0$, the only consistent first-order theory is that obtained in the well-known random-phase approximation, and that our formalism does indeed approach this limit as $T\ensuremath{\rightarrow}{T}_{c}$. We are able, therefore, to provide a satisfactory interpolation theory covering both the low-temperature region and the region near ${T}_{c}$. In a series of appendices it is shown precisely where and how the inconsistencies in various earlier decoupling schemes arise, mainly as a result of neglecting certain crucial two-spin correlations.

An accurate numerical steady-state one-dimensional solution of the P- N junction

A numerical method of solution of the fundamental semiconductor steady-state one-dimensional transport equations, already available in the literature, is improved and extended, and is applied to a single-junction device. A reduced set of ‘exact’ relations is derived directly from the fundamental set with none of the conventional assumptions or approximations, and is solved numerically by a simple iterative procedure. Freedom is available in the choice of the doping profile, recombination law, mobility dependencies, injection level, and boundary conditions applied solely at the external contacts. In spite of the generality of the original method, its analytical formulation is shown to be unsuitable for generating a sound numerical algorithm sufficiently acccurate and valid for high reverse-bias conditions. Difficulties and limitations are exposed, and overcomeby an improved formulation extended to any bias condition. Emphasis is on the selection of a numerical algorithm sufficiently sound and efficient to cope with the several fundamental difficulties present in the numerical analysis, and on achieving a high degree of accuracy in the final results (the most delicate problem). As a simple application of the improved formulation, ‘exact’ and first-order theory results for an idealized structure are presented and compared. The poorness of some of the basic assumptions of the conventional first-order theory is exposed, in spite of a satisfactory agreement between the exact and first-order results of the terminal properties for particular bias conditions. The computation time for the achievement of one set of very accurate solutions for a specified applied voltage amounts to approx 1 min on an IBM 7094/7040 shared-file system.