Journal of Applied and Computational Mechanics
Volume:9 Issue: 2, Spring 2023

In this study, an exact analytical solution for the heat conduction problem in a truncated conical shell is presented. The cone is made of functionally graded materials and it is considered that the material properties vary according to power-law functions. The general thermal boundary conditions are applied to cover a wide variety of actual applications. The results are successfully validated. Two examples, which are tried to mimic practical conditions, are studied using the derived solution, and a parametric study is done to shed light on the problem. The outcomes of this research provide useful information for understanding the nature of heat transfer behavior in the specific geometry of a cone. Regarding the specific applications of conical shells, the results can be used in the prefabrication process of these shells and tailoring the design parameter of functionally graded materials.

Decision making and path planning in case of highly transient dynamics of the surrounding as well as the effect of road condition are the issues that are not completely solved in the previous researches. The goal is to perform a safe and comfortable lane change that includes flexible re-planning capabilities. In this paper, a novel structure for path planning and decision making part of a vehicle automatic lane change has been introduced which comprehensively considers both longitudinal and lateral dynamics of the vehicle. The presented method is able to perform re-planning even in the middle of a lane change maneuver according to new traffic condition. Inclusion of the dynamics of all involved vehicles and providing online performance are the other advantages of the proposed system. The algorithm is simulated and various scenarios are constructed to evaluate the efficiency of the system. The results show that the system has completely acceptable performance.

This study evaluates the performance of the SLAU, AUSM+UP upwind schemes, and CUSP artificial dissipation scheme for the flow through the convergent-divergent nozzles and turbine stator blades under different pressure ratios by developing an in-house code. By comparing the results with analytical and experimental results, it is found that, despite the simplicity of the SLAU scheme in the absence of tuning variables, it provides reasonable predictions for different turbine blades in point of location and strength of the shocks. The SLAU scheme could converge at a much higher rate, leading to very much lower values of residuals. The SLAU scheme causes about 30% and 20% improvements over the prediction of the shock-induced losses in supersonic and subsonic outlet flows, respectively.

Numerical simulations of the airflow around a hatchback and a sedan vehicle without and with spoilers are carried out, besides, its effect on drag and lift coefficients are investigated with and without crosswinds. The effects of crosswind on aerodynamic forces are considered and its results are compared with the case without considering the effects of crosswind. For this purpose, the steady-state three-dimensional Navier-Stokes equations are solved by the Simple Method. Moreover, for turbulence modeling, the Realizable k-e model is implemented. The spoiler angle and its length are changed for both car models; furthermore, the effects of two spoilers on drag and lift coefficients are investigated in detail. All cases are simulated with and without crosswind. The results show that the impact of the spoiler for without crosswind conditions to decrease the lift coefficient in both models is significant; in addition, the drag coefficients are reduced for some cares. It can be concluded that the increase of spoiler length for both sedan and hatchback vehicles can increase the downward force and vehicle stability.

Research on the microdroplet splitting phenomenon has intensified in recent years. Microdroplet splitting has numerous applications in chemical synthesis, biology, and separation processes. The current paper covers the numerical study of ferrofluid microdroplet splitting at various lengths and velocities inside the T-junction with branches of unequal widths under asymmetric magnetic fields. Microdroplet splitting can be controlled by using an asymmetric magnetic field and the asymmetry in the width of T-junctions branches. Three geometrical models of the T-junction with different widths ratio (0.7, 0.85, and 1), along with a magnetic field with various intensities are studied. This magnetic field is generated by a line dipole. In this study, the distance between the dipole and origin is kept constant. The splitting ratio of ferrofluid microdroplets at different velocities (different capillary numbers), different non-dimensional lengths and different magnetic force (different magnetic Bond numbers) at the center of T-junction are calculated for each amount of branch width. The results are verified with previous works and their correctness is proved. The splitting ratio is defined as the volumetric ratio of the larger daughter droplet to the mother droplet. The results indicate that generally, the stronger the asymmetric magnetic force is, the more asymmetric the splitting will become, with the splitting ratio becoming closer to 1. Also, as asymmetry increases between the widths of the two branches of the T-junction, the splitting ratio approaches 1.

This paper aims to provide a concentrated photovoltaic thermal (CPVT) system regarding the high potential of receiving solar energy in Iran. Generated thermal energy of the system supplies the average thermal load of a commercial building and also its generated electricity is sold to the grid according to Iran's feed-in tariff (FiT). In order to calculate the system profitability, an economic evaluation is done in 20 years that is regarded as a novel approach. Furthermore, sensitivity analyses are performed to develop the results to the other locations with different economic conditions and various potential of energy resources, and also to present an appropriate financial outlook. The results demonstrate that the system is highly profitable given net present value (NPV) of 551.55 k$, internal rate of return (IRR) of 150.79%, benefit to cost ratio (BCR) of 10.32, payback time (PBT) of 0.51 years, and levelized cost of energy (LCOE) of 0.1293 $/MWh. Moreover, sensitivity analyses show that the system profitability is greatly appropriate even regarding the variety of unpredictable parameters. For instance, if the generated energy decreases by 20%, IRR and PBT will equal 120.63% and 0.63 years respectively, and the system can still maintain its high profitability. Moreover, it has been revealed that the enhancement of FiT can increase the system's economic efficiency. According to the results, it is noticeably profitable to use the CPVT systems to produce electrical and thermal power in countries with a high potential of receiving solar energy (especially middle-eastern countries).

Graphs are an effective tool for planetary gear trains (PGTs) synthesis and for the enumeration of all possible PGTs for transmission systems. In the past fifty years, considerable effort has been devoted to the synthesis of PGTs. To date, however, synthesis results are inconsistent, and accurate synthesis results are difficult to achieve. This paper proposes a systematic approach for synthesizing PGTs depending on spanning trees and parent graphs. Trees suitable for constructing rooted graphs are first identified. The parent graphs are then listed. Finally, geared graphs are discovered by inspecting their parent graphs and spanning trees. To precisely detect spanning trees, a novel method based on two link assortment equations is presented. Transfer vertices and edge levels are detected without the use of any computations. This work develops the vertex matrix of the rooted graph, and its distinctive equation is used to arrange the vertex degree arrays according to the vertex levels and eliminate the arrays that violate the distinctive equations. The precise results of the 5-link geared graphs are confirmed to be 24. The disparity between the recent and previous synthesis results can be attributed to the fact that the findings of the current method, which employs rooted graphs, are more comprehensive than those obtained with graphs lacking multiple joints. A novel algorithm for detecting structural isomorphism is proposed. By comparing the vertex degree listings and gear strings, non-isomorphic geared graphs are obtained. The algorithm is simple and computationally efficient. The graph representation is one-to-one with the vertex degree listing and gear string representation. This allows for the storage of a large number of graphs on a computer for later use.

Motorcycles under heavy braking conditions can experience a self-excited oscillation known as ‘chatter’. A simplified three degrees of freedom model of the rear of a motorcycle is developed to study the stability of this mode with the inclusion of lateral dynamics introduced by roll angle. Since motorcycles achieve high roll angles during operation, the study of chatter during these manoeuvres is a topic of interest. The equations of motion are linearised about a quasistatic equilibrium and simplified to accommodate symbolic inspection. Power analysis, eigensystem analysis, eigenvalue sensitivity and Routh-Hurwitz stability criterion are used to study the stability of the system in the braking region. It was found that a driveline mode can become unstable at about 19 Hz, and that its tendency towards instability is increased with added roll angle. This mode is sensitive to model parameters affecting the system inertia and stiffness, as well as the chain geometry. Finally, it is found that the lateral dynamics and roll angle play no direct role in chatter but have a significant indirect effect on it through the working point of the force characteristic function of the tyre.

Hollow blocks are widely used in construction to reduce the thermal resistance of building walls. The air within the blocks has a low thermal conductivity, which makes it possible to consider such hollow blocks as a good insulating material. This work presents a numerical investigation of the impact of thermal radiation on energy transport and airflow inside a hollow block. The coupled heat transport by free convection, thermal radiation and conduction through the solid walls is taken into account. The finite-difference procedure is applied to work out numerically the control equations of conservation of momentum, energy and mass in both solid walls and air filled enclosure. The main parameters governing the problem are surface emissivity, Rayleigh number and thermal conductivity of solid walls. The influence of these factors on the overall heat transfer through hollow block is presented and investigated. The outcomes show that the low emissivity of the inner walls inside the hollow blocks will significantly help to reduce the energy consumption of buildings.

The motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the first time studying all necessary measures that increase the accuracy of the obtained results. These parameters are essential to perform a completely nonlinear analysis and consider the effects of the Earth’s rotation around its axis. Unlike most modeling of nonlinear partial differential equations in applied mechanics that only considers nonlinear effects in a particular direction, the general nonlinear terms are considered in the present study, which increases the accuracy of the amount of displacement of the Earth's inner layers. Also, the fully nonlinear and dynamic differential equations are solved by a semi-analytical polynomial method which is an innovative and efficient method. Determining the amount of critical pressure at the fault location that will cause phenomena such as earthquakes is one of the useful results that can be obtained from the mathematical modeling in this research.

Elevated cylindrical and conical steel tanks are widely used to conserve water or chemical liquids. These important structures are required to stay protected and operative at any time. The wall angle inclination of conical tank part, as well as the presence of the vertical earthquake component, can cause damage to this structure and even lead to its failure. The purpose of this study is to examine the effect of wall angle inclination of the tank and the vertical earthquake acceleration component on the nonlinear dynamic stability of the elevated steel conical tanks under seismic excitation. The elevated steel conical tank is simulated utilizing the finite element analysis method using ANSYS software. The fluid-structure interaction is considered using a suitable interface that allows the fluid to apply hydrodynamic pressures on the structure. Three different models, namely Model –A-30°, Model –B-45°and Model –C-60° are investigated; it has been concluded that the impact of inclination of the tank wall significantly affects the nonlinear stability of the elevated steel conical tank. While considering the vertical ground acceleration, inclination plays a significant role in the design of this type of structures. Therefore, it should be appropriately included in the seismic analysis of elevated steel conical tanks to satisfy the safety of the elevated steel conical tank response under seismic loading.

The head-discharge relationship for sharp-crested weirs is developed based on the energy consideration upstream and at the crest of the weir. The discharge for weirs of finite crest length is estimated by correlating the critical depth and total energy at the upstream of the weir. In both cases, discharge is linked with the total head. Therefore, prediction of discharge for both sharp-crested weirs and weirs of finite crest length requires an iterative solution method. The present technical note formulates the relationship between the discharge coefficients based on water and total heads to estimate the error associated with implementation of head-discharge equation based on the head. The proposed prediction curves are used to convert the iterative solution method based on the total head to a direct solution strategy based on the water depth at the upstream of sharp-crested weirs and weirs of finite crest length with either a sharped-edge or rounded entrance. Based on the similarity of velocity profiles in gate flow, it is concluded that a distance as short as 2.4 times of the water head is suitable enough to measure the upstream water depth. In sharp-crested weirs, the effect of velocity head is negligible for the approach velocity ratio smaller than 0.1. Different correction curves were developed for weirs of finite crest length based on the ratio of water head to the crest length of weirs.

The progress reached in the high heat flux systems has required the development of appropriate thermal management approaches for dissipating the high heat fluxes, especially for small-scale devices. One of the most advantageous thermal management techniques is the utilization of subcooled flow boiling. In this work, the subcooled flow boiling of FC-72 is numerically simulated in a minichannel using ANSYS Fluent to investigate the effects of system pressure and gravitational orientation on the subcooled flow boiling thermal transfer performances. Two different orientations (vertical downflow and vertical upflow) were examined in the same conditions of heat flux (q = 191553 W/m2), mass flux (G = 836.64 kg/(m2s)) and inlet temperature (Tin = 304.54 K), and under three different system pressures (102000, 120000, and 209900 Pa). The present computational study has been validated and a good agreement with the experimental data was demonstrated. The predicted results demonstrate that the increase in system pressure improves the thermal performance of subcooled flow boiling by an average enhancement of 15.94%. In addition, the vertical upflow orientation is more advantageous than the downflow orientation due to the buoyancy force that moves the bubbles towards the flow direction and leads to less chaotic liquid-vapor interactions. An average enhancement of 1.65% in the heat transfer coefficient is reached in the upflow orientation compared to the downflow orientation for the higher system pressure of 209900 Pa.

Modern thermal energy storage (TES) systems rely laboriously on finding a low-cost method to improve heat transfer. In the present analysis, adding CuO nanoparticles and tilting the enclosure simultaneously is compared with a novel approach that employed water as a supplemental fluid to improve the melting process using the density difference between PCM and supplemental fluid. Oleic acid is selected as an immiscible PCM in water, which causes PCM and auxiliary fluid utterly separate at the end of the melting process to be usable in more additional TES cycles. By placing water as a heavier material directly on top of oleic acid, the melted oleic acid is replaced by water at the bottom of the enclosure when it melts because water has a heavier density than oleic acid. At first, adding 1% and 2% of CuO nanoparticles in an enclosure with different inclinations of 0°, 45°, and 90° is studied to identify the energy storage rate. Continuity, momentum, and energy equations are used to formulate a mathematical model of the TES system. In the next step, the melting process of the combined system is analyzed to determine the energy storage rate of the combined system compared to the system, including CuO nanoparticles in the inclined enclosure. Comparing the combined system with the optimal case of nano-PCM in the inclined enclosure, it was found that the energy storage rate in the system using auxiliary fluid is 1.396 times higher.

The current paper examines the impact of radiation and Marangoni convective boundary conditions on the flow of ternary hybrid nanofluids in a porous medium with mass transpiration effect on it. Estimated PDEs are converted to ODEs with consideration of the corresponding similarity transformations. The obtained non-dimensional reduced equations are solved by analytical process. A unique access based on the Laplace transform (LT) is used to find analytical solutions to the resulting equations. With the use of graphs, the exact solution may be investigated in the presence of many physical parameters such as solid volume fraction parameter, mass transpiration, porosity, radiation. The fluid flow contains three types of nanoparticles: spherical Silver (Ag), cylindrical SWCNT, and platelet graphene. Because of the shape composition of ternary hybrid nanoparticles, variation in concentrations is a primary factor of thermal performance. The shape of nanoparticles in ternary hybrid nanofluids has a major impact, and its application has the advantage of improving the cooling system's thermo-hydraulic performance.

A new topology optimization methodology for reinforced concrete structures is proposed. The structures are optimized in two iterative loops, where different sensitivity criteria are used to determine the regions to be topologically optimized. For the first loop, the compliance criterion is used to determine the higher compliance elements and, consequently, remove the concrete from the computational domain. In the next loop, only failed concrete regions (Ottosen failure surface) are replaced by reinforcement, ensuring that complies with the von Mises criterion. In the end, the sizing of the reinforcements is obtained based on the principal forces in the steel regions. Results regarding the mechanical behavior, cost, volume, and mass of the optimized structures are presented in this study. A case study indicated that the proposed methodology can lead to volume, mass, and cost reductions of 20%, 21.5%, and 56%, respectively.

The paper addresses the problem of attitude stabilization of an artificial Earth satellite with the aid of an electrodynamic control system. Our objective is to stabilize the satellite in a special coordinate system, whose axes are directed along the Lorentz force vector and the geomagnetic induction vector. Thus, natural magneto-velocity coordinate system (NMVCS) is used. We consider the general case of the satellite mass distribution. Therefore, the disturbing action of the gravitation torque is taken into account. The satellite moves along a circular near-Earth orbit. The nonlinear stability analysis based on the Lyapunov direct method is applied in the paper. The proposed approach gives us admissible domains of control parameters for which attitude stabilization in NMVCS is guaranteed without restrictions on the Earth’s magnetic field model. Stabilization conditions are formulated in the form of explicit inequalities for the control parameters. As a result, a control strategy for the satellite attitude stabilization in the NMVCS is elaborated.

The paper generalizes the partial class of exact solutions to the Navier–Stokes equations. The proposed exact solution describes an inhomogeneous three-dimensional shear flow in a layer of a viscous incompressible fluid. The solution is studied for the case of the motion of a steady-state isobaric fluid. One of the longitudinal velocity components is represented by an arbitrary-degree polynomial. The other longitudinal velocity vector component is described by the Couette profile. For a particular case (the quadratic dependence of the velocity field on two coordinates), profiles of the obtained exact solution are constructed, which illustrate the existence of counterflows in the fluid layer. The components of the vorticity vector and the tangential stresses are analyzed for this exact solution.

This paper is the first part of a two-part research work aimed at performing a systematic computational and experimental analysis of the principal data-driven identification procedures based on the Observer/Kalman Filter Identification Methods (OKID) and the Numerical Algorithms for Subspace State-Space System Identification (N4SID). Considering the approach proposed in this work, the state-space model of a mechanical system can be identified with the OKID and N4SID methods. Additionally, the second-order configuration-space dynamical model of the mechanical system of interest can be estimated with the MKR (Mass, Stiffness, and Damping matrices) and PDC (Proportional Damping Coefficients) techniques. In particular, this first paper concentrates on the description of the fundamental analytical methods and computational algorithms employed in this study. In this investigation, numerical and experimental analyses of two fundamental time-domain system identification techniques are performed. To this end, the main variants of the OKID and the N4SID methods are examined in this study. These two families of numerical methods allow for identifying a first-order state-space model of a given dynamical system by directly starting from the time-domain experimental data measured in input and output to the system of interest. The basic steps of the system identification numerical procedures mentioned before are described in detail in the paper. As discussed in the manuscript, from the identified first-order state-space dynamical models obtained using the OKID and N4SID methods, a second-order configuration-space mechanical model of the dynamic system under consideration can be subsequently obtained by employing another identification algorithm described in this work and referred to as the MKR method. Furthermore, by using the second-order dynamical model obtained from experimental data, and considering the hypothesis of proportional damping, an effective technique referred to as the PDC method is also introduced in this investigation to calculate an improved estimation of the identified damping coefficients. In this investigation, a numerical and experimental comparison between the OKID methods and the N4SID algorithms is proposed. Both families of methodologies allow for performing the time-domain state-space system identification, namely, they lead to an estimation of the state, input influence, output influence, and direct transmission matrices that define the dynamic behavior of a mechanical system. Additionally, a least-square approach based on the PDC method is employed in this work for reconstructing an improved estimation of the damping matrix starting from a triplet of estimated mass, stiffness, and damping matrices of a linear dynamical system obtained using the MKR identification procedure. The mathematical background thoroughly analyzed in this first research work serves to pave the way for the applications presented and discussed in the second research paper.

This paper is the second part of a two-part research work intended at realizing a systematic computational and experimental analysis of the principal data-driven identification procedures based on the Observer/Kalman Filter Identification Methods (OKID) and the Numerical Algorithms for Subspace State-Space System Identification (N4SID). More specifically, this second paper treats the presentation of the numerical analysis and the experimental testing carried out in this study. To perform a systematic comparison, the identification methods mentioned before are implemented in a general-purpose computer program developed in the MATLAB computational environment. To this end, a simple two-degrees-of-freedom dynamical model of a vibrating mechanical system is considered first as a demonstrative example. The demonstrative example is used to carry out a numerical analysis of the performance of the computational methods of interest for this investigation. Subsequently, an experimental analysis is carried out focusing on a three-dimensional structure that vibrates under the effect of an external source of impulsive excitation. To perform a thorough analysis, the flexible structure employed as an experimental case study is modeled starting from its CAD geometric model and assuming different levels of complexity, which range from a simple three-degrees-of-freedom lumped parameter model to a relatively more complex linear finite element model. In the paper, the mechanical models of the structural system considered as illustrative examples are principally employed for comparing the results arising from the modal analysis. The computational and experimental analysis of these structural models turned out to be useful to trace guidelines for evaluating the effectiveness and the efficiency of the numerical and experimental results obtained from the identification process. In this study, a numerical and experimental analysis of the OKID algorithms and the N4SID methods is developed. Both classes of techniques enable the time-domain state-space system identification, that is, they construct an estimation of the state, input influence, output influence, and direct transmission matrices which characterize the dynamic properties of a mechanical system. The present investigation demonstrates that, if properly tuned, both the OKID methods and the N4SID algorithms lead to consistent numerical and experimental results, even in the case when the input-output measurements used for performing the identification procedure are affected by a certain degree of noise. The numerical and experimental results found in this second part of the research work confirmed the efficacy of the time-domain system identification methodologies described in the first part of the paper.