Closed-form Formulation Research Articles

Development of an analytical method for optimum design of reinforced concrete beams considering both flexural and shear effects

Optimization is an important subject which is widely used in engineering problems. In this paper, an analytical method is developed for optimum design of reinforced concrete beams considering both flexural and shear effects. A closedform formulation is derived for optimal height and rebar of beams. The total material cost of steel and concrete is considered as the objective function which is minimized during the optimization process. The ultimate flexural and shear capacities of the beam are considered as the main constraints. The ultimate limit state is considered for deriving the relations for flexural capacity of the beam. The design requirements are considered according to the item 9 of the Iranian National Building. Analytical formulas and some curves are proposed to be used for optimum design of RC beams. The proposed method can be used to perform the optimization of RC beams without the need of any prior knowledge in optimization. Also, the results of the studied numerical example show that the proposed method results in a better design comparing with the other methods.

Closed-Form Formulation for Continuous Prediction of at-Rest Coefficient for Saturated Soils

Closed-Form Formulation for Continuous Prediction of at-Rest Coefficient for Saturated Soils

Estimation of optimum tuned mass damper parameters via machine learning

The performance of tuned mass dampers (TMDs) relies on a tuning process in which the parameters are optimized for one or several objectives. For this purpose, several formulations and numerical optimization methods have been developed. The existing closed form formulation may not be suitable for a desired objective, and numerical optimization methods must be applied to every different system. For that reason, optimum TMD parameters such as period and damping ratio can be estimated by using machine learning. Since the use of machine learning in TMD optimization is a novel field of research, a well-known Artificial Neural Network (ANN) model is proposed. Training of the ANN was done by using optimum TMD values of several sets of single degree of freedom (SDOF) structures. The optimum values were found according to an optimization process using a flower pollination algorithm (FPA) and transfer function amplitude as an objective in the frequency domain. The generated ANN model is generally effective to find the same optimum results as the FPA approach up to two decimal places. Also, the ANN model was used to generate three basic tuning formulations, which are tested on SDOF and multiple degrees of freedom (MDOF) structural models. Including the responses under seismic excitation by considering stroke of the TMD, the optimum TMD parameters defined according to the developed formulations are more effective than optimum results found by existing formulations for reduction of maximum structural responses.

A New Approach to the Statistical Analysis of Non-Central Complex Gaussian Quadratic Forms With Applications

This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable that replaces the original CGQF and converges in distribution to it. This technique is valid for both definite and indefinite CGQFs and yields simple expressions of the probability density function (PDF) and the cumulative distribution function (CDF) that only involve elementary functions. This overcomes a major limitation of previous approaches, where the complexity of the resulting PDF and CDF does not allow for further analytical derivations. Additionally, the mean square error between the original CGQF and the auxiliary one is provided in a simple closed-form formulation. These new results are then leveraged to analyze the outage probability and the average bit error rate of maximal ratio combining systems over correlated Rician channels.

Development of allowable bearing capacity for strip foundations in unsaturated soils

An allowable bearing capacity formulation of strip foundations is developed for unsaturated soils under the non–hydrostatic in–situ stress. Four cases are analyzed according to both in–situ stress states and suction distributions. The proposed closed–form formulation is easy to use along with non–negative factors as an application condition. Furthermore, the obtained results are compared against three published results reported in the literature, and good agreements between these results are observed. Finally, a parametric study is performed to present how unsaturated strength characteristics and in–situ stress states affect the allowable bearing capacity.

Peak Temperature Minimization for Hard Real-Time Systems Using DVS and DPM

With the increasing power densities, managing the on-chip temperature has become an important design challenge, especially for hard real-time systems. This paper addresses the problem of minimizing the peak temperature under hard real-time constraints using a combination of dynamic voltage scaling and dynamic power management. We derive a closed-form formulation for the peak temperature and provide a genetic-algorithm-based approach to solve the problem. Our approach is evaluated with both simulations and real measurements with an Intel i5 processor. The evaluation results demonstrate the effectiveness of the proposed approach compared to related works in the literature.

Impacts of imperfect SIC and imperfect hardware in performance analysis on AF non-orthogonal multiple access network

In normal non-orthogonal multiple access (NOMA) network, perfect successive interference cancellation (SIC) and perfect hardware impairments are usually admitted at transceivers. However, imperfections of SIC and hardware exist in mathematical analysis of practical system, and such imperfections provide guideline to deploy NOMA in practical circumstances effectively. To overcome these disadvantages, this paper considers relaying NOMA as existence of hardware noise and interference of imperfect SIC operation and hence degraded performance under related factors can be addressed. We examine the system performance of the proposed system and develop a closed-form formulation of outage probabilities for each user. In high signal to noise ratio regime, we consider the corresponding asymptotic outage probability to provide meaningful insights in our proposed schemes. We also exhibit comparison study with other works related performance evaluation and with Decode and Forward based NOMA as useful benchmark. To further examine system performance of the proposed scheme, we derive formula and verify results in term of the throughput performance. Finally, numerical examples are performed to validate the effectiveness of the proposed scheme as practical challenges are raised, and compare these performance considerations with that in other system models with respect to outage behavior as varying related parameters.

Monocular Visual-Inertial Odometry with an Unbiased Linear System Model and Robust Feature Tracking Front-End.

The research field of visual-inertial odometry has entered a mature stage in recent years. However, unneglectable problems still exist. Tradeoffs have to be made between high accuracy and low computation for users. In addition, notation confusion exists in quaternion descriptions of rotation; although not fatal, this may results in unnecessary difficulties in understanding for researchers. In this paper, we develop a visual-inertial odometry which gives consideration to both precision and computation. The proposed algorithm is a filter-based solution that utilizes the framework of the noted multi-state constraint Kalman filter. To dispel notation confusion, we deduced the error state transition equation from scratch, using the more cognitive Hamilton notation of quaternion. We further come up with a fully linear closed-form formulation that is readily implemented. As the filter-based back-end is vulnerable to feature matching outliers, a descriptor-assisted optical flow tracking front-end was developed to cope with the issue. This modification only requires negligible additional computation. In addition, an initialization procedure is implemented, which automatically selects static data to initialize the filter state. Evaluations of proposed methods were done on a public, real-world dataset, and comparisons were made with state-of-the-art solutions. The experimental results show that the proposed solution is comparable in precision and demonstrates higher computation efficiency compared to the state-of-the-art.

No Gap Second-Order Optimality Conditions for Circular Conic Programs

In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.

Fast Phased Array Calibration by Power-Only Measurements Twice for Each Antenna Element

This paper proposes a novel power-only measurement method for phased array antenna calibration. Besides the total array power, only one phase shift and two power measurements for each array element are required to determine the element complex electric field distortion, one by shifting the element’s phase of π/2 and the other by turning the element under test off. The theory of the proposed calibration method is given, and the closed form formulation of the element amplitude and phase distortions is derived. From the mathematical point of view, it is the minimum required measurements that use two scalar values to determine one complex vector. Numerical simulations and experiments are conducted to validate and demonstrate the effectiveness of the proposed calibration method.

A closed form railway line delay propagation model

Railway service quality can be measured by the aggregate delay over a time horizon due to an event that delays a given train. Timetables for railway services may dampen delay propagations to subsequent trains by adding either supplement time or buffer time to the timetable. The evaluation of these variables is often performed by time consuming analysis with simulation software, or other complex, time-consuming calculations. This paper proposes instead an analytical closed form formulation of aggregate delay, which offers theoretical insights into railway delays and managerial insight into the properties of timetables at an aggregate level, and which may function as a fast sub-algorithm for timetable evaluations in larger optimization and transport models. Analysis of the function recommends a restraint in the utilization of timetable supplement and buffer, as their delay-damping effect decreases with their magnitude. Further, the effect of different threshold values in delay measurement is demonstrated, giving information valuable to the design of service contracts. Numerical analysis of a common suburban railway line shows that the polynomial function provides guidance and insight even when theoretical assumptions are violated.

Nondestructive Extraction of Parameters of Multilayered Media Using Terahertz Pulse Technique

Abstract In this work, an efficient non-invasive terahertz pulse technique is proposed and investigated to determine the thickness and refractive index of each layer in an optically thick stratified media. A closed form formulations are derived for simultaneous extraction of the thickness and complex refractive index of each layer with the help of primary reflected signals from the multilayered structure. The proposed technique is numerically tested using a full wave electromagnetic simulator and is experimental verified in the millimeter wave frequency range by utilizing the power peaks corresponding to the primary reflected signals. The numerical and measured results of multilayered samples under test are in good agreement with the reference data. The proposed terahertz pulse technique can be used for non-destructive testing of the multilayered system existing in various industries.

On Hirth Ring Couplings: Design Principles Including the Effect of Friction

Rings with Hirth couplings are primarily used for the accurate positioning of axial-symmetric components in the machine tool industry and, generally, in mechanical components. It is also possible to use Hirth rings as connection tools. Specific industries with special milling and grinding machines are able to manufacture both tailor made and standard Hirth rings available on stock. Unfortunately, no international standard (for instance ISO, DIN or AGMA) is available for the production and the design of such components. In the best-case scenario, it is possible to find simplified design formulae in the catalogue of the suppliers. The aim of this work is to provide some accurate formulae and computational methods for design to provide better awareness on the limitations and the potential of this type of connection. The work consists of five parts: (i) a review of the base calculation derived mainly from the catalogues of manufacturers; (ii) an improved calculation based on a new analytical method including the friction phenomenon; (iii) an experimentation run for validating the method; (iv) a case study applied to a machine tool; and, (v) a closed form formulation to determine an upper threshold for friction, thus ensuring the Hirth coupling regular performance.

A closed-form formulation for the conformal articulation of metal-on-polyethylene hip prostheses: Contact mechanics and sliding distance.

Using Hertz contact law results in inaccurate outcomes when applied to the soft conformal hip implants. The finite element method also involves huge computational time and power. In addition, the sliding distance computed using the Euler rotation method does not incorporate tribology of bearing surfaces, contact mechanics and inertia forces. This study, therefore, aimed to develop a nonlinear dynamic model based on the multibody dynamic methodology to predict contact pressure and sliding distance of metal-on-polyethylene hip prosthesis, simultaneously, under normal walking condition. A closed-form formulation of the contact stresses distributed over the articulating surfaces was derived based upon the elastic foundation model, which reduced computational time and cost significantly. Three-dimensional physiological loading and motions, inertia forces due to hip motion and energy loss during contact were incorporated to obtain contact properties and sliding distance. Comparing the outcomes with that available in the literature and a finite element analysis allowed for the validation of our approach. Contours of contact stresses and accumulated sliding distances at different instants of the walking gait cycle were investigated and discussed. It was shown that the contact point at each instant was located within the zone with the corresponding highest accumulated sliding distance. In addition, the maximum contact pressure and area took place at the stance phase with a single support. The stress distribution onto the cup surface also conformed to the contact point trajectory and the physiological loading.

Fracture analysis of cracked thin-walled structures using a high-order XFEM and Irwin’s integral

We develop a novel fracture mechanics framework for cracked thin-walled structures based on the Mindlin-Reissner plate theory. The mixed interpolation of tensorial components (MITC) plate element within the extended finite element method (XFEM) is used for the discretization. High-order crack-tip enrichment functions are employed to resolve the linear elastic near field solutions and the stress intensity factors (SIFs) are extracted by using an analytical derivation of Irwin’s crack closure integral.The closed-form formulation of Irwin’s integral, given in terms of enriched degrees of freedom (DOFs), is shown to be valid for both structured and unstructured meshes. The SIFs of through-the-thickness cracks in thin-walled structures can thus be directly obtained upon the solution of the XFEM discrete system, without the need of constructing auxiliary fields for mode separation.The performance of the proposed approach is studied on several benchmark examples consisting of cracked plates and shells. We first consider plate examples with an inclined crack and two cracks approaching each other. Excellent accuracy in terms of SIFs, on structured and unstructured meshes is reported, even on rather coarse meshes. In particular, the case of two approaching cracks showcases the potential of Irwin’s integral in addressing crack coalescence problems. Finally, we demonstrate the accuracy of the proposed method on cylindrical-shell type problems with a crack subjected to either tension, torsion, or internal pressure.

Ultimate strength formulation of stiffened panels under in-plane compression or tension with cracking damage

The aim of the present study is to develop closed-form formulations for predicting the ultimate compressive and tensional strength of stiffened steel panels with crack damages. First, a numerical database is generated. This database includes the ultimate strength levels of stiffened steel panels with cracks subjected to axial compressive or tensile loads. It was carried out with a series of nonlinear FEM analyses by varying the size of crack damage. In the following sections, regression analysis is used for deriving the empirical formulations. The results of the present paper can be used for the reliability and risk assessment of structures, including stiffened steel panels with cracks.

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

The size-dependent static, free vibration and buckling behaviours of functionally graded (FG) sandwich plates are analysed in this study. Utilising the modified couple stress theory and variational principle, governing equations of motion are developed with a refined shear deformation theory. The rectangular plates embedded on two opposite simply-supported edges with the arbitrary combinations of the other two. Based on the state-space Levy solution, the deflections, stresses, natural frequencies and critical buckling loads are analytically solved for the closed-form formulations. The effects of material distribution and graded schemes, geometric parameters and boundary conditions are also investigated to examine the size-dependent behaviours of FG sandwich microplates.

Outage Analysis for Downlink NOMA With Statistical Channel State Information

Conventional non-orthogonal multiple access (NOMA) schemes assume perfect channel state information (CSI) at the transmitter side, which is nearly impractical for many communication scenarios. Instead, this letter considers a practical downlink NOMA system in the Nakagami-m fading channels, of which the transmitter only knows the statistical CSI associated with each user. We analyze the outage performance of the proposed system and derive a closed-form formulation of each user's outage probability. Moreover, based on statistical CSI, the transmitter can optimize the system's sum throughput over power allocation for different users. The accuracy of our outage analysis and the efficacy of the proposed optimization algorithm are both confirmed by simulation results.

Throughput Analysis on 3-Dimensional Underwater Acoustic Network with One-Hop Mobile Relay.

Underwater acoustic communication network (UACN) has been considered as an essential infrastructure for ocean exploitation. Performance analysis of UACN is important in underwater acoustic network deployment and management. In this paper, we analyze the network throughput of three-dimensional randomly deployed transmitter–receiver pairs. Due to the long delay of acoustic channels, complicated networking protocols with heavy signaling overhead may not be appropriate. In this paper, we consider only one-hop or two-hop transmission, to save the signaling cost. That is, we assume the transmitter sends the data packet to the receiver by one-hop direct transmission, or by two-hop transmission via mobile relays. We derive the closed-form formulation of packet delivery rate with respect to the transmission delay and the number of transmitter–receiver pairs. The correctness of the derivation results are verified by computer simulations. Our analysis indicates how to obtain a precise tradeoff between the delay constraint and the network capacity.

An investigation of AASHTO’s requirements for providing continuity in simple span bridges made continuous

AASHTO’s requirements for providing continuity in simple span bridges made continuous are investigated by performing a parametric study which consists of 140 time dependent analyses for various precast concrete beam shapes. The beam shapes considered include three precast concrete bulb tees (PCBT), two AASHTO type beams, and two Florida I-beams (FIB). Various beam spacing and span configurations are considered. A sectional analysis approach that employs the age adjusted effective modulus method for capturing creep effects is presented for calculating restraint moments. AASHTO models for creep and shrinkage are used to conduct the parametric study. For each case considered a minimum girder age for when continuity can be established is recommended such that the total restraint moment at the intermediate support is equal to or smaller than zero. The recommended minimum girder ages at continuity vary from 55 to 90 days for PCBTs, 55–70 days for AASHTO type beams, and 55–80 days for FIBs. The influence of fci′, choice of creep and shrinkage model, and choice of analysis method on the magnitude of restraint moments is investigated. The specification of a higher fci′ is an effective technique to reduce the minimum required girder age at continuity. The magnitude of restraint moments appears to be highly sensitive to the selected creep and shrinkage model. The proposed analysis method addresses the shortcomings of other closed form formulations and results in restraint moments that are more sensitive to the girder age at continuity.