Dimensionless Geometric Parameters Research Articles

Systems of Inclusions in a Spatial Elastic Wedge

Contact problems are considered for two identical thin rigid elliptic inclusions in a three-dimensional elastic wedge of two-sided angle outer faces of which are subjected to rigid or sliding support. The problems are reduced to integral equations with symmetric kernels. Two dimensionless geometric parameters are introduced to characterize location of the inclusions in the bisecting half-plane of the wedge. Assuming linear connection between the parameters, the regular asymptotic method is used to solve the problems. The asymptotic for two inclusions is compared with corresponding solutions for unit inclusion in the wedge as well as for a periodic chain of inclusions the axis of which is parallel to the wedge edge.

Optimization of dissipative mufflers

The method of selecting the configuration of dissipative mufflers with the required acoustic efficiency is considered. The peculiarity of the considered approach is the use of an integral indicator of acoustic efficiency and dimensionless geometric parameters. The studies were carried out using finite element calculations. In the finite element model of a dissipative mufflers, acoustic characteristics of a fibrous sound-absorbing material obtained from experimental studies were used.

Study on mechanical response control of metal-ceramic dual phase hybrid lattice structure

Different from the previous trial-and-error and empirical development process of new materials, the failure and deformation of meso-structure of lattice structures are considered as a means to customize the mechanical response in this paper. Based on this, we propose a novel metal-ceramic dual-phase hybrid lattice structure (DPHLS) that exhibits both high peak stress and a prolonged plateau stage in its mechanical response. This design aims to meet the complex mechanical response requirements of impact target materials in hard target penetration research. The DPHLS is composed of a ceramic-based SC plate lattice structure and a metal-based FCC plate lattice structure, allowing for a broad range of mechanical properties control. Besides, by combining the advantages of both ceramic and metal, the DPHLS exhibits seemingly conflicting properties of load-bearing capacity and energy absorption. In the present work, the contribution of failure and deformation behavior to the mechanical response of the structure is deeply analyzed at the mesoscopic level using theoretical analysis and numerical simulation. The quantitative relationship between the geometrical parameters of the structure and the mechanical response is established actively. The results show that the three dimensionless geometric parameters, which characterize the geometry of DPHLS, can effectively regulate its mechanical response. This study not only provides a reliable theoretical basis for the design of mesostructures in DPHLS, but also proposes a novel strategy for the customization of mechanical response.

Исследование изменения геометрии внутренней полости передающих устройств для гидроструйных технологий с целью улучшения их теплового состояния

The paper is devoted to the study of the influence on changes in their thermal balance during operation by improving the cooling conditions of sections of the drill shaft with contact surfaces of changes in geometric characteristics, such as diameter and length, of the internal cavity for supplying working fluid in high-pressure hydro-puller device for hydro-jet technologies. The axisymmetric simulation not on a full-size transmit-ting device was carried out, but on one-eighth part in order to reduce the time of both creating the model itself and the amount of calculations. A model created in the computing environment «Ansys» with a computational grid for calculating equivalent stresses is shown. The stress distributions calculated by the finite element method for various combinations of the geometry of the transfer device revealed the corresponding boundaries for the rational change in the diameter and length of the internal cavity, allowing to ensure its operability of the structural unit in combination with maximum cooling of the most thermally loaded sections of the shaft. Dimensionless geometric parameters (reduced diameter and reduced length of the internal cavity) are introduced for a general description of the geometry of transmitting devices for hydro-jet technologies. Graphs of the dependences of voltage values on the given values were obtained.

Buckling of planar curved beams with finite prebuckling deformation

The serpentine structure with a sufficiently thick cross section has recently been proposed as an important design concept in stretchable electronics, which features mechanically stable in-plane deformation mechanism and very low electrical resistance, bringing unique advantages for devices compared with the traditional thin ribbon layout. However, unduly increasing the thickness is well known to sacrifice the overall flexibility and functionality of devices. Such a contradiction leads to challenges in structural stability, as a relatively thick but insufficient serpentine structure may eventually undergo the out-of-plane buckling after significant in-plane prebuckling deformation and appreciable alterations in initial configuration, which is ignored by most conventional buckling theories (CBTs) and linear buckling analysis in commercial finite element analysis software, producing intolerable errors when predicting the critical loads. In this paper, a systematic and straightforward theory considering the finite prebuckling deformation (FPD buckling theory) is established to investigate the underlying mechanism. Two sets of governing equations related to the prebuckling and FPD buckling behavior are obtained. Four representative examples, including two classical problems of planar curved beams and two typical loading conditions of serpentine structures, have been carefully studied. Comparisons with the accurate geometrically-nonlinear-analysis-based (GNAB) buckling analysis have amply demonstrated the validity of our theory in predicting the reinforcement effect of prebuckling deformation on the buckling resistance of structures. Key dimensionless geometric parameters that govern this effect have also been identified, providing direct and effective guidance for the design and optimization of stretchable electronic devices.

Cavitation mitigation via curvilinear barriers in centrifugal pump

Cavitation is a significant problem in hydraulic machinery that leads to the deterioration of hydraulic performance, material damage, and flow instability. While current methods partially address cavitation instability, there is a lack of comprehensive understanding of the control mechanisms. This study focuses on controlling cavitation flow instability in a centrifugal pump by proposing an active method using obstacles on the blade's surface. A low-specific speed centrifugal pump was chosen as the research object, and a three-dimensional unsteady full-flow channel numerical simulation was conducted. The findings indicate that in the absence of cavitation, the wake vortex induced by obstacles increases energy loss in the centrifugal pump, resulting in a slight drop in efficiency. However, when cavitation occurs, the obstacles effectively improve the flow field, reduce the vortex strength near the back of the blade in the flow channel, and significantly reduce the growth rate of cavitation volume. This reduction is observed in both the cavitation volume and its first derivative. Thus, the obstacles optimize the flow structure, reduce vortex strength, and slow the growth rate of cavitation. The main control mechanism involves inducing high-pressure waves to collapse cavities and improving flow transition characteristics. To solve the inverse problem of cavitation control with obstacles inside a centrifugal pump, dimensionless geometric parameters are studied to determine better suppression effects.

Standard series of transmitting equipment for hydra-jet technology based on dimensionless geometric parameters development

Introduction. The work is devoted to the calculation of series standards for the design of high-pressure transmission devices used in various hydra jet technologies, which will provide the design of these devices based on dimensionless indicators describing the relationship between their geometric and technological parameters.Materials and methods. The methodology includes the use of mathematical models and analytical approaches to assess the influence of various parameters on heat generation processes in equipment, as well as methods for statistical processing of results.Results. A histogram of temperature distribution was constructed and the data was approximated using the distribution curve of temperature values and parametric series were generated for dimensionless parameters depending on various factors such as temperature, pressure, rotational speed and linear speed. It is possible to obtain parametric series for linear dimensions from five temperature ranges and seven standard sizes depending on the pressure and rotation speed of the drill shaft.Discussion and conclusions. The results obtained provide a better definition of the relationships between rotation speed, geometric characteristics and temperature parameters through the use of dimensionless indicators and it is possible to optimize the design of such devices taking into account operating conditions and ensuring increased efficiency.

Coupled surface diffusion and mean curvature motion: An axisymmetric system with two grains and a hole

Thin polycrystalline solid state films, which are used in many technological applications, can exhibit various phenomena, such as wetting, dewetting, and hole formation. We focus on a model system containing two contacting grains which surround a hole. For simplicity, the system is assumed to be axisymmetric, to be supported by a planar substrate and to be bounded within an inert semi-infinite cylinder. We assume that the exterior surfaces of the grains evolve by surface diffusion and the grain boundary between the adjacent grains evolve by motion by mean curvature. Boundary conditions are imposed following W.W. Mullins, 1958. Parametric formulas are derived for the steady states, which contain two nodoids describing the exterior surfaces, which are coupled to a catenoid which describes the grain boundary. At steady state, the physical parameters of the system may be prescribed via two angles,β\beta, the angle between the exterior surface and the grain boundary, andθc\theta _c, the contact angle between the exterior surface and the substrate; additionally, there are two dimensionless geometric parameters which must satisfy certain constraints. We prove that ifβ∈(π/2,π)\beta \in (\pi /2, \pi )andθc=π\theta _c=\pi, then there exists a continuum of steady states. Numerical calculations indicate that steady state profilescan exhibit physical features, such as hillock formation; a fuller numerical study of the steady states and their properties recently appeared in Zigelman and Novick-Cohen [J. Appl. Phys. 134 (2023), 135302], which relies on the formulas and results derived here.

Theoretical analysis of inflated tube wrinkling behavior under pure bending

Inflatable tubes, owing to their lightweight and foldable characteristics, have important applications in soft robots and space expandable structures. The application of a bending load to the inflated tube might induce local instability on its compressed side, leading to the formation of wrinkles that could potentially compromise the structural strength. Therefore, it is necessary to have a comprehensive understanding of the wrinkling behavior exhibited by inflated tubes under bending load. Initially, a theoretical solution is developed for the critical wrinkling behavior of inflated tubes under pure bending, drawing upon the principle of minimum potential energy. According to the energy expression of the system, the critical wrinkling behavior of inflated tubes depends on dimensionless geometrical and internal pressure parameters. The critical wrinkling load and wrinkle pattern of the system are influenced by the thickness-radius ratio and the ratio of internal air pressure to Young's modulus. Subsequently, the theoretical solutions are validated through several finite element analysis examples and a systematic investigation is conducted into the influence of dimensionless geometrical and internal pressure parameters. Finally, the evolution of morphology in post-buckling is investigated through numerical results. The findings suggest that during post-buckling, the wrinkles may undergo a secondary bifurcation and evolve into a non-axisymmetric diamond-like pattern. These results hold significant implications for understanding the bending instability and failure mechanisms of inflated tubes.

Coordinated suction and blowing of a cylinder array for thrust generation

Various systems of mechanical devices and natural organisms use the repeated expansion and contraction of deformable structures to draw in and blow out fluid. Instead of such deformable continuous structures, a system that consists of multiple discrete bodies can also generate a directional flow through the cooperative movement of the individual bodies. In this study, we numerically investigate the collective effects of a multi-body system composed of eight circular cylinders, each of which oscillates separately in the radial direction to generate thrust. The cylinder array performs cooperative motion regulated by three motion parameters: phase difference, oscillation amplitude and frequency at a low Reynolds number ( $Re = 10$ ). The phase difference between the cylinders is critical in determining the extent of the directional flow and the time-averaged thrust. The optimal phase difference that yields the maximum time-averaged thrust is consistent, regardless of the oscillation amplitude and frequency. However, the thrust generation performance becomes significantly weaker at a higher Reynolds number ( $Re = 100$ ). This highlights that the hydrodynamic blockage in gaps between cylinders, which is induced by strong viscous diffusion at the low Reynolds number, is essential for the cooperative force generation of multiple closely spaced bodies. A new dimensionless geometric parameter based on the motion of the array is proposed to characterize the degree of bias in the generated flow and it successfully predicts the trend in the time-averaged thrust at the low Reynolds number with strong hydrodynamic blockage.

Substantial curvature effects on compliant serpentine mechanics

Serpentine interconnects (serpentines) with various degrees of curvature are often designed to absorb deformations and protect brittle active components in flexible devices. Serpentines with small curvature are modelled well using the traditional theory for doing so, but this overestimates the stretchability of serpentines with large curvature (e.g. the relative error exceeds 90%). Proposed here is a novel theoretical model in which a non-buckling serpentine is characterized as a large-curvature beam. Analytical solutions are derived, and systematic experiments and numerical simulations are reported to validate the accuracy and investigate geometrical dependence. It is found that (i) dimensionless geometrical parameters regulate the compliant mechanics of a serpentine, (ii) there is a certain arc angle that produces abnormal stretchability (i.e. the normalized stretchability is less than unity) and (iii) the flexibility and stretchability can be enhanced by between two and five orders of magnitude. This work offers a new way to construct optimal serpentine ribbons with large curvature for various applications.

Transition from volcano-sagging to volcano-spreading

Many volcanoes exhibit evidence of long-term deformation driven by gravity. This deformation influences the development of magmatic plumbing systems and volcanic vent locations, and it manifests as earthquakes and ground surface motions. Two end-member deformation styles are volcano sagging (flexure) and volcano spreading. Previous modeling studies indicated that the mechanical and geometric properties of basement rocks below the volcano can control whether a volcano spreads or sags, but these works differed on exactly how. Furthermore, evidence in nature that a volcano may progress from sagging to spreading as it grows has not been tested experimentally. Using Digital Image Correlation (DIC) and a revised scaling approach, we here revisit the classic experiments in which a sand–plaster cone is emplaced upon a basement comprising an upper brittle layer and a lower ductile layer. In a first experiment series, we emplaced the cone instantaneously. By normalizing both brittle and ductile layer thicknesses to cone height, we provide new insight into the dimensionless geometric controls on spreading and sagging. In a novel second experiment series, we emplaced the cone incrementally. We show that as a growing cone migrates through the dimensionless geometric parameter space, its deformation style changes successively in time from sagging to spreading. DIC shows that the horizontal velocity of the cone flank increases linearly or non-linearly during cone construction, but it decreases exponentially after construction ceases. Despite their geometric simplification and the omission of several sedimentological, magmatic, and regional-tectonic processes, our models' results are compatible with a range of observations of volcanoes on Earth and Mars. In particular, they help to explain: (i) why lithosphere-scale loading results in sagging rather than spreading, and (ii) why ocean island volcanoes of >2-3 km in height develop stellate forms and rift zones.

Periodic system of rigid inclusions in a spatial elastic wedge

A periodic contact problem (tangential contact) on a chain of thin rigid inclusions located along the edge of a three-dimensional elastic wedge of a dihedral angle in its middle half-plane (rigid sealing of the wedge faces, the axis of the chain of inclusions is parallel to the edge of the wedge) is considered. To derive the integral equation, the previously obtained fundamental solution of the problem of the action of a concentrated force inside a three-dimensional elastic wedge is used. The nucleus has latent symmetry, then it is reduced to a form with explicit symmetry. To solve the integral equation, a regular asymptotic method is used, which is effective for relatively sparse and far from the edge chains of inclusions in a three-dimensional elastic wedge. Contact characteristics are calculated for different values of dimensionless geometric parameters. Previously, similar problems were considered about one inclusion (stringer) in a strip [1] and a three-dimensional wedge [2], as well as in an unbounded elastic body [1].

Enhancing Performance of a MEMS-Based Piezoresistive Pressure Sensor by Groove: Investigation of Groove Design Using Finite Element Method.

The optimal groove design of a MEMS piezoresistive pressure sensor for ultra-low pressure measurement is proposed in this work. Two designs of the local groove and one design of the annular groove are investigated. The sensitivity and linearity of the sensor are investigated due to the variations of two dimensionless geometric parameters of these grooves. The finite element method is used to determine the stress and deflection of the diaphragm in order to find the sensor performances. The sensor performances can be enhanced by creating the annular or local groove on the diaphragm with the optimal dimensionless groove depth and length. In contrast, the performances are diminished when the local groove is created on the beam at the piezoresistor. The sensitivity can be increased by increasing the dimensionless groove length and depth. However, to maintain low nonlinearity error, the annular and local grooves should be created on the top of the diaphragm. With the optimal designs of annular and local grooves, the net volume of the annular groove is four times greater than that of the local groove. Finally, the functional forms of the stress and deflection of the diaphragm are constructed for both annular and local groove cases.

Fire resistance and design assessment of Q355 circular hollow section joints

This paper presents an experimental investigation on fire resistance of circular hollow section (CHS) T-, Y- and K-joints. A total of 15 specimens subjected to brace axial load were heated inside an electric furnace, including 5 T-joints, 5 Y-joints and 5 K-joints. The temperature inside furnace follows ISO 834 standard fire curve. The principal parameters considered in this study include the dimensionless geometric parameters of joints β and γ, as well as the load ratio n. It is found that the failure mode of the axially loaded CHS joints under fire is chord plastification. Referring to the temperature-deformation curves of these CHS joints, it is suggested to adopt 1.5% ovalisation of the chord diameter as the failure criteria of the CHS joints under fire. The fire resistance of the CHS joints is seriously reduced with an increase in the load ratio n. By comparing the temperature development and the critical temperatures of the CHS joints obtained in the tests with the ones predicted by design codes, it is found that the measured temperature development curves of the CHS joints are significantly different from the calculated ones before the joint temperature reaches 550 °C. Further investigation is essential for temperature development analysis of CHS joints, especially in the aspects of the section factor Am/V of CHS joint. The fire resistance performance of CHS T- and Y-joints is shown to be reasonably estimated with the resistance method provided in modern design codes, even though the estimation on CHS K-joints is relatively conservative.

Influence of cross-section shape on energy harvesting from transverse flow-induced vibrations of bluff bodies

Hydroelastic experiments have been carried out in a free surface water channel to study the influence of the cross-section shape on the mechanical energy transfer from a uniform flow to a self-excited crossflow oscillating prism. Seventeen cross-section shapes were tested with the same mechanical properties (say, mass ratio and mechanical damping) and aspect ratio. Then, the study was focused on the role of the cross-section shape and reduced velocity on the prism dynamics and energy transfer from the fluid flow. It has been found that the geometric centroid of the semi-cross-section and the afterbody length of the cross-section represent a simple and effective metric to characterise the energy transfer. Two related dimensionless geometric parameters are introduced. The dependence of the energy transfer with these two parameters is studied and used to design successfully ‘in advance’ cross-section shapes with high energy transfer efficiencies. It has been observed from particle image velocimetry measurements that large energy transfer shapes are those in which, under strong oscillations, the flow follows the cross-section contour of one side and is fully detached on the other side.

Experimental and numerical analysis for improving the suction capacity of the manufactured water jet ejectors

Water jet ejectors are the silent pumping fluid devices which doesn’t have any rotating parts in functional industrial applications. The dimensionless geometrical parameters effects ejector suction capacity. In this study, it is found that optimum design intervals have been determined by using the Response Surface Method (RSM). Design ranges determined in the dimensionless study have been used in the improvement of the suction capacity of an existing ejector. The suction capacity of the existing ejector is investigated via numerical and experimental analysis. Two new water jet ejector designs (D1 and D2) are built to improve the suction capacity of the initial water jet ejector (D0). The generated design parameters have been analyzed by using SolidWorks flow analysis and optimization software. The suction capacity of the ejector has been determined through the iterative numerical analysis for the selected geometrical parameters under the applied design conditions. The effect of design parameters on the suction capacity of the water jet ejectors is unveiled through numerical and experimental analysis. The established designs were produced as two novel bronze water jet ejectors. The suction capacities of the produced bronze water jet ejectors have been investigated experimentally. The numerical results have been validated using the experimental results. It is achieved that the suction capacity of the manufactured water jet ejector with the improved design (D2) is suddenly increased from 52.05 m3/h to 103.4 m3/h.

Fabrication and failure mechanisms of all-composite honeycomb sandwich cylinder under the axial compression

Winding-based method, an innovative technology, is proposed to successfully fabricate the all-composite honeycomb sandwich cylinder (CHSC). Excellent mechanical properties of CHSC can be achieved owning to continuous prepreg winding. The critical force of intracell buckling for exact hexagonal boundaries is proposed based on the energy principle, which has small difference between the simulation and experimental results. Three-dimensional failure maps are derived to reveal failure mechanisms of fabricated CHSC. Multi-failure mechanisms of CHSC under axial compression are explored by failure mechanism maps, which can more intuitively express the influence of dimensionless geometric parameters on failure modes. Failure modes of intracell buckling and face crushing were obtained by typical experiments under axial compression. The honeycomb sandwich cylinder prepared in this paper shows excellent bearing capacity compared to other types of sandwich cylinders. Winding-based method is expected to provide an important support for the fabrication of curved multifunctional honeycomb.

Effect of reinforcement on the crack resistance of concrete slabs

A preliminary analysis of the available publications devoted to the study of crack resistance of reinforced concrete structures showed the absence of established general patterns of influence of important geometric parameters inherent in reinforced concrete elements on the distribution of the characteristics of fracture mechanics along the crack front. Based on the analysis, the purpose of the study was formulated: to establish these regularities for a concrete slab reinforced with a system of longitudinal steel rods. When conducting the research, a linear and elastic model of concrete was used, and the stress intensity factor was considered as a characteristic of the fracture mechanics. A surface crack of constant depth located in the cross-section of the slab was postulated. It was assumed that its faces completely cover the cross-section of reinforcing rods. The crack depth, the depth of reinforcing rods, their diameter, and the distance between adjacent rods were chosen as dimensionless geometric parameters relative to the thickness of the slab. The slab was loaded with two types of loads applied to its ends: constant tensile stresses (pure tension) and linearly variable axial stresses (pure bending). The problem of determining the stress intensity coefficient depending on geometric parameters was reduced to the boundary problem of elasticity theory. The CalculiX finite element analysis package was used to solve it and obtain the stress-strain state of the slab. More than four hundred finite element models were constructed for various combinations of parameters. Based on the known displacements of the crack face points, the values of the stress intensity factor along the crack front were calculated using the relation obtained in the study. It is established that its values significantly depend on the diameter of the reinforcement, and therefore, when conducting practical calculations, it is not recommended to replace the action of reinforcement on concrete with concentrated force. Polynomial approximations with a relative error of 10% are obtained for extreme values of the stress intensity factor. The materials of the study can be useful in the design of reinforced concrete structures, and when studying or teaching a course in fracture mechanics

Effect of reinforcement on the crack resistance of concrete slabs

A preliminary analysis of the available publications devoted to the study of crack resistance of reinforced concrete structures showed the absence of established general patterns of influence of important geometric parameters inherent in reinforced concrete elements on the distribution of the characteristics of fracture mechanics along the crack front. Based on the analysis, the purpose of the study was formulated: to establish these regularities for a concrete slab reinforced with a system of longitudinal steel rods. When conducting the research, a linear and elastic model of concrete was used, and the stress intensity factor was considered as a characteristic of the fracture mechanics. A surface crack of constant depth located in the cross-section of the slab was postulated. It was assumed that its faces completely cover the cross-section of reinforcing rods. The crack depth, the depth of reinforcing rods, their diameter, and the distance between adjacent rods were chosen as dimensionless geometric parameters relative to the thickness of the slab. The slab was loaded with two types of loads applied to its ends: constant tensile stresses (pure tension) and linearly variable axial stresses (pure bending). The problem of determining the stress intensity coefficient depending on geometric parameters was reduced to the boundary problem of elasticity theory. The CalculiX finite element analysis package was used to solve it and obtain the stress-strain state of the slab. More than four hundred finite element models were constructed for various combinations of parameters. Based on the known displacements of the crack face points, the values of the stress intensity factor along the crack front were calculated using the relation obtained in the study. It is established that its values significantly depend on the diameter of the reinforcement, and therefore, when conducting practical calculations, it is not recommended to replace the action of reinforcement on concrete with concentrated force. Polynomial approximations with a relative error of 10% are obtained for extreme values of the stress intensity factor. The materials of the study can be useful in the design of reinforced concrete structures, and when studying or teaching a course in fracture mechanics