Spherical Dome Research Articles

Large Amplitude Free Vibration of Spherical Dome Structures with Variable Thickness

Large Amplitude Free Vibration of Spherical Dome Structures with Variable Thickness

High spatial resolution underwater confocal LiDAR: reduction of optical aberrations in air-water interfaces using a dome port.

We study the impact of optical aberrations in underwater scanning confocal inelastic imaging arising from refraction at oblique incidences on a refractive index-mismatched air-glass-water interface. We experimentally demonstrate that optical aberrations at non-normal incidence drastically reduce the intensity of the inelastic signal and deteriorate the system resolution. At a 2.5° incidence angle, the return signal decreases to about 20% of its peak value at normal incidence. We implement passive correction using a spherical glass dome that is co-centered with the pivot point of the scanning mirror to ensure near-normal incidence on the interface irrespective of the scanning angle and depth. This configuration provides a drastic reduction in the optical aberrations within an angular range from -20° to 20°. The optical system is modeled in ray tracing software for validation. The interfacing of a scanning confocal system with a dome port unlocks near-diffraction-limited underwater imaging over wide areas without resorting to complex adaptive wavefront manipulation.

Fire Endurance of Spherical Concrete Domes Exposed to Standard Fire

Fire is considered a common hazard for civil structures. Public and administrative buildings are commonly designed by considering the standard fire rating and, in many cases, contain large compartments with central domes, in which fire growth can be significant. Moreover, tanks and underground fortified structures may be constructed as domes to support the heavy soil above. This paper numerically addressed such a case. First, an axisymmetric finite element model was developed and validated to predict the dome’s transient, thermal, structural, and thermal-structural behavior. Next, the model was used to conduct a parametric study to investigate the effects of the dome ring reinforcement, thickness, stiffness, central angle, base restraints, load type (external pressure or gravitational), and load ratio on the fire endurance of the dome. Design recommendations to increase the fire endurance of concrete domes were formulated based on the parametric study.

Parametric study of spherical domes for efficient housing construction using finite element method

Parametric study of spherical domes for efficient housing construction using finite element method

Enhancing wet surface adhesion in walking robots: finite element-based analysis and morphology-changeable soft pads

In recent studies concerning walking robots, there has been a notable emphasis on investigating tribological phenomena and elucidating the role of capillary forces in tangential resistance. However, majority of these investigations have been restricted to specific geometric shapes, primarily spherical domes. In this research, we propose a novel approach based on the finite element method to address broader challenge of wet adhesion applicable to objects of various shapes. Additionally, we investigate the role of distributed domes on a soft foot in quantifying the tangential capillary force, which plays a crucial role in enhancing the performance of walking robots on wet surfaces. Through the optimization application, we identify that our designed foot (measuring 20 mm × 14 mm, comprising 78 domes with a radius of 0.5 mm and a distance of 1.5 mm between the two nearest domes) maximizes the value of the tangential capillary force. Moreover, we develop a finite element method using the Simulation Open Framework Architecture (SOFA) to model the interaction between wet liquid on a solid object's curved surface, enabling the calculation of wet adhesion force and capillary forces. Finally, to demonstrate the effectiveness of our proposed morphology-changeable soft pads foot, we conduct a presented a demonstration of a hexapod robot walking on different dry/wet condition of the surface. The obtained results are expected to pave a way to morphological design of soft pads for facilitating locomotion in various conditions. Supplementary video URL: https://youtu.be/yVteC95eqbo

Rotated Thrust Network Analysis (rTNA) for stability assessment of vaulted structures subjected to horizontal loading

Thrust network analyses are commonly used in the stability analysis of three-dimensional masonry structures. Stability under gravity loading is ensured if a permissible thrust network can exist within the geometry of a structure. The maximum and minimum thrust networks are typically found using linear optimisation of the thrust network coordinates along the axis aligned with the gravity loading. When subject to lateral loading, optimisation along this axis does not result in equilibrium thrust networks. To address this issue, optimisation of the thrust network needs to be coordinated along an axis aligned with the resultant of gravity and lateral loading. In this paper, an extended thrust network analysis is presented that uses a stepwise procedure to effectively rotate the optimisation axis. This rotated Thrust Network Analysis (rTNA) results in more conservative solutions for the case examined of a spherical dome subject gravity and lateral loading. Numerical applications of the method, with the inclusion of lateral loading, are shown for changes in the embrace angle of a spherical dome and the effect of reduction in the acceleration due to gravity that may be experienced in the lunar environment.

Analysis of Lightweight Structure Mesh Topology of Geodesic Domes

This paper presents two methods of shaping the mesh topology of lightweight structures as spherical domes. The two given methods of dividing the initial face of the polyhedra determine the obtained structures, which differ in the way of connecting the nodal points. These points were obtained by applying the algorithm for calculating spherical coordinates presented in the paper, which were then converted to the Cartesian system using transformation formulas. Two models of dome structures are presented, based on a 4608-hedron according to the first division method, and on a 4704-hedron, using the second proposed method with numerical analysis. Thus, the novelty of this paper is an implementation of the formulas and algorithms from geodesic domes based on the regular dodecahedron to the regular octahedron, which has not been presented so far. The choice of the shape of the structure has impacts on sustainable development, dictated by structural and visual considerations, leading to the design of a light structure with low consumption of construction material (steel), which can undoubtedly be helpful when making the final structure shape. In addition, according to this research, it can be concluded that using the first method to create a geodesic dome mesh is more straightforward, safer, and requires less design experience.

Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments

Nowadays, engineers possess a wealth of numerical packages in order to design civil engineering structures. The finite element method offers a variety of sophisticated element types, nonlinear materials, and solution algorithms, which enable engineers to confront complicated design problems. However, one of the difficult tasks is the verification of the produced numerical results. The present paper deals with the in-depth verification of a basic problem, referring to the axisymmetric loading by edge forces/moments of a spherical dome, truncated at various roll-down angles, φo. Two formulations of analytical solutions are derived by the bibliography; their results are compared with those produced by the implementation of the finite element method. Modelling details, such as the finite element type, orientation of joints, application of loading, boundary conditions, and results’ interpretation, are presented thoroughly. Four different ratios of the radius of curvature, r and shell’s thickness, and t are examined in order to investigate the compatibility between the implementation of the finite element method to the “first-order” shell theory. The discussion refers to the differences not only between the numerical and analytical results, but also between the two analytical approaches. Furthermore, it emphasizes the necessity of contacting even linear elastic preliminary verification numerical tests as a basis for the construction of more elaborated and sophisticated models.

METHOD FOR CALCULATING SPHERICAL DOMES FOR STRENGTH AND BUCKLING

METHOD FOR CALCULATING SPHERICAL DOMES FOR STRENGTH AND BUCKLING

Spherical dome: design, digital twin manufacturing, and testing of a glubam structure

ABSTRACT Domes are common architectural elements in real life, with spherical or sphere-like shapes being the most common. Nonetheless, there has been limited research on incorporating modern design and manufacturing technologies into spherical domes, especially those made of bio-based materials. This paper presents a comprehensive study of the design pipeline for spherical domes. In terms of spherical tessellation for dome design, a set of innovative algorithms and programs is made available as open-source resources, comprising both manual and numerical approaches, where the numerical approaches are validated by existing results while also expanding these results, and new manual approaches are proposed and benchmarked as alternatives to conventional methods with similar or better performance, condition-wise. A proof-of-concept prototype is constructed according to the proposed pipeline to demonstrate its feasibility for later experiments. A preliminary loading test was conducted, validating its satisfactory mechanical behavior. In summary, a comprehensive design pipeline for spherical domes is proposed and validated through a prototype project, during which various innovations are made, from spherical tessellation to parametrical design, analysis, and digital twin manufacturing.

An isogeometric collocation method for the static limit analysis of masonry domes under their self-weight

A novel isogeometric collocation method is proposed for the static limit analysis of axially-symmetric masonry domes subject to their self-weight. A shell-based static formulation is employed, alongside Heyman’s assumptions on masonry, to characterize the equilibrated and statically admissible stress states in the dome. As a distinctive feature of the approach, a vector stress function is introduced, generating point-wise self-equilibrated shell stress resultants in the dome. Accordingly, the classical minimum-thrust problem is formulated in terms of the unknown vector stress function, and the static admissibility conditions are enforced as the only optimization constraint. NURBS-based isogeometric analysis is adopted to accomplish the need for an accurate geometric description of the dome and a high-order continuous interpolation of the vector stress function. A discrete minimum-thrust problem is derived as a linear programming problem, with the static admissibility conditions checked at suitable collocation points. Instrumental to its solution is the computation of a particular solution of the equilibrium equations, which is obtained by an isogeometric collocation method. By a mechanical interpretation of the dual optimization problem, the settlement mechanism of the dome corresponding to its minimum-thrust state is also computed. Numerical results, dealing with a thorough convergence analysis, parametric analyses on spherical and ogival domes with parameterized geometry, and the real case of the Taj Mahal central dome are presented to prove the computational merit of the proposed approach.

4D printing of shape-adaptive tactile sensor with tunable sensing characteristics

Using 4D printing to fabricate tactile sensors is promising, which will bring exciting functionalities to sensors, such as action self-sensing, environment self-adaptation, and self-healing. Here, we introduce 4D printing technology to fabricate the versatile smart tactile sensor with an adjustable measuring range and sensitivity, and shape adaptation for sensing in unstructured objects, which can sense touch from. The 4D-printed sensors (4DPS) with unique coplanar designs are achieved using a multi-material extrusion process for manufacturing interdigital electrodes composed of nanocarbon black/polylactic acid composites and shape memory polyurethane. The variability in the detection range and sensitivity stems from the changes in the electrode height and spacing caused by the deformation of shape memory polymer (SMP) under heat treatment. By setting printing parameters, not only can the diameter of the interdigital electrodes be precisely regulated, but 3D sensors that adapt to different curved surfaces can also be realized by utilizing thermal stress during the printing process. Moreover, the 4DPS is applicable to non-developable surfaces, such as spherical dome surfaces or saddle surfaces. Therefore, the shape-changing tactile sensor may offer great potential in environment self-adaptation and test range self-adjustment for human-robot cooperation in sensing.

Fluctuating Wind Pressure Characteristics of Dome Roofs with Low Rise-Span Ratio

In this study, the flow patterns and fluctuating wind pressure characteristics around the roof of a spherical dome with a low rise–span ratio (f/D) were analyzed in detail. Significant differences were observed when compared to the results of previous studies on spherical dome roofs with relatively high f/D. The flow-pattern-based zone divisions and zone-specific pressure spectra models proposed in previous studies have limitations when applied to a spherical dome with an f/D ratio of 0.1, which is the subject of this study. Therefore, this study modified and proposed zone division and pressure spectra modeling methods based on the zone division and pressure spectra models of previous studies, and applied them to spherical dome roofs with a low rise–span ratio. Based on spectral statistics, the average error between the measured and simulated spectra was less than 4%, demonstrating high accuracy.

Influence of a saltwater film on a radio-transparent dome on the amplitude-phase distribution of a millimeter-range antenna

Transition of communication systems installed on naval ships to the millimeter range requires an analysis of the effect of the saltwater film formed on the radio-transparent dome (RTD) on the radiotechnical characteristics of the mirror antenna. The latter are determined by the amplitude-phase distribution in the antenna aperture, so the topic of research is relevant. The objective of the article is to analyze the effect of the salt-water film on the surface of a marine mounted RTD, as well as the effect of millimeter wavelength antenna placement inside the RTD on the distortion of the field generated in the outer region. It has been shown that when installing millimeter-wave range antennas on a naval ship under a radio-transparent dome it is necessary to consider the distortions introduced by the water film on the dome surface into the generated amplitude-phase distribution when calculating the radio technical characteristics. We do so because most of the known methods for calculating the directivity characteristics of mirror antennas are based on the known amplitude-phase distribution in the antenna aperture. In the paper, the influence of the spherical dome wall and the saltwater film on the amplitude-phase distribution is taken into account as follows. Distortions in the amplitude distribution are caused by energy losses of the electromagnetic wave due to the passage of the curved dielectric wall at different angles. Phase distribution losses are due to the phase shift from the original phase as the dome wall is passed through at different angles. The angles of radio wave entry into the dome wall depend on the location of the antenna inside the radio-transparent dome. The electrical parameters of the saltwater film are determined using the well-known ITU methodology, while its thickness is found using the Gibbs formula, assuming that sea spray is similar to the intensity of drizzle rain. The studies have been conducted for the highest stiffness mode. Studies for a single-mirror antenna with a parabolic reflector 5.4 m in diameter and a radio-transparent dome 18 m in diameter showed that the water film influence is manifested in the phase front distortion, as well as a symmetry violation of the generated amplitude distribution. The degree of water salinity is manifested mainly in the distortion of the phase distribution. This is due to the fact that the electrical parameters of salt and fresh water do not differ much. The detected distortions are stronger for the horizontally polarized waves and in the case when the antenna swing center is offset with respect to the dome symmetry line. The detected patterns allow to give a scientific justification for the choice of the amplitude-phase distribution of the mirror antenna when installing it inside the RTD on the naval ship.

Morphology-Changeable Soft Pads Facilitate Locomotion in Wet Conditions

Stable robot walking requires effective gait planning and control. The mechanical properties of contact between feet and ground are important factors in this process. In this paper, we propose and test a design for a robot foot that houses soft pads, which adapt to facilitate locomotion on wet and dry floors. The morphology of each soft pad distributed in the sole of the foot is changed from a thin elastic sheet to a spherical dome that protrudes from the sole with the use of compressed air to adapt the foot for walking. We constructed an analytical model to estimate how soft pad dome shape is effected by air pressure and associated properties regarding friction and forces when in contact with a dry or wet floor. The contribution of wet adhesion to enhance shear force among the floor and the soft pads was elaborated theoretically. We report results of practical experiments with a sole (35 mm×15 mm) housing 14 such soft pads (radius 1.5 mm) comparing walking in dry and wet conditions. Finally, we present a setup of a walking robot leg with the proposed foot and soft pad on flat ground. The results demonstrate that soft pad domes improved walking stability under wet conditions on flat ground whereas they made no noticeable difference under dry conditions. Changeable morphology of the soft pads (stiffness, radius of the domes), which is controlled by adjusting air pressure, contributed to adaptive walking. The results obtained here may inform attempts at morphological design of soft pads to facilitate locomotion of legged robots under various terrain conditions.

Wind effect on scallop domes with negative amplitude and prominence using Experimental and Numerical Study

This study investigates the wind effect on hexa-sectored scallop domes using Computational Fluid Dynamics (CFD) and wind tunnel tests. Similar to the shape of a seashell, the scallop dome is one of the most common domes used to cover large spans. The scallop dome has an additional curvature equal to its sectors compared to a base dome (spherical). Hence, it has better structural efficiency compared to a spherical dome under the same condition. The curvatures on the scallop dome create alternate “ridges” and “grooves” on it. According to the computations of the article, the grooves created on this dome in the sector, as well as their position angle to the wind direction significantly affect pressure coefficient value. Due to these differences, wind pressure on scallop domes significantly differs from wind pressure on spherical domes. The results indicate that the ridges cause negative wind pressure coefficients whose magnitude reaches a maximum of −2.0 for an angle of alignment of 30°. The analyses have been conducted through Ansys-Fluent. This study presents the equation of wind pressure coefficient in the most critical of dome groove positions. The arch created between the grooves of a scallop dome is another effective parameter on maximum negative pressure. In the case study scallop dome, if the wind effect angle is considered α = 15, the maximum deformation in the structure will be created, which is 20% higher than that of α = 0.

МОДЕЛЮВАННЯ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ТОНКОСТІННИХ КУПОЛІВ З ПОЛІКАРБОНАТУ ДЛЯ РАЦІОНАЛЬНОГО ПРОЕКТУВАННЯ

The paper contains the further developed of method for calculating thin-walled dome systemswithout a stationary foundation. Have been carried out the detailed analysis of the fundamental design solutions for frameless collapsible spherical polycarbonate domes, which are used by modern world manufacturers of these structures. Have been done a brief description of the momentless theory of the operation of spherical shells, which is adapted for polycarbonate domes. Have been considered a simplified analytical model of the stress-strain state of a spherical shell with an equatorial diameter of up to5 m under the influence of climatic influences for the subsequent verification of detailed models. Have been developed highly detailed finite element models of domes of different sizes, taking into account technological openings and structural stiffeners (support ring and door frame) under the wind, snow, ice loads and under other climatic influences. Have been identified the fragments with the highest stresses from various loads and forms of the deformation of the structure.Have been considered separately the issues related to the loss of shape stability, position and balance of a thin-walled spherical shell, as a light temporary structure. Have been proven that the worst influence on the dome structures is the windinfluence, based on the stability criterion. Have been determined the estimated value of the aerodynamic lifting force from wind effects on the dome. Have been proven that the lifting force far exceeds the stabilizing force of the weight of a thin-walled dome. Have been revealed with the help of the performed calculations, it was that a frameless spherical polycarbonate dome inevitably БУДІВЕЛЬНІ КОНСТРУКЦІЇНАУКОВО-ТЕХНІЧНИЙ ЖУРНАЛ “СУЧАСНІ ТЕХНОЛОГІЇ, МАТЕРІАЛИ І КОНСТРУКЦІЇ В БУДІВНИЦТВІ”84loses its balance stability due to the action of wind loads and requires unfastening with anchors. Have been proposed a rational method for anchoring dome structures at temporary earthen construction sites using geo-screws or metal screw piles. Have been revealed the addiction between the radius of curvature of a spherical dome and the rational thickness of polycarbonate based on the criteria of stiffness and strength. Have been formulated the constructive recommendations regarding the rational design of polycarbonate dome systems. Have been developed the technological regulations for the further safe operation of domes, and have been outlined the directions for further scientific research on this topic

Measurement of ultrasound velocity in yolk and blastula of fish embryo in vivo

An acoustic microscopy method for measuring the velocity of ultrasound in the yolk and blastula of bony fish embryos at early stages of development was proposed. The yolk and blastula were approximated as a sphere and a spherical dome, respectively, consisting of a homogeneous liquid. A theoretical model of ultrasonic wave propagation through a spherical liquid drop located on a solid substrate was developed in the ray approximation. The dependence of the wave propagation time on the speed of sound in the drop, its diameter, and the position of the focus of the ultrasonic transducer has been determined. It was shown that the velocity in the drop can be found by solving the inverse problem by minimizing the discrepancy between the experimental and model spatial distributions of the propagation time, assuming that the velocity in the immersion liquid and the radius of the drop are known. The velocities in the yolk and blastula of the loach (Misgurnus fossilis) embryo at the stage of development of the middle blastula were measured in vivo using a pulsed scanning acoustic microscope operating at a central frequency of 50 MHz. The yolk and blastula radii were determined from ultrasound images of the embryo. Acoustic microscopy measurements conducted with four embryos provide velocities of the acoustic longitudinal wave in the yolk and blastula. They were measured to be 1581 ± 5 m/s and 1525 ± 4 m/s when the temperature of the liquid in the water tank was kept at 22 ± 2 °C.

Janus nanoplates, -bowls, and -cups: controlling size and curvature via terpolymer/homopolymer blending in 3D confinement.

The synthesis and properties of Janus nanoparticles with spherical, cylindrical, and disk-like shapes are nowadays rather well understood. Other topologies such as nanorings and bowl-shaped Janus nanoparticles are believed to show distinctly different solution behavior and interaction with interfaces, but limitations in their synthesis currently prevents a proper investigation of these properties. Especially the combination of shape- and surface-anisotropy of bowl-shaped Janus nanoparticles could result in enhanced selectivity in uptake of cargo and enhanced directional diffusion. We here produce bowl-shaped Janus nanoparticles without noticeable side products through evaporation-induced confinement assembly (EICA) of triblock terpolymers blended with high molecular weight homopolymer. The triblock terpolymer phase separates from the homopolymer into spherical domes, where the terpolymer adopts a hemispherical lamella-lamella morphology (ll). Selective cross-linking, removal of the homopolymer, and disassembly of the microparticles releases the bowl-shaped Janus nanoparticles. The amount of blended homopolymer determines the size of the spherical dome, allowing to control particle curvature into flat Janus nanoplates, hemispherical Janus nanobowls, and deep Janus nanocups. The use of Shirasu Porous Glass (SPG) membranes with pore sizes in the range of dpore = 0.2-2.0 μm further provides control of particle diameter. Size and shape were analyzed with electron microscopy and the Janus character through selective surface decoration. The diffusion behavior of bowl-shaped Janus nanoparticles was investigated depending on particle curvature and anisotropy using angle-dependent dynamic light scattering.

Admissible shell internal forces and safety assessment of masonry domes

The present paper illustrates a methodology for the safety assessment of masonry domes. The dome is modelled as a thin shell made of a material satisfying Heyman’s hypotheses. Based on the static theorem of limit analysis, the method searches for statically admissible distributions of internal forces within the shell, suitably combining membrane forces and bending moments, by solving a convex optimisation problem. The solution is pursued numerically by means of an expressly developed collocation method that enables obtaining the analytical expressions for each internal force component. In its present formulation the method can be applied to domes of any shape, as well as to arbitrary load distributions. After validation against the benchmark case of the spherical dome under its self-weight, the paper illustrates application of the method to the dome of Pisa Cathedral under vertical loads as a first real case study.