Geometric Boundary Conditions Research Articles

Constraint-based analysis of heat transport and irreversibility in magnetic nanofluidic thermal systems

Purpose This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems. Design/methodology/approach The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility. Findings This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor. Research limitations/implications Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study. Originality/value This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications. Graphical Abstract

Multi-objective optimization of CO2 ejector by combined significant variables recognition, ANN surrogate model and multi-objective genetic algorithm

The ejectors are crucial in enhancing the efficiency of the CO2-based refrigeration cycle. Although the ejector can be optimized by experimental and computational fluid dynamic simulation to improve its performance, these methods are time-consuming and complicated. This research aims to present a fast and systematic approach for optimizing CO2 ejector by combining variance analysis, surrogate model, and non-dominated sorting genetic algorithm. Firstly, the key geometric structures affecting the performance of ejector were determined by variance analysis. Secondly, the influence of key geometric structures and boundary conditions on ejector efficiency and entrainment ratio was analyzed by using computational fluid dynamic simulation, and the database was generated. Next, the artificial neural network surrogate model was established to forecast the ejector performance. Finally, the non-dominated sorting genetic algorithm was involved to optimize the ejector for maximizing ejector efficiency and entrainment ratio. The results show that the efficiencies of the optimized ejectors are above 42%, and the entrainment ratios exceed 0.7. Compared with the basic model, the average efficiencies have increased about 13.20%. When the pressure lift is 0.7 MPa, the entrainment ratios of the optimized ejectors are 0.696 (−20 °C ≤ Te < −15 °C), 0.82(-15 °C ≤ Te < −5 °C), 0.60 (−5 °C ≤ Te < 5 °C) and 0.90 (5 °C ≤ Te < 15 °C), respectively. The above research demonstrates that the success of this approach in addressing time-consuming multi-optimization problems. It offers a fast and systematic approach for the multi-objective optimization of CO2 ejector as a valuable reference for engineering applications.

In-Plane Vibrations of Deep Sandwich Arches with Different End Conditions Based on a Logarithmic Shear Deformation Theory

This paper deals with the vibrational frequencies of deep sandwich arches to enhance their application domain and possibly use them for energy harvesting. The circular arch with porous nanocomposite core and titanium alloy face sheets having different end conditions is numerically analyzed. The middle core of the sandwich arch is made of a six-layered porous aluminum reinforced with graphene nanoplatelets. The kinematic equations are formulated in this study based on the higher-order shear deformation theory using a logarithmic function of radius. The effective properties of the nanocomposite media are modeled by employing the Halpin–Tsai modified rule. The equations of motion are determined by applying the principle of virtual displacement. The partial differential equations are reduced using the generalized differential quadrature technique to solving an algebraic eigenvalue problem. Novel numerical results are given to show the effects of geometrical parameters, material properties, and boundary conditions on the vibrations of deep sandwich arch.

An energy-balanced method for determining the optimized parameter of the incompatible generalized mixed element

A novel method for determining the optimized parameter of the four-node incompatible generalized mixed element is presented based on the equilibrium between strain energy and complementary energy. The presented energy formulations are derived from the generalized mixed variational principle, which contains an arbitrary additional parameter. The initial solutions expressed by the displacement field are firstly assumed for the description of the energy of each generalized mixed element. Then, the identical relationship between strain energy and complementary energy is subsequently expressed at element level, which includes the arbitrary parameter. At the same time, a formulation for determining the optimized parameter at element level is proposed. Several representative examples with varying geometrical parameters, boundary and loading conditions are used to validate this method. By contrasting with the results of generalized mixed elements with different parameter values and other traditional finite elements. The effectiveness of the presented method has been demonstrated. On one hand, by ensuring the strain energy and complementary energy remain consistent under both coarse and fine meshes, the optimized parameter can adjust the stiffness of the generalized mixed element, thereby enhancing its resemblance to the real elastic body. On the other hand, the generalized mixed element has the additional advantage of conveniently introducing stress boundary conditions, thereby satisfying the requirement for zero-conditions of shear stresses on the exterior surfaces of beams. The numerical results obtained by the proposed method are accurate and stable.

Investigation of mechanical behaviors of spoke-wheel cable structures through experimental and numerical analysis driven by digital-twin

Ascertaining the mechanical behaviors of large-scale space structures (e.g. spoke-wheel cable structure) is essential for guaranteeing their structural safety. This study proposed a digital-twin (DT)-based method for analyzing the mechanical behaviors of spoke-wheel cable structures. A spoke-wheel cable structure with a span of 6 m was used as a case study to validate the proposed method. The structural behaviors, such as cable forces and structural displacements under five loading conditions (i.e. dead load and dead load plus 3/10, 5/10, 8/10 or full-areal live load), were investigated experimentally and numerically. A comparative analysis was conducted to compare the results using the proposed method with the traditional method. Results show that the proposed DT method could help to update geometric details and boundary conditions of the twin model for ensuring effective numerical analysis. Moreover, the changing trends of general force for the same type of cables were basically the same under different loading conditions. Besides, the forces of upper spoke cables and inner-ring decreased under the action of live load, whereas the forces of lower spoke cables and inner-ring increased. The displacement directions of loaded and unloaded nodes were downward and upward, respectively, when subjected to uneven live loads. In addition, the vertical displacements of the outer nodes were greater than thoseof the inner ones. Furthermore, the cable forces and displacements of the structure changed more obviously under the action of asymmetric load. The established high-fidelity DT model could support effective numerical analysis of mechanical behaviors of large-scale space structures.

Aerothermoelastic flutter analysis of variable angle tow composite laminated plates in supersonic flow

A theoretical model is developed to investigate the aerothermoelastic flutter behavior of variable angle tow (VAT) composite laminated plates on elastic foundation in supersonic flow with general boundary conditions. The equations of motion of the VAT composite laminated plate are established by adopting the first-order shear deformation theory and the supersonic piston theory. The composite laminated plate is considered to be lying on an elastic foundation (such as a thermal protection shield) on one side and exposed to supersonic airflow on the other side. The displacement components of the structure are expanded into Chebyshev polynomials multiplied by the boundary characteristic functions to satisfy the geometric or natural boundary conditions. To validate the proposed theoretical model, a finite element (FE) model is also established by ABAQUS, and the numerical results fit well with that of the developed theoretical model. The effects of the boundary conditions, thermal loads, elastic foundations and laminate layouts on the flutter characteristics of the VAT composite plate are revealed and discussed in detail. This work can provide a reference for the dynamic design of the VAT composite laminates in the aerospace engineering.

Physics-informed neural network for solution of forward and inverse kinematic wave problems

The one-dimensional kinematic wave (KW) model (KWM) is widely used in surface water and water quality hydrology as well as for modeling the movement of traffic on long highways. The KW model involves a first-order nonlinear partial differential equation which is solved numerically for realistic geometric representation, input, and initial and boundary conditions. This paper developed a method to solve the partial differential equation using a neural network structure, called the physics-informed neural network (PINN). The PINN was applied to solve the one-dimensional nonlinear KWM for forward and inverse problems. To enhance the accuracy and convergence and to suppress the spurious oscillation at the steep front, a technique with redistributed collocation points as an improved algorithm of PINN was employed. To deal with the fractional order of the nonlinear advection term, a stop-gradient technique was proposed. For validation, the KWM for steady and unsteady overland flow, and open channel flow without lateral inflow was analyzed for the forward problem. For the inverse problem, the unknown Manning coefficient was correctly computed, demonstrating the capability of the proposed algorithm for the identification of KWM parameters.

Hexahedral finite elements with enhanced fixed‐pole interpolation for linear static and vibration analysis of 3D micropolar continuum

AbstractThe spotlight of this research is on the application of the fixed‐pole interpolation, sometimes used in the analysis of three‐dimensional (3D) geometrically non‐linear beams, but for which no attempts have been made to apply it to linear analysis so far. Particular attention is given to the correlation between the linearised forms of the fixed‐pole and helicoidal interpolation with the linked interpolation. Knowledge of this interdependence is crucial for identifying paths for possible enhancement and extension from the Timoshenko beam of arbitrary order to the new hexahedral finite element of arbitrary order for linear analysis of 3D micropolar continuum. After ensuring the convergence of the newly developed micropolar element through a set of patch tests, three numerical examples of a 3D micropolar continuum in static equilibrium and free vibration of 3D micropolar plates with different geometric properties and boundary conditions have been analysed. Based on these results, the newly proposed finite elements have been critically assessed against the conventional elements.

Symmetric and asymmetric free vibrations of rotating eccentric annular plate

The symmetric and asymmetric free vibrations of rotating eccentric annular plate in uniform thermal environment are studied in present paper. The priority of research is clarifying the different combined effects of various factors on symmetric and asymmetric vibrations of eccentric annular plate. In order to conveniently obtain the natural frequency and vibration mode of eccentric annular plate with irregular physical domain, the transformed differential quadrature method is employed. Due to the rotational motion, the initial configuration caused by centrifugal force is calculated before vibration analyses. Then the traveling wave vibration arisen from the Coriolis force is investigated. By comparing the vibration characteristics of annular plate with/without eccentricity, the different impacts of interaction between the geometrical size, boundary conditions, temperature rise, rotational motion, and eccentricity on symmetric and asymmetric vibrations are discussed. Results show that eccentricity leads to the splitting phenomena only in asymmetric vibrations. And it does not affect the symmetry of vibration. Temperature rise results in that the fundamental vibration mode shape shifts from symmetric to asymmetric. However, eccentricity inhibits the change. Rotational motion causes the occurrence of traveling wave vibration in asymmetric vibration whereas not in symmetric vibration.

Methodical Design of a Subframe for a Novel Modular Chassis Concept without Knowledge of Final Vehicle Parameters

&lt;div&gt;This article presents the methodical development of a subframe for a novel on-the-road-modular vehicle concept, which was developed for the U-Shift project. The subframe serves as the basis for a modular chassis. This chassis offers the possibility to exchange chassis components by the operator, which means after completion by the manufacturer, and thus to adapt the vehicle to different purposes. According to the applied methodology, the relevant wheel loads are determined and a geometric reference model is created. By defining the relevant load cases, the forces acting on the subframe, and thus the physical boundary conditions, can be determined from the wheel loads. In addition to the wheel loads and the geometric boundary conditions, no other vehicle parameters are required for the development of the subframe. The results of the topology optimization are used to identify areas of the geometric reference model that are not exposed to high loads. Based on the results of the topology optimization, a suitable combination of manufacturing processes and suitable materials can also be determined. After the basic topology has been determined, a welded construction is derived from square tubes and plates. Subsequently, excess stresses at critical points are identified in simulation and analysis processes, and constructive changes are made to reduce them. Through validation by simulation of the relevant load cases, a proof of compliance with the physical boundary conditions can be provided. The actually manufactured subframe is presented, and the potential of the modular construction for the development of a chassis modular kit is explained.&lt;/div&gt;

Pre-conceptual design of the fixed mirrors for the DEMO Electron Cyclotron Heating antenna

The M1 mirrors are part of the in-vessel quasi-optical Electron Cyclotron beam propagation system of the DEMO nuclear fusion reactor. These four mirrors are all non-movable and with a plane reflecting surface. Based on their functionality they are divided into two groups, the Mid-Steering Antenna (MSA) and the Multi-Beam Mirror (MBM) antenna. The MSA is responsible for controlling the neoclassical tearing modes, while the MBM is available for plasma bulk heating, current drive and thermal instability control.These mirrors are designed to withstand the thermal loads generated during operation: neutron heating, ohmic losses and stray radiation caused by the mm-wave beam reflection. To fulfil the design requirements, efficient heat removal strategies based on water cooling principles minimizing pressure drop are implemented.This paper presents the pre-conceptual design of the MBM and MSA M1 mirrors, validating the structural and geometric boundary conditions, as well as the appropriate selection of materials. Using FEA tools, thermal-hydraulic and thermo-mechanical simulations were performed with the available thermal loads to optimize the cooling parameters and perform a first stress assessment on the two M1 mirrors.

Improved-FSDT-based solid-shell element for buckling analysis of plate, spherical cap, and cylindrical shell of FG porous materials

This study's objective is to propose a full three-dimensional finite element modeling for examining the buckling behaviors of functionally graded (FG) porous materials with plates, spherical cap, and cylindrical shapes. An improved first-order shear deformation theory (IFSDT) is utilized in order to develop the three-dimensional solid-shell element. The governing equations are developed in a way that offers a parabolic distribution of the transverse shear strains through the FG porous shell thickness and a zero condition of the transverse shear stresses on the top and bottom surfaces. The given IFSDT solid-shell element has the ability to model any kind of shell structures and incorporates a three-dimensional material law. In this study, two types of porosity distribution functions are considered. The performance of the current IFSDT solid-shell element has been demonstrated by examining the buckling behavior of Functionally Graded Porous plates, spherical caps, and cylindrical shells. The effect of the porosity distribution, porosity coefficient, power-law index, geometrical design parameters and boundary conditions on the buckling behaviors of FG porous shells structures is evaluated.

Geometrical wetting boundary condition for complex geometries in lattice Boltzmann color-gradient model

A wetting boundary condition for dealing with moving contact lines on complex surfaces is developed in the lattice Boltzmann color-gradient model. The wetting boundary condition is implemented by combining the geometrical formulation of contact angle and the idea of the prediction–correction wetting scheme, which not only produces the desired contact angles with high accuracy but also avoids the necessity to select an appropriate interface normal vector from multiple solutions that satisfy the contact angle condition. Through the implementation in the framework of color-gradient model, the developed wetting boundary condition is validated against analytical solutions by a series of benchmark cases, including a droplet resting on a cylindrical surface and on a tilt wall, a liquid film migrating between two parallel plates, and the forced imbibition into a pore doublet. The simulation results of static contact angles show that the wetting boundary condition is able to simulate arbitrary values of contact angle and leads to negligible mass leakage across the boundary. For dynamic problems, the wetting boundary condition is found to correctly capture the imbibition dynamics under various flow and viscosity ratio conditions and produce dynamic contact angles that match well with the Cox–Voinov law.

Analitičko određivanje postupaka struganja sa velikim pomakom primenom konstruktivnog geometrijskog modeliranja

The development of different machining procedures requires the exact mathematical description of those. This is especially important in finishing procedures, where the final geometry and surface characteristics of the parts are produced. In this paper, three high-feed turning procedures are analysed: skiving turning, tangential turning, and rotational turning. All three promise the creation is ground-like surfaces with low roughness characteristics, while reaching high values of productivity. The analytical determination of these procedures is carried out by the application of constructive tool geometric modeling. After the analysis of the kinematic and geometric relations of each procedure, the proper coordinate systems are defined. The transformational equations are determined, which describe the geometric boundary conditions and the movement of the workpiece and the tool. In the next step, the equation of motion is defined for the three studied procedure. Finally, the one variable equation of the cut surface section in the base plane is determined. Experiments were also carried out, which validated the achieved results.

Nonlinear isogeometric analysis of axially functionally graded graphene platelet-reinforced composite curved beams

The linear and nonlinear isogeometric finite element models of an axially functionally graded graphene platelet-reinforced composite (AFG-GPLRC) curved beam are established within the framework of the third-order shear deformation beam theory (TSDT) and von-Kármán’s nonlinear geometric relation. The AFG-GPLRC curved beams can be seen as composite structures in which the graphene platelets (GPLs) are continuously distributed in the matrix along the length direction of the curved beam according to different patterns. The modified Halpin-Tsai parallel model and the rule of mixture are implemented to predict the effective Young’s modulus and mass density as well as Poisson’s ratio, respectively. Hamilton's principle, TSDT, and von-Kármán’s strain-displacement relation are combined to derive the governing partial differential equation of motion and corresponding boundary conditions. Furthermore, the Non-Uniform Rational B-splines (NURBS)-based isogeometric analysis (IGA) approach together with a direct iterative technique are utilized to solve the nonlinear governing equation. The accuracy and efficiency of the proposed IGA framework are confirmed by comparing corresponding numerical solutions with other available results. The parametric investigations, such as the curved beam’s geometric parameters, boundary conditions, and GPL’s distribution patterns, on the nonlinear bending and vibration responses of the AFG-GPLRC curved beams are carried out by some illustrative examples.

Theoretical analysis for free vibration of submerged conical motor stator

The conical rim-driven motor stator is a structure with variable thickness and non-standard boundaries, which can be treated as an orthotropic conical shell. To prevent resonance and reduce electromagnetic noise, a modal analysis of the stator is necessary. This paper presents an analytical model for the free vibration of the conical stator in both onshore and underwater environments. Due to the relatively large thickness of the motor stator, the first-order shear deformation theory (FSDT) is employed. The fluid loading is calculated by discretizing the conical shell into a series of narrow cylindrical shells featuring diverse radii and thickness. The resulting equations are solved employing the transfer matrix method (TMM), which is capable of different types of boundary conditions (BCs). The convergence and accuracy of the proposed method are validated through a comparative analysis involving numerical simulations and outcomes derived from the thin shell theory. The importance of considering shear deformation and rotatory inertia in determining the natural frequency of motor stators is demonstrated. Finally, the impact of fluid loading on the vibration behavior of stators with various geometric parameters and boundary conditions are investigated and discussed. The proposed model presents a precise and convenient approach for analyzing the free vibration of submerged conical motor stators, and can be extended to conventional cylindrical motor stators through appropriate degradation procedures.

Predicting monotonic lateral load-displacement behavior of offshore flexible piles in saturated MCC soils: An application of the cavity expansion theory

This paper proposes an application of the cavity expansion theory to predict the load-displacement response of monotonically laterally loaded piles and the effective stress distribution of saturated modified Cam-clay (MCC) soil surrounding the pile. This approach incorporates geometric relationship, equilibrium equation, and boundary conditions to derive governing equations. These equations are subsequently solved to obtain monotonic p-y curves, which encompass the elastic, elastoplastic, and critical processes. To determine the load-displacement behavior and effective stress distribution of the soil, the proposed approach combines the deflection equilibrium differential equation with the finite-difference method. The accuracy and effectiveness of the approach are validated through a comparison with a Finite Element Method (FEM) simulation. Parametric studies are also presented to investigate the effects of overconsolidation ratio, in-situ coefficient, and mean effective stress. The validity and capacity of the proposed model are further demonstrated using model pile tests. The results affirm that this approach can well predict the monotonic load-displacement response of the pile and effectively captures important phenomena observed in pile tests.

Minimum-time and minimum-energy trajectory planning under dynamic constraints for a quadrotor

This article proposes an approach for optimizing the trajectory planning of quadrotors in structured environments, taking into consideration the trade-off between task execution time and energy consumption. The constraints taken into account are geometrical (boundary conditions in position and orientation, obstacle avoidance), kinematic (boundary conditions in velocity, linear velocity, and acceleration limits of the system), and dynamic (limit capacities in torque of the actuators, constraints related to the under-actuation of the system). The approach extends the Random Trajectory Profile Approach (RPA) to the case of quadrotors. The results of this approach are validated through experimental tests and compared with those in the literature, demonstrating its effectiveness in offline and online scenarios. The proposed approach offers a promising solution for achieving optimal trajectory planning of quadrotors in structured environments.

A rapid performance prediction method for Two-Phase liquid metal MHD generators based on Quasi-One-Dimensional model

Liquid metal magnetohydrodynamic (LMMHD) power generation is a novel and highly efficient technology with broad application prospects. In our previous study, a novel LMMHD enhanced Closed-Brayton-Cycle power generation system for hypersonic vehicles was proposed, and its excellent power generation performance was demonstrated by thermodynamic analysis. The most important component of LMMHD system is the power generation channel, and the rapid and accurate performance prediction and optimization design methods of which are the prerequisites for further research. In this study, a quasi-one-dimensional modeling method for LMMHD power generation channels based on a two-fluid model is developed. The performance variation laws with the geometric structure, magnetic field and boundary conditions, as well as the potential loss mechanisms are investigated. Results indicate that the most optimal or appropriate design can be achieved by optimizing the channel geometry and magnetic field, such as the optimal aspect ratio of 1 and the optimal Hartmann number of 2000. But it is difficult to balance the power output and efficiency through the boundary condition optimization. The gas–liquid slip can lead to approximately 20–40% of energy losses, making the elimination and suppression of slip effects a significant research focus in the relevant field.

A study of the natural frequencies of the functionally graded curved beams including porosities: Deterministic and stochastic modeling

In this research article, an investigation into the natural frequencies of functionally graded porous curved beams is presented, covering both deterministic and stochastic domains. The stochastic finite element analysis is based on a three-node, C0 continuous element, and higher-order shear deformation theory, utilizing the first-order perturbation technique (FOPT). The study includes a comparative analysis of three porosity distribution models, including a recently proposed sinusoidal model. Additionally, the study examines the influence of various factors, such as porosity distributions, boundary conditions, volume fraction indices, and geometric configurations, on the natural frequencies. The analysis encompasses uncertain natural frequencies in functionally graded curved beams, accounting for material stochasticity through FOPT. Monte Carlo simulation (MCS) is used to validate the accuracy of the FOPT model, increasing the approach’s reliability. Potential future research in this area could investigate the effects of stochastic variations in geometric parameters, including dimensions and boundary conditions.