Shallow Dome Research Articles

The Mosque of the Blessed Tree in Safawi, Jordan

The Mosque of the Blessed Tree in Mafraq, Jordan represents a revival of Islamic architectural heritage. Situated near an ancient terebinth tree where the Prophet Muhammad is believed to have rested, the mosque was erected according to traditional building techniques and Islamic principles. The design, led by MAS Design Office, involved careful integration of local materials along with load-bearing structures. Despite challenges, including limited time and budget constraints, the project was completed in six months. The mosque's design emphasizes simplicity and balance, with features such as a central dome, shallow domes in prayer halls, and pinnacles echoing traditional minarets. The project also involved training local craftsmen in complex stonemasonry techniques.

Evaluating the effect of dome geometry on acoustical quality of a pavilion

Acoustic performance of structures is an emerging field of research enquiry, with limited number of studies conducted in the Indian context. To address this gap, this study examines the effect of varied dome geometry on the acoustic quality of a pavilion. In-situ measurements pertaining to energy decay curve from impulse sound were collated at a historical 'Baradari'. The square shaped pavilion considered in the study is surmounted by a shallow dome and has three doorways on each side. Virtual simulation models of the pavilion were built thereafter and validated. In this study, dome geometries that emerged between the 15th-19th century (corbelled, shallow, single-shell, bulbous, and onion) in the Indian subcontinent are examined. Acoustic simulation was conducted on treble software to assess and compare the sound quality of each dome geometry. The study found that the reverberation, RT30, for the flat dome was approximately half to that of the single-shell dome. The study established that the choice of dome geometry is crucial as it impacts the reverberation time. The study findings vary with building typology, size, and architectural features. Nevertheless, this study should be viewed as a case-specific analysis that identifies optimal dome geometry for improved pavilion acoustics.

Η Παναγία Γαλακτοτροφούσα στην Ανθούσα Τρικάλων παρά τον Αχελώο ποταμό

The Virgin Galaktotrophousa (1799), the main church of an old monastery close to the village Anthousa near Trikala in the region of Aspropotamos, is a single-nave church with an abbreviated dome, lateral apses and a later narthex to the west. Above the narthex there was a chapel dedicated to the Beheading of Saint John the Forerunner. It is covered by a gabled roof from which the dome springs. The protrusion on the exterior of the tiled roof of the west part of the naos leads to the hypothesis that the narthex was vaulted, possibly with a shallow dome. The abbreviated form of the dome, the placement of a chapel above the narthex, and the latter’s shallow dome are common practices in the wider region of Aspropotamos.

Saint, Hagiographer and Translator: St Jerome in the Triumphal Heavenly Procession/Translation in Štrigova (Croatia)

Fresco decoration in the sanctuary of the Church of St Jerome in Štrigova in north-western Croatia was completed in 1744 by Ioannes Baptista Ranger, the most prominent painter of the first half of the 18th century on the territory of the Zagreb Diocese. The three-foil ground plan of the sanctuary retains memory of an older-smaller church, erected before 1447, on the place that holds an enduring memory of St Jerome’s native soil, and from 1644 the church was in pastoral care of the Pauline order (Order of St Paul the First Hermit). The book Natale solum sancti Hieronymi (Native soil of St Jerome, 1752) by Joseph Bedeković was a part of a collective effort - mainly by Pauline authors, but not exclusively - to confirm Štrigova as St Jerome’s homeland, in particular in the eyes of the Bollandists, preparing at the time the volume containing the saint’s Vita. St Jerome was the hagiographer of the spiritual founder of the Pauline Order, St Paul the First Hermit. The most elaborate part of the fresco decoration is a procession in a tambour of a shallow dome that is interpreted as a Triumphal Heavenly Translation of St Jerome’s relics. They came from Bethlehem, where he was buried, to Santa Maria Maggiore in Rome, where the relics of St Jerome have reposed since the 13th century. First they were found near the older Chapel of the Manger (Cappella del Presepe), where the relics of the Sacra Culla or the Holy Crib were venerated as “Bethlehem in Rome”. On that site the Sistine Chapel was later erected, and on the other side the Pauline Chapel with the icon Salus Populi Romani (copied in Štrigova). Both chapels are visible on the rear facade of the basilica, depicted as the destination of the miraculous procession.

Diffusion on Membrane Domes, Tubes, and Pearling Structures

Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.

Reliability Assessment of Shallow Domes Using a Semi-Empirical Evaluation Procedure

Like other structures, shallow domes have imperfections from the prescribed values obtained by specifications during the construction process. Specifications define some tolerance values for imperfections. Despite consideration of these values, the critical load of a dome varies for each imperfection pattern. So the reliability plays an important role in domes safety. Theoretical evaluation procedure is the most accurate one to obtain reliability function, but it is only applicable to small structures. Semi-empirical evaluation procedure, on the other hand, is more implemented. In the present research reliability of real domes with stochastic initial imperfections has been investigated by comparing finite elements method, theoretical and semi-empirical results. Also, it has been shown that the automatic perturbed analysis is not sufficiently reliable for domes. So it is recommend that a suitable safety factor be applied on the automatic perturbed load or the method utilized in this paper be used to obtain the critical load – reliability diagram.

Load Stress Controls on Directional Lava Dome Growth at Volcán de Colima, Mexico

During eruptive activity of andesitic stratovolcanoes, the extrusion of lava domes, their collapse and intermittent explosions are common volcanic hazards. Many lava domes grow in a preferred direction, in turn affecting the direction of lava flows and pyroclastic density currents. Access to active lava domes is difficult and hazardous, so detailed data characterizing lava dome growth are typically limited, keeping the processes controlling the directionality of extrusions unclear. Here we combine TerraSAR-X satellite radar observations with high-resolution airborne photogrammetry to assess morphological changes, and perform finite element modeling to investigate the impact of loading stress on shallow magma ascent directions associated with lava dome extrusion and crater formation at Volcan de Colima, Mexico. The TerraSAR-X data, acquired in ~1-m resolution spotlight mode, enable us to derive a chronology of the eruptive processes from intensity-based time-lapse observations of the general crater and dome evolution. The satellite images are complemented by close-range airborne photos, processed by the Structure-from-Motion workflow. This allows the derivation of high-resolution digital elevation models, providing insight into detailed loading and unloading features. During the observation period from Jan-2013 to Feb-2016, we identify a dominantly W-directed dome growth and lava flow production until Jan-2015. In Feb-2015, following the removal of the active summit dome, the surface crater widened and elongated along a NE-SW axis. Later in May-2015, a new dome grew toward the SW of the crater while a separate vent developed in the NE of the crater, reflecting a change in the direction of magma ascent and possible conduit bifurcation. Finite element models show a significant stress change in agreement with the observed magma ascent direction changes in response to the changing surface loads, both for loading (dome growth) and unloading (crater forming excavation) cases. These results allow insight into shallow dome growth dynamics and the migration of magma ascent in response to changing volcano summit morphology. They further highlight the importance of detailed volcano summit morphology surveillance, as changes in direction or location of dome extrusion may have major implications regarding the directions of potential volcanic hazards, such as pyroclastic density currents generated by dome collapse. Introduction

Response characterization of multistable shallow domes with cosine-curved profile

The multistable elastic behavior of a shallow dome with a cosine-curved profile is investigated in this work. The dome exhibits snap-through instability and could be used as a building block for energy dissipation mechanism in structures subjected to cyclic loading and high deformation demands. Numerical and experimental studies were carried on the geometric and material properties of the cosine-curved domes (CCD) under concentrated load at the apex. Finite element analyses (FEA), validated by experimental tests on 3D printed specimens, were conducted to study the controlling geometric and material properties of the CCD. Three types of response were recognized and discussed based on the force- and strain energy-displacement curves. Limitations on the geometric parameters that govern the recoverability of the original shape and the stability state upon load removal are also identified. In addition, empirical relations to estimate the limit-point load and displacement, and to characterize the snap-through response were developed. Good agreement was observed using the determined limits on the geometric parameters and the developed relations with the results from FEA and experimental tests.

SMALL HELIOSTATS CSP SYSTEMS ON LONG-SPAN HANGING ROOFS

ABSTRACT Building Integrated Concentrating Solar Power (BI-CSP) schematic studies with small scale exterior two-axis tracking heliostats anchored on and semi-shading long span hanging roofs with elevated receiver(s) are presented for populated urban and rural locations. Hanging roofs (inverted shallow dome shape) with two-way structural cables and mostly square infill prefabricated slabs/panels supported from a perimeter horizontal circular donut shape rim-girder-platform without a center tension ring studies are for comparing to radial cable structural configurations with a center tension ring. Cable gap grouting between slabs/panels form a pre-tensioned inverted shell structure after temporary weights are removed. Securing vertical heliostat posts studies include: three vertical bolts cast in grout gap two-way cables intersections for three point adjustment of horizontal post base plates; and one-axis adjustable manufactured post brackets bolted to sloped roof surfaces at holes cast in the gaps/slabs. A main case study schematic is around a 30m/100ft diameter hanging roof with a 0.07 sag/diameter ratio with around 271 1m2 heliostats for 230kWt solar thermal steam or air to around 300degC/572degF building integrated thermal energy storage (molten salt, firebricks, etc.) and applications (water purification, cooling, industrial process heat, etc.). A BI-CSP hanging roofs R&D project proposal is outlined: with a circular roof study diameter range of around 25m/82ft–200m/656ft diameter for comparing two-way and radial cable structural configurations for distributed steam stations and a wide range of application temperatures.

Finding the worst imperfection pattern in shallow lattice domes using genetic algorithms

Like other structures, shallow domes have imperfections from the construction process. Specifications prescribe some construction tolerance values for imperfections. Despite consideration of these values, the critical load of a dome varies for each imperfection pattern. Analytical and Monte Carlo approaches are among the main methods for finding the worst imperfection pattern that is playing significant role in safety of dome. Analytical methods are reliable but cannot be implemented for large structures. On the other hand, uncertainties and high computational costs are the most important weaknesses of Monte Carlo approaches. In the present research employing genetic algorithms, the worst imperfection pattern is analyzed, calculated, and plotted.

Mallomonas skogstadii sp. nov. and M. bakeri sp. nov.: Two New Fossil Species from the Middle Eocene Representing Extinct Members of the Section Heterospinae?

Two new fossil species of the synurophyte genus Mallomonas, M. skogstadii and M. bakeri, are described from Giraffe Pipe, an Eocene locality situated near the Arctic Circle in northern Canada. Scales of both new species share a suite of characters, including an oval-shaped rib encircling approximately half of the base plate and most of the dome, a series of thick ribs on the posterior flange, but lacking on the shield, a thin posterior rim, and a flat and shallow dome. In addition, both species possess two types of scales, body scales and apical scales. Apical scales of M. bakeri form a unique forward–projecting dome, and those of M. skogstadii are significantly different in shape than the body scales. Scales of M. skogstadii are significantly larger and have a different base plate pore pattern than those of M. bakeri, and remains of both taxa were uncovered in strata deposited hundreds of years apart. Based on comparison made with modern species, M. bakeri, and to a lesser extent M. skogstadii, are placed into, and likely represent basal representatives of section Heterospinae. The floras associated with each species reflect acidic environments, probably high in dissolved humic content.

Structural behavior of shallow geodesic lattice domes

This paper describes experiments and analysis of the complete post-buckling behavior of shallow geodesic lattice domes. Although individual members are straight, their geometric arrangement approximates a curved surface and typical behavior is highly nonlinear, including the possibility of sudden jumps in which there may be multiple discontinuous pops from one equilibrium configuration to another. A number of shallow domes were produced using a 3D printer and tested using a load cell and proximity laser sensor. In contrast to most previous studies, rather than pinned or semi-rigid joints, the lattices studied here incorporate moment-transmitting joints and clamped boundary conditions at the perimeter. Thus, flexure is the dominant mode of deformation under lateral loading and coupled instability behaviors are possible in practice. The complete load-displacement relationship and multiple equilibrium configurations are exhibited both in experiment and in simulation. The experimental data shows a close correlation with nonlinear finite element analysis using path-following techniques. A typical member (coupled) buckling behavior and its influence on the critical load are presented. Conclusions are drawn with respect to symmetry and geometric sensitivity.

A New Light

Louvre Abu Dhabi was designed by Ateliers Jean Nouvel to resemble a group of islands at sea topped by a shallow dome that appears to float above. BuroHappold Engineering first created water-resistant basements and foundations, then designed tidal pools at the plaza level to ensure that the architect’s vision for connecting the museum to the water was realized. Building information modeling helped the engineers design the eight-layer dome so that light would dapple the plaza and galleries below in precisely the right way.

O gradnji, funkciji i rušenju krstionice-zvonika dubrovačke romaničke katedrale

Članak okuplja do sada poznate likovne i pisane izvore o krstionici dubrovačke romaničke katedrale, kojima se pridužuju neki novi – prvenstveno dokumentacija o njenome rušenju iz ranih 1830-ih godina, te na temelju njihove usporedne analize dopunjava dosadašnje znanje o njenome izgledu (posebice artikulacija interijera zgrade krstionice s plitkom, segmentnom, kupolom s rebrima). Predlaže se povezivanje dubrovačke krstionice ne samo s formalnim uzorima iz biskupskih središta Padske nizine (Parma), već i s općenitijim konceptom rituala uskršnjeg krštenja, razvijenog u talijanskim srednjovjekovnim komunama. Usporedbom izvora također se uspostavlja kronologija promjene funkcije građevine, od prvotnog naglaska na zvonik, preko posvjedočene krstioničke funkcije krajem XIV i početkom XV stoljeća, do preostale funkcije crkve za svakodnevno bogoslužje, nakon prenošenja obreda krštenja u samu katedralu.

Free vibration analysis of shallow and deep ellipsoidal shells having variable thickness with and without a top opening

A three-dimensional (3-D) method of analysis is presented for determining the natural frequencies and the mode shapes of hemi-ellipsoidal domes having non-uniform thickness with and without a top opening by the Ritz method. Instead of mathematically two-dimensional (2-D) conventional thin shell theories or higher-order shell theories, the present method is based upon the 3-D dynamic equations of elasticity by the Ritz method. Mathematically minimal or orthonormal Legendre polynomials are used as admissible functions in place of ordinary simple algebraic polynomials which are usually applied in the Ritz method. The analysis is based upon the circular cylindrical coordinates instead of the shell coordinates which are normal and tangential to the shell mid-surface. Potential (strain) and kinetic energies of the hemi-ellipsoidal dome having variable thickness with and without a top opening are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the Legendre polynomials is increased, the frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Numerical results are presented for a variety of shallow and deep hemi-ellipsoidal domes having variable thickness of five values of aspect ratios with and without a top opening, which are completely free and fixed at the bottom. The frequencies from the present 3-D analysis are compared with those from other 3-D analysis and a 2-D thin shell theory.

Shape optimization of shallow domes subjected to external pressure

Shallow domes subjected to external pressure are extensively used in missile structures. The critical failure mode for these domes is buckling due to external pressure. Different closed form solutions are available to evaluate buckling pressure of dome shapes like ellipsoid and torisphere. The torisiphere dome is the optimum dome shape among conventional domes. Shape optimization is carried out to find the optimal dome shape among shallow domes subjected to external pressure. Dome geometry is generalized by cubic bezier polynomials. For carrying out shape optimization, a low fidelity model is preferred which can predict the critical buckling pressure of a general dome shape. Towards this a unified model is proposed which meets the above requirement. Using this unified model, shape optimization of dome for minimization of mass is carried out subjected to buckling constraint. The study yielded a dome shape different from conventional dome shapes with a mass saving of 6% over torispherical dome while meeting the buckling constraint. The results of unified model are also validated with high fidelity Finite Element Analysis.

One novel method to improve surface quality in incremental sheet forming

Abstract Incremental sheet forming receives widespread study with its advantages of economy and flexibility in low-volume sheet metal parts. However, local loading leads to poor surface quality in formed parts, such as friction trace caused by direct contact between blank and forming tool, and waved impression caused by forming instability or local bending of blank. The formed parts with above surface problems cannot be used as outer panels of one car or aircraft. For this reason, one novel method is proposed that a sheet, namely interpolater, is placed between blank and forming tool to increase the contact area of blank. In this paper, a shallow dome specimen, showing poor surface quality in traditional incremental sheet forming, is selected to analyze the influence of interpolater on surface quality. The specimen is made of aluminum AA2024 which is widely used for aircraft skins. Meanwhile, the interpolater is made of deep drawing steel DC04. Then, a Box–Behnken design is provided and the specimens are formed with various process parameters, such as thickness of interpolaters, tool diameter and step size. With measurement of surface roughness horizontally and perpendicular to the tool path through application of roughness tester, arithmetic mean surface roughness (Ra) and maximum peak to valley height (Rz) are obtained. Then, the specimens formed with interpolaters show better surface roughness compared with those formed without interpolaters. Furthermore, comparing surface roughness of specimens formed with different process parameters, the influence of process parameters on surface roughness is obtained. Finally, the best combination of process parameters with minimum surface roughness is obtained with mathematical analysis.

A novel forming method of aluminum sheet based on superposition principle of electromagnetic local forming

A novel forming method aimed at large size aluminum sheet is introduced. In this method, aluminum sheet is clamped between a common flat spiral electromagnetic actuator and a punch matrix. Driven by pulsed electromagnetic force and restrained by punch matrix, the blank sheet will form local shallow dome accordingly. Moving actuator along sheet surface and triggering the pulsed power generator in sequence results in dome matrix that is uniformly distributed. Superposition of those spherical domes leads to macroscopically curved figuration of aluminum sheet. This paper demonstrates the newly proposed method experimentally, which verifies its feasibility. The mechanism analysis of this method is also presented using a simplified analytical model. The results show that this novel method is feasible and can be explained by the proposed mechanism well.

Balloon-assisted coil embolization of small intracranial aneurysms.

It is generally considered difficult and risky to treat a small aneurysm (less than 4 mm) by use of coil embolization. The main issues are related to the following factors: frequently broad-based aneurysm with shallow dome, complex in shape, difficult to maintain microcatheter stability in an aneurysm, difficult to achieve complete coil packing, and higher risk of intra-procedure rupture hemorrhage. However, routine use of balloon-assisted coiling technique will enable us to achieve successful aneurysm embolization with safety. This video demonstrates some key nuances in the balloon-assisted coil embolization of small aneurysms via three case examples. The video can be found here: http://youtu.be/E1il3oPnUD8 .

Second-Order Analysis and Experiments of Semi-Rigid and Imperfect Domes

Since the recent introduction of second-order analysis in codes, engineers begin to realize the advantages of the second-order analysis in enhancing the safety and economy of the design output. The method is especially useful for design of complex structures like the shallow dome where failure is commonly due to snap-through buckling with the collapse load difficult to be assessed by the effective length method. In this paper, the second-order analysis is used to study the behavior and to determine the snap-through buckling load of the shallow domes. A comparison on the failure loads of a shallow dome between the laboratory test and second-order analysis is carried out to demonstrate the application of the second-order analysis. Further, the importance for inclusion of global imperfection in the analysis is demonstrated because the snap-through buckling load can be greatly reduced if the practically unavoidable and unfavorable global imperfection is included.