Closed-form Analysis Research Articles

Non-linear in-plane postbuckling of arches with rotational end restraints under uniform radial loading

This paper presents a thorough and comprehensive investigation of non-linear buckling and postbuckling analyses of pin-ended shallow circular arches subjected to a uniform radial load and which have equal elastic rotational end-restraints. The differential equations of equilibrium for non-linear buckling and postbuckling are established based on a virtual work approach. Exact solutions for the non-linear bifurcation, limit point and lowest buckling loads are obtained; in particular, exact solutions for the non-linear postbuckling equilibrium paths are derived. The criteria for switching between fundamental buckling and postbuckling modes are developed in terms of critical values of a geometric parameter for an arch, with exact solutions for these critical values of geometric parameter being obtained. Analytical solutions of non-linear buckling and postbuckling problems for arches with rotational end-restraints are of great interest, since they constitute one of the very few closed-form analyses of buckling and postbuckling behaviour of continuous structural systems. These exact solutions are a contribution to the non-linear structural mechanics of arches, as well as providing useful benchmark solutions for verifying non-linear numerical analyses.

Steady-state performance analysis of HOS-based blind adaptive multiuser detection

The blind adaptive multiuser detections based on higher-order statistics (HOS) can obtain higher steady-state decorrelating performance than the conventional linear algorithm under the high SNR condition. However, the closed-form analysis for this steady-state performance is scarce due to the complication of analyzing the nonlinear updates of the adaptive algorithm. An analysis approach based on ordinary differential equation (ODE) method is proposed to get the closed-form excess mean-square error (EMSE) expression of the HOS-based multiuser detections. The simulation and the comparison verify the results of the analysis.

Explicit local buckling analysis of stiffened composite plates accounting for periodic boundary conditions and stiffener–plate interaction

Abstract The present contribution is devoted to the closed-form analysis of orthotropic plates under uniaxial uniform compressive load. The plates under consideration are stiffened by open-profile stiffeners in the longitudinal direction which represents a structural situation that is typical, e.g. for many aircraft parts such as tailplanes, wing covers or, at least in an approximate sense, fuselage sections. The analysis method explicitly accounts for periodicity properties of the given structural situation as well as for stiffener–plate interaction and is based on adequate displacement shapes for both the plate as well as the stiffeners in the form of simple polynomials and trigonometric functions. While the plates and the stiffener webs are treated as shear-rigid Kirchhoff-type plates, the stiffener flanges are modeled as Bernoulli-type beam elements in order to allow for a feasible solution of the problem. Using a Ritz-type approach, explicit expressions for the buckling loads are achieved which allow for a straightforward, efficient and yet reliable buckling analysis of stiffened composite panels. The excellent accuracy of the derived analysis method is established through comparison with the results by other authors and with results generated from the exact transcendental elasticity solution that is derived from the governing partial differential equations and the underlying boundary conditions. The characteristic buckling behaviour of stiffened composite plates is discussed for several representative plate-stiffener configurations.

Debonding analysis of FRP–concrete interface between two balanced adjacent flexural cracks in plated beams

A cohesive interface modeling approach to debonding analysis of adhesively bonded interface between two balanced adjacent flexural cracks in conventional material (e.g., concrete or wood) beams strengthened with externally bonded FRP plates is presented. Both the strengthened beam and strengthening FRP are modeled as two linearly elastic Euler–Bernoulli beams bonded together through a thin adhesive layer. A bi-linear cohesive model, which is commonly used in the literature, is adopted to characterize the stress-deformation relationship of the FRP–concrete interface. Completely different from the single-lap or double-shear pull models in which only the axial pull force is considered, the present model takes the couple moment and transverse shear forces in both the substrates into account to study the second type of intermediate crack-induced debonding (IC debonding) along the interface. The whole debonding process of the FRP–concrete interface is discussed in detail, and closed-form solutions of bond slip, interface shear stress, and axial force of FRP in different stages are obtained. A rotational spring model is introduced at locations of the two adjacent flexural cracks to model the local flexibility of the cracked concrete beam, with which the relationship between the local bond slip and externally applied load is established and the real bond failure process of the FRP-plated concrete beam with the increasing of the externally applied load is revealed. Parametric studies are further conducted to investigate the effect of the thickness of adhesive layer on the bond behavior of FRP–concrete interface. The present closed-form solution and analysis on the local bond slip versus applied load relationship for the second type of IC debonding along the interface shed light on the bond failure process of structures externally strengthened with FRP composite plates and can be used effectively and efficiently to predict ductility and ultimate load of FRP-strengthened structures.

Overestimation of the field-effect mobility via transconductance measurements and the origin of the output/transfer characteristic discrepancy in organic field-effect transistors

Paramount to the rational design of electronic materials is the accurate characterization of their intrinsic properties. In particular, many applications of conducting and semiconducting soft materials have been driven by the development of materials with high, bias-stable field-effect mobility. Here, we demonstrate the effect of parasitic resistance and bias-dependent mobility on device electrical characteristics. Specifically, we analyze two of the most commonly employed test algorithms—the output and transfer curves—via a closed-form analysis. The analysis exhibits characteristics endemic to those published in literature, such as effective mobilities with maxima with respect to gate voltage that may lead to overstatements of mobility by manyfold. Furthermore, analysis reveals that common overestimation relative to intrinsic and output-estimated mobilities is caused solely by gate-bias-dependent mobility, and parasitic resistance can only lead to an underestimation of the effective mobility. We introduce a method for accurate mobility estimation and a dimensionless variable for evaluating the importance of contact resistance.

Broadband Equivalent Circuit Modeling of Self-Complementary Bow-Tie Antennas Monolithically Integrated with Semiconductors for Terahertz Applications

We identify a broadband equivalent circuit of an on-chip self-complementary antenna integrated with a µm-sized semiconductor mesa structure whose circuit elements can be interpreted by using closed-form analysis. Prior to the equivalent circuit analysis, an electromagnetic simulation is done to investigate frequency independency of the input impedance for the integrated self-complementary antenna in terahertz range.

Closed-form analysis of dual-branch switched diversity with binary nonorthogonal signalling

An exact closed-form analytical expression is derived for the average bit error probability of dual-branch switched diversity over Rayleigh fading. A practical scheme is considered employing binary nonorthogonal signalling with noncoherent detection. The analytical results are useful to evaluate the performance-bandwidth trade-off in systems that intentionally employ nonorthogonal signalling.

Closed-form analysis of end-to-end network delay with Markov-modulated Poisson and fluid traffic

This paper develops a method for using traffic sources modelled as a Markov-modulated Poisson process (MMPP) and Markov-modulated fluid process (MMFP) in the framework of the bounded-variance network calculus, a novel stochastic network calculus framework for the approximated analysis of end-to-end network delay. The bounded-variance network calculus is an extension to multi-hop end-to-end paths of the Choe’s and Shroff’s Central-Limit-Theorem-based analysis of isolated network nodes. The input of the analysis is the statistical traffic envelope of sources, which is not available for generic MMPP and MMFP sources. The paper provides two statistical traffic envelopes, named two-moment and linear envelope, for general MMPP and MMFP sources, which can be used as an input of Central-Limit-Theorem-based frameworks for the analysis of network delay and, in turn, make it possible to use the rich collection of MMPP and MMFP models of voice, audio, data and video sources available in the literature. In this way, it is possible to avoid the computational complexity of traditional Markov analysis of end-to-end delay with MMPP and MMFP sources. With the linear envelope we can use simple analytical closed-form solutions for many important schedulers.

Analytical closed-form investigation of PWM inverter induction motor drive performance under DC bus voltage pulsation

The voltage unbalance conditions at the input rectifier stage of the AC–DC–AC rectifier-inverter fed induction motor drive is analysed. This unbalance can cause significant voltage harmonic of twice the line frequency 2f1 in the DC bus. This voltage ripple can have a degrading effect on the induction-machine performance characteristics. The authors present an analytical closed-form mathematical model and analysis of the impact of DC bus ripple voltage of the three-phase voltage source inverter with the space-vector PWM on the induction machine phase voltages, currents and torque pulsations. The analytical expressions for the voltage and current space vectors as a function of the DC bus voltage pulsation are derived. Using superposition, the separate parts of the motor currents can be determined. From the current space vectors, the torque behaviour is estimated, again as a function of DC link voltage pulsation. Next, it is shown that the DC link voltage ripple components may cause large torque pulsation. The proposed analytical method is based on the mixed p–z approach, enabling presentation of the results in lucid and closed form. To verify the effectiveness of the proposed analytical model, experimental results based on laboratory setup were obtained.

Progressive Accumulative Routing: Fundamental Concepts and Protocol

This paper considers a multi-hop network in which relay nodes cooperate to minimize the total energy consumed in transmitting a (unicast) packet from a source to a destination. We propose the Progressive Accumulative Routing (PAR) algorithm, which progressively performs relay discovery, relay ordering and relay power allocation in a distributed manner, such that each relay node only needs local information. We assume Destination Energy Accumulation, in which the destination accumulates the energy of multiple received copies of a packet, each of which is too weak to be reliably decoded by itself, while the lower complexity relay nodes use a decode-and-forward approach. We also provide a closed-form analysis of the energy-savings achieved by the PAR when a relay node is added to an already existing DEA route. Simulations verify that the algorithm considerably reduces the total energy consumption, and can be implemented efficiently.

Design and validation of composite patch repairs to cracked metallic structures

This paper describes an approach to a patch design for a crack repair, based largely on the simple closed-form analyses. For simplicity, the design approach does not include the effect of the out-of-plane bending nor polygon-shaped patch. However, once the basic design was brought out by that design approach, it can be re-analysed by using other advanced analytical models to account for those latter complexities. These advanced analytical methods are therefore also reviewed briefly in the paper. In addition, test data to validate the mentioned design and analysis methods are also presented and discussed.

Closed-form Analysis of Lossy Cosine-Squared Tapered Nonuniform Transmission Lines

The rigorous analytical solutions and the ABCD matrix of the lossy Cosine-Squared tapered nonuniform transmission lines (CSTNTL) are presented in this paper. According to different boundary conditions, the unique solution is obtained mathematically. Through the numerical calculations based on analytical solutions, the distributed voltages and currents in different terminated cases are shown to explain the transmission characteristics of CSTNTL. Especially in the lossy case the distributed power values are simulated to show the attenuation phenomenon.

Analysis and Identification of Wiener-Hammerstein System in Frequency Domain Using Two-Tone Measurements for Nonlinear RF Transmitters

This paper presents analysis and identification method of Wiener-Hammerstein system to characterize a nonlinear RF transmitter in fundamental frequency zone. A two-tone signal is used to analyze and identify a Wiener-Hammerstein model. A RF signal is converted to baseband-equivalent complex signal, and Wiener-Hammerstein model is considered to have a baseband equivalent complex polynomial and linear filters. For a two-tone input signal, closed form descriptions of the output signal in the time domain and frequency domain are developed using a newly suggested nonlinearly modulated two-tone phasors (NMTP). The relationship between frequency terms of input and output signals in RF transmitters are represented with linear matrix-vector equation based on NMTP analysis. An advantage of the proposed method is its simplicity using closed form analysis and linear approximation. In addition, we can model a wideband system with relatively narrowband measurements by sweeping two-tone signal. The prediction of spectral regrowth and the predistortion performance for WiBro 1FA signal demonstrate the validity of the proposed approach in identifying the nonlinear RF transmitters.

Recoding Patterns of Sensory Input: Higher-Order Features and the Function of Nonlinear Dendritic Trees

Here analytical and simulation results are presented characterizing the recoding arising when overlapping patterns of sensor input impinge on an array of model neurons with branched thresholded dendritic trees. Thus, the neural units employed are intended to capture the integrative behavior of pyramidal cells that sustain isolated Na(+) or NMDA spikes in their branches. Given a defined set of sensor vectors, equations were derived for the probability of firing of both branches and neurons and for the expected overlap between the neural firing patterns triggered by two afferent patterns of given overlap. Thus, both the sparseness of the neural representation and the orthogonalization of overlapping vectors were computed. Simulations were then performed with an array of 1000 neurons comprising 30,000 branches to verify the analytical results and confirm their applicability to systems (which include any practicable artificial system) in which the combinatorically possible branches and neurons are severely subsampled. A means of readout and a measure of discrimination performance were provided so that the accuracy of discrimination among overlapping sensor vectors could be optimized as a function of neuron structure parameters. Good performance required both orthogonalization of the afferent patterns, so that discrimination was accurate and free of interference, and maintenance of a minimum level of neural activity, so that some neurons fired in response to each sensor pattern. It is shown that the discrimination performance achieved by arrays of neurons with branched dendritic trees could not be reached with single-compartment units, regardless of how many of the latter are used. The analytical results furnish a benchmark against which to measure further enhancements in the performance of subsequent simulated systems incorporating local neural mechanisms which, while often less amenable to closed-form analysis, are ubiquitous in biological neural circuitry.

Closed-form buckling analysis of stiffened composite plates and identification of minimum stiffener requirements

Longitudinal stiffeners attached to composite plates may significantly increase the overall buckling loads of the resultant stiffened structure. As long as the bending stiffness EI of the stiffener remains beneath some a priori unknown threshold value EI min (with E being Young’s modulus and I being the bending moment of inertia), the buckling pattern will usually be of a more or less global nature, meaning that both the plate and the stiffener will exhibit some certain buckling modes. Once a threshold value EI min for the bending stiffness, also called minimum stiffness, is exceeded, the stiffener more or less remains in its original position in the state of the onset of buckling while the buckling pattern of the stiffened plate is dominated by local buckling modes of the plate itself. The knowledge of this minimum bending stiffness EI min of longitudinal stiffeners of composite plates is of high practical importance and a predominant design criterion and will be considered in this paper. For the basic load cases uniform compression and pure shear and their combination, simple closed-form analytical approaches will be presented which enable a straightforward and quick yet accurate estimation of the buckling loads N 11 0 (compression) and N 12 0 (shear) of stiffened composite plates on the one hand, and the minimum bending stiffness EI min of the attached stiffeners on the other hand.

Reddy's layerwise laminate plate theory for the computation of elastic fields in the vicinity of straight free laminate edges

Reddy's layerwise laminate plate theory is employed for the closed-form analysis of free-edge effects in layered plates of arbitrary non-orthotropic layups. The approach consists of the subdivision of the physical laminate layers into an arbitrary number of mathematical layers through the plate thickness. In each interface, a set of unknown displacement functions with respect to the inplane width coordinate is introduced while in the thickness direction layerwise linear Lagrangian interpolation polynomials are employed. The unknown inplane functions are determined from the governing Euler–Lagrange differential equations, derived from the principle of minimum potential energy. A solution approach in the form of decaying exponential functions leads to closed-form analytical representations for all free-edge state variables in a straightforward manner while in the inner laminate regions, the stress state corresponding to Classical Laminate Plate Theory is recovered exactly. The present approach is applicable on a standard personal computer, needs insignificant computational effort even in cases of thick laminates consisting of a high number of layers and is in excellent agreement with reference results from the literature.

A closed-form analysis of perimeter member behavior in a steel building frame subject to fire

This paper outlines a closed-form methodology that can be used to predict the increase in demand experienced by the perimeter columns that are part of a fire-exposed steel building frame. The two-dimensional elevation-view subassembly considered for this study includes a two-storey length of the perimeter column and the floor beam framing into the column in the direction perpendicular to the building’s exterior. When heated, this beam will expand and induce bending moment and lateral deflection in the column as well as increased axial force in the beam itself. Our proposed approach has two primary components: (1) a material model that approximates nonlinearity and considers temperature effects, and (2) a mechanical model that represents the perimeter column and beam interaction. These models are used to develop a simplified closed-form solution for beam axial force and perimeter column bending moment that may be used as part of a performance-based design for fire exposure. The simplified model solutions are compared to the results of a more complex and detailed multi-story finite element analysis model. A comparison of these results shows that the simplified model results give good estimations of structural behavior.

Closed-form buckling analysis of compressively loaded composite plates braced by omega-stringers

In this contribution, the stability problem of composite plates braced by longitudinal omega-stringers under compression is treated in a closed-form analytical manner. Given that no global buckling modes of both plate and stringers occur and further assuming certain periodicity properties of the occurring local plate buckling modes, the given situation is reduced to the bifurcation buckling problem of an elastically restrained plate wherein the edge restraints depend on the geometric and material properties of the stringers and are calculated via the principle of virtual work. The buckling modes of the plate itself are approximated using an interpolation scheme consisting of rather simple trigonometric functions which allows for a closed-form analytical description of both the buckling modes as well as of the buckling loads of the elastically restrained composite plates. Accompanying detailed finite element computations show that the closed-form analytical approach is in very satisfying agreement with the numerical results and as such can be used with confidence in day-to-day engineering practice. Furthermore, the exact elasticity solution for the buckling problem of a compressively loaded elastically restrained composite plate is shortly discussed which can be derived from the governing partial differential equation in conjunction with the underlying boundary conditions of the plate. The closed-form approach can be shown to be in excellent agreement with the exact results which are generated in a numerical manner. Lastly, based on non-dimensional characteristic quantities, the exact elasticity solution is used to generate generic buckling curves which may be useful for practical engineering analysis and design purposes.

Explicit analysis and design equations for buckling loads and minimum stiffener requirements of orthotropic and isotropic plates under compressive load braced by longitudinal stiffeners

In the framework of lightweight engineering, especially in the conceptual phase of a structural analysis, closed-form analysis methods are of high practical importance since these usually work with negligible computational effort when compared to purely numerical approaches. In this paper, simple closed-form analytical formulas for the buckling loads N 11 0 of compressively loaded orthotropic composite and isotropic plates braced by longitudinal stiffeners are derived. Furthermore, closed-form expressions for the minimum bending stiffness EI min of the stiffeners are presented. The derived methods lead to a very satisfying accuracy when compared to the exact transcendental elasticity solution, to accompanying purely numerical analyses and to reference results from the literature, which makes the introduced analysis equations very suitable for the preliminary analysis and design of stiffened isotropic and orthotropic composite plates. Furthermore, due to their very simple nature, the introduced closed-form approaches can be recommended for direct use in an industrial environment for any practical engineering purpose.

Tunable laser-based design and analysis for fractional lambda switches

Fractional lambda switching (FlambdaS) is a novel approach for traffic management over all-optical networks with sub-wavelength provisioning capability. The unique characteristic of FlambdaS is the utilization of UTC (coordinated universal time) for switching with minimum or no buffers. Several central research issues are still open in FlambdaS and need to be formally defined and analyzed. In this paper, we introduce three novel switch designs that are based on the use of tunable lasers (which can be replaced in the future with wavelength converters). First, the paper presents analytical results of scheduling feasibility, which measures the total number of possible different schedules for each switch design. Then it is shown that the architecture with the highest scheduling feasibility is strictly non blocking in the space domain. Next, the paper provides a closed form analysis of the blocking probability in the time domain, which is applicable for any strictly non-space blocking switch, using combinatorics. In addition, the paper provides measures of the switching hardware complexity, which, for the strictly non-blocking architecture, has the same switching complexity as Clos interconnection network, i.e., O(N'radic(N')) where N' is the number of optical channels.