Analytical model for stress-strain response of plastic waste mixed soil

Recycling plastic water bottles has become one of the major challenges world wide. The present study provides an approach for the use of plastic waste as reinforcement material in soil, which can be used for ground improvement, subbases, and subgrade preparation in road construction. The experimental results are presented in the form of stress-strain-pore water pressure response and compression paths. On the basis of experimental test results, it is observed that the strength of soil is improved and compressibility reduced significantly with the addition of a small percentage of plastic waste to the soil. In this paper, an analytical model is proposed to evaluate the response of plastic waste mixed soil. It is noted that the model captures the stress-strain and pore water pressure response of all percentages of plastic waste adequately. The paper also provides a comparative study of failure stress obtained from different published models and the proposed model, which are compared with experimental results. The improvement in strength attributable to the inclusion of plastic waste can be advantageously used in ground improvement projects.

Analytical Determination of Residual Strength and Linkup Strength for Flat Panels, with Multiple Site Damage

The problem of multiple site damage in aged airplane fuselage is handled in this paper. The analytical and numerical procedures used for the estimation of the strength of a flat panel with such multi-site damage are presented. Further, numerical results are presented on the residual strength of the panel using fracture mechanics-based approach and the stress levels when the leading crack is likely to link up with multiple site damage cracks. The presence of multiple site damage cracks in the vicinity of leading crack significantly decreases the residual strength of the panel. The model is verified using experimental data from the open literature and the predictions are in good agreement with the measured residual strength.

Analytical solutions for transient temperature distribution in a geothermal reservoir due to cold water injection

An analytical solution to describe the transient temperature distribution in a geothermal reservoir in response to injection of cold water is presented. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. Results show that heat loss to the confining rock layers plays a vital role in slowing down the cooling of the reservoir. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be profound on the results.

Analytical Closed-Form Expressions for Harmonic Distortion Corresponding to Novel Switching Sequences for Neutral-Point-Clamped Inverters

Analytical closed-form expressions for harmonic distortion factors corresponding to various pulsewidth modulation (PWM) techniques for a two-level inverter have been reported in the literature. This paper derives such analytical closed-form expressions, pertaining to centered space-vector PWM (CSVPWM) and eight different advanced bus-clamping PWM (ABCPWM) schemes, for a three-level neutral-point-clamped (NPC) inverter. These ABCPWM schemes switch each phase at twice the nominal switching frequency in certain intervals of the line cycle while clamping each phase to one of the dc terminals over certain other intervals. The harmonic spectra of the output voltages, corresponding to the eight ABCPWM schemes, are studied and compared experimentally with that of CSVPWM over the entire modulation range. The measured values of weighted total harmonic distortion (WTHD) of the line voltage V-WTHD are used to validate the analytical closed-form expressions derived. The analytical expressions, pertaining to two of the ABCPWM methods, are also validated by measuring the total harmonic distortion (THD) in the line current I-THD on a 2.2-kW constant volts-per-hertz induction motor drive.

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Analytical evaluation of harmonic distortion factor corresponding to generalised advanced bus-clamping pulse width modulation

A few advanced bus-clamping pulse width modulation (ABCPWM) methods have been proposed recently for a three-phase inverter. With these methods, each phase is clamped, switched at nominal frequency, and switched at twice the nominal frequency in different regions of the fundamental cycle. This study proposes a generalised ABCPWM scheme, encompassing the few ABCPWM schemes that have been proposed and many more ABCPWM schemes that have not been reported yet. Furthermore, analytical closed-form expression is derived for the harmonic distortion factor corresponding to the generalised ABCPWM. This factor is independent of load parameters. The analytical expression derived here brings out the dependence of root-mean-square (RMS) current ripple on modulation index, and can be used to evaluate the RMS current ripple corresponding to any ABCPWM scheme. The analytical closed-form expression is validated experimentally in terms of measured weighted total harmonic distortion (THD) in line voltage (V-WTHD) and measured THD in line current (I-THD) on a 6 kW induction motor drive.

Analytical approach to quantile estimation in regional frequency analysis based on fuzzy framework

Regional frequency analysis is widely used for estimating quantiles of hydrological extreme events at sparsely gauged/ungauged target sites in river basins. It involves identification of a region (group of watersheds) resembling watershed of the target site, and use of information pooled from the region to estimate quantile for the target site. In the analysis, watershed of the target site is assumed to completely resemble watersheds in the identified region in terms of mechanism underlying generation of extreme event. In reality, it is rare to find watersheds that completely resemble each other. Fuzzy clustering approach can account for partial resemblance of watersheds and yield region(s) for the target site. Formation of regions and quantile estimation requires discerning information from fuzzy-membership matrix obtained based on the approach. Practitioners often defuzzify the matrix to form disjoint clusters (regions) and use them as the basis for quantile estimation. The defuzzification approach (DFA) results in loss of information discerned on partial resemblance of watersheds. The lost information cannot be utilized in quantile estimation, owing to which the estimates could have significant error. To avert the loss of information, a threshold strategy (TS) was considered in some prior studies. In this study, it is analytically shown that the strategy results in under-prediction of quantiles. To address this, a mathematical approach is proposed in this study and its effectiveness in estimating flood quantiles relative to DFA and TS is demonstrated through Monte-Carlo simulation experiments and case study on Mid-Atlantic water resources region, USA. (C) 2015 Elsevier B.V. All rights reserved.

FRP-Confined Clay Brick Masonry Assemblages under Axial Compression: Experimental and Analytical Investigations

Unreinforced masonry (URM) structures that are in need of repair and rehabilitation constitute a significant portion of building stock worldwide. The successful application of fiber-reinforced polymers (FRP) for repair and retrofitting of reinforced-concrete (RC) structures has opened new avenues for strengthening URM structures with FRP materials. The present study analyzes the behavior of FRP-confined masonry prisms under monotonic axial compression. Masonry comprising of burnt clay bricks and cement-sand mortar (generally adopted in the Indian subcontinent) having E-b/E-m ratio less than one is employed in the study. The parameters considered in the study are, (1) masonry bonding pattern, (2) inclination of loading axis to the bed joint, (3) type of FRP (carbon FRP or glass FRP), and (4) grade of FRP fabric. The performance of FRP-confined masonry prisms is compared with unconfined masonry prisms in terms of compressive strength, modulus of elasticity and stress-strain response. The results showed an enhancement in compressive strength, modulus of elasticity, strain at peak stress, and ultimate strain for FRP-confined masonry prisms. The FRP confinement of masonry resulted in reducing the influence of the inclination of the loading axis to the bed joint on the compressive strength and failure pattern. Various analytical models available in the literature for the prediction of compressive strength of FRP-confined masonry are assessed. New coefficients are generated for the analytical model by appending experimental results of the current study with data available in the literature. (C) 2014 American Society of Civil Engineers.

Electromagnetic analysis of novel class of multiple core/multiple clad step index single mode optical fiber by analytical means

General propagation properties and universal curves are given for double clad single mode fibers with inner cladding index higher or lower than the outer cladding index, using the parameter: inner cladding/core radii ratio. Mode cut-off conditions are also examined for the cases. It is shown that dispersion properties largely differ from the single clad single mode fiber case, leading to large new possibilities for extension of single mode operation for large wavelength tange. Paper demonstrates that how substantially we can extend the single mode operation range by using the raised inner cladding fiber. Throughout we have applied our own computations technique to find out the eigenvalue for a given modes. Detail derivations with all trivial mathematics for eigenmode equation are derived for each case. Paper also demonstrates that there is not much use of using depressed inner cladding fiber. We have also concluded that using the large inner cladding/inner core radius we can significantly increase the single mode operation range for the large wavelength region. (C) 2015 Elsevier GmbH. All rights reserved.

Benchmark analytical solutions from beams with shared eigenpair

Structures with governing equations having identical inertial terms but somewhat differing stiffness terms can be termed flexurally analogous. An example of such a structure includes an axially loaded non-uniform beam and an unloaded uniform beam, for which an exact solution exists. We find that there exist shared eigenpairs (frequency and mode shapes) for a particular mode between such structures. Non-uniform beams with uniform axial loads, gravity loaded beams and rotating beams are considered and shared eigenpairs with uniform beams are found. In general, the derived flexural stiffness functions (FSF's) for the non-uniform beams required for the existence of shared eigenpair have internal singularities, but some of the singularities can be removed by an appropriate selection of integration constants using the theory of limits. The derived functions yield an insight into the relationship between the axial load and flexural stiffness of axially loaded beam structures. The derived functions can serve as benchmark solutions for numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.