Journal articles: 'Shape'

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Franceschi, Eleonora, Astrid Moser-Reischl, Mohammad A. Rahman, Stephan Pauleit, Hans Pretzsch, and Thomas Rötzer. "Crown Shapes of Urban Trees-Their Dependences on Tree Species, Tree Age and Local Environment, and Effects on Ecosystem Services." Forests 13, no. 5 (May 12, 2022): 748. http://dx.doi.org/10.3390/f13050748.

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Crown shapes of common European urban tree species differ from tree species to tree species and are modified by the age of a tree and its local environment. A tree’s crown shape has a great influence on the crown volume and thus on the ecosystem service provision of a tree such as the shade area or the shade density. We used the data of 3852 tree individuals from eight German cities and the crown shape data of 528 trees for the species Acer platanoides, Acer pseudoplatanus, Aesculus hippocastanum, Fraxinus excelsior, Platanus × acerifolia, Robinia pseudoacacia and Tilia cordata to analyze tree structural dimensions and the crown volume and shade dependency on a tree’s crown shapes. Ovoid (57% of all tree individuals) and spherical (24%) crown shapes were mostly observed. However, columnar shape was observed for light-demanding R. pseudoacacia in close proximity of objects. The greatest shade areas were measured for spherical shape and the highest shade density for ovoid shape. Logistic regression analysis showed significant effects of age and distance to objects on crown shapes. Significant probability of crown shapes was found for different tree species, e.g., A. hippocastanum strongly showed half-ellipsoid crown shapes.

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Than, Thida, Labang Hkawn, Anjuna Radhakrishnan, Yupa Min, Hlaing Thaw Dar, and Nurul Hazliana Harun. "Variation in the shape of the knee meniscus and incidence of the discoid shape in Myanmar's adult population: A cross-sectional study." Journal of Biomedical Sciences 10, no. 2 (December 31, 2023): 32–39. http://dx.doi.org/10.3126/jbs.v10i2.61357.

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Background: A meniscal injury is one of the most common sports-related problems and the most frequent injury to the knee joint. The method for determining meniscus shape is used in designing therapies for treating various joint diseases. Material and methods: Anatomy dissection was performed, and the shapes of knee menisci were studied in 160 menisci from 40 autopsy bodies (20 males and 20 females) from Medical Universities in Myanmar. The bodies were embalmed with 4% formaldehyde and then preserved in a weak formalin solution. Results: The number of crescentic-shaped medial menisci was 5 (6.25%), horseshoe-shaped menisci were 6 (7.5%), sickle shapes were 48 (60%), U shapes were 8 (10%), V shapes were 12 (15%), and complete discoid shapes were only 1 in number (1.25%). There was no incomplete discoid, circular, or C shape at all. The commonest shape of the medial meniscus was a sickle. The number of C-shaped lateral menisci was 6 (7.5%), the complete discoid shape was 1 (1.25%), the incomplete discoid shapes were 13 (16.25%), and the circular shapes were 60 (75%). Crescentic, horseshoe, sickle, U, and V-shaped lateral menisci were absent. Circular was the commonest of all. Among 160 menisci, an incomplete discoid shape was found in 13 menisci, and a complete discoid shape was found in two: one meniscus as a primitive disc and a very rare infantile shape in another. Conclusion: Our findings will help morphologists and orthopaedic surgeons with surgical procedures and knee joint arthroscopy. It will also help patients with effective rehabilitation after meniscal injuries and surgery.

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Phuong, Lam-Huy, Cao-Minh Dai, Quach-Ngo Diem-Phuong, and Tran-Quoc Tan. "Comparing of antioxidant ability, α-glucosidase inhibition and cytotoxicity of three fruiting body shapes of Ganoderma lingzhi." Research Journal of Biotechnology 18, no. 8 (July 15, 2023): 119–27. http://dx.doi.org/10.25303/1808rjbt1190127.

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In the process of artificial culture, Ganoderma mushrooms will appear with several different shapes of fruiting bodies, even though they share the same species. The differences in shape can influence and create differences in bioactivity and active ingredients. This study looked at the biological activities of ethanol crude extracts from three shape kinds of fruiting bodies of Ganoderma lingzhi mushroom and herb tablets made from kidney-shaped fruiting body including antioxidant, α-glucosidase inhibition and cytotoxic activity in some cell lines. Besides, the content of ganoderic acid A was also evaluated among the tested samples. The results showed that different shapes of G. lingzhi could possess differences in bioactivities. The shapes with elongated fruiting body stem including antler- and intermediate form, have better antioxidant and α-glucosidase inhibitory capacity than the common kidney shape. Furthermore, the antler and intermediate forms' cytotoxic activity against cell lines including fibroblast, NCI H469 and Hep G2, were higher than the kidney-shaped mushroom extracts. Similarly, the results of ganoderic acid A content from the extracts of antler- and intermediate form samples were also higher than that of the other form. Meanwhile, the herb tablets had the same pattern to the kidney-shaped extract in several activities. The ganoderic acid A content of the tablet sample was lower than that of three samples extracted from different mushroom shapes. Interestingly, the tablets showed the best-reducing power among the investigated samples.

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Rosen, Jeffrey J. "Shapes That Shape the Shape of Brain and Society." Contemporary Psychology: A Journal of Reviews 35, no. 2 (February 1990): 138–39. http://dx.doi.org/10.1037/028258.

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Wiegers, Tjamme, Lau Langeveld, and Joris Vergeest. "Shape language: How people describe shapes and shape operations." Design Studies 32, no. 4 (July 2011): 333–47. http://dx.doi.org/10.1016/j.destud.2011.03.002.

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CHEN, CHAO, and HO-LUN CHENG. "SUPERIMPOSING VORONOI COMPLEXES FOR SHAPE DEFORMATION." International Journal of Computational Geometry & Applications 16, no. 02n03 (June 2006): 159–74. http://dx.doi.org/10.1142/s0218195906001987.

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Edelsbrunner et al. defined a framework of shape deformations with shapes bounded by skin manifold. We prove that the infinitely many synthesized shapes in the deformation sequence share finitely many common Voronoi complexes. Therefore, we propose a new algorithm to compute the common Voronoi complexes efficiently for the deformations, and use these common complexes to compute the synthesized shapes in real time. This makes generating, visualizing, and customizing shape deformations feasible.

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Shi, Ding, Feng Ji, Yin-su Bao, and Yong-pan Liu. "A Multicenter Randomized Controlled Trial of Malignant Gastric Outlet Obstruction: Tailored Partially Covered Stents (Placed Fluoroscopically) versus Standard Uncovered Stents (Placed Endoscopically)." Gastroenterology Research and Practice 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/309797.

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The aim of our study is to compare the efficacy and safety of “outlet-shape” tailored stents with standard stents for the management of distal gastric cancer causing gastric outlet obstructions (GOOs) with varying gastric cavity shapes and sizes. To determine the shape and size of the GOOs, stomach opacifications were performed using contrast media before stenting. Two basic shapes of the residual cavity of the proximal GOO were observed: cup shaped or approximately cup shaped and funnel shaped or approximately funnel shaped. Other shapes were not found. In the GOO tailored group, the size and shape of the proximal ends of the tailored stent were suited for the residual cavity of the proximal GOO. The tailored stents included large cup-shaped stents and large funnel-shaped stents. GOO tailored covered stents led to less restenosis and reintervention rates compared to standard uncovered stents but with the same survival.

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Formby, C. "Simple Triangular Approximations of Auditory Filter Shapes." Journal of Speech, Language, and Hearing Research 33, no. 3 (September 1990): 530–39. http://dx.doi.org/10.1044/jshr.3303.530.

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At present, the most popular auditory filter shape model is one with a rounded peak and exponentially decaying filter skirts (Patterson & Moore, 1986). Unfortunately, the complex nature of this “roex” filter model may, in some instances, have hindered the application of the auditory filter shape in clinical measurements of frequency selectivity. Moreover, some of the assumptions of the roex filter model may be violated at high sound-pressure levels (SPLs) and this limitation has also been a factor when considering the roex auditory filter shape in the clinic. Our purpose is to introduce a simplified method that is adequate for obtaining clinically useful estimates of triangular-shaped auditory filters. Although the triangular-shaped filter model faces the same problems as the roex model at high SPLs, the calculations and assumptions underlying the former are far less complicated. The triangular filter model also retains many of the qualitative properties and advantages afforded by roex-fitted auditory filter shapes. In this report, we review the basic concepts underlying auditory filter shape estimates and describe our methods for measuring and fitting the triangular-shaped filter model. We then present normative triangular filter shapes and compare these estimates with auditory filter shapes fitted by other means. Finally, we present selected examples of triangular filter shapes fitted to the masked thresholds of hearing-impaired patients. For the most part, the triangular-shaped filter model offers the clinician a satisfactory compromise for obtaining estimates of auditory filter shape and frequency selectivity at moderately intense and high SPLs.

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McCane, Brendan. "Shape Variation in Outline Shapes." Systematic Biology 62, no. 1 (November 8, 2012): 134–46. http://dx.doi.org/10.1093/sysbio/sys080.

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Tanveer, Muhammad, and Kwang-Yong Kim. "Effects of Bridge-Shaped Microchannel Geometry on the Performance of a Micro Laminar Flow Fuel Cell." Micromachines 10, no. 12 (November 27, 2019): 822. http://dx.doi.org/10.3390/mi10120822.

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A laminar flow micro fuel cell comprising of bridge-shaped microchannel is investigated to find out the effects of the cross-section shape of the microchannel on the performance. A parametric study is performed by varying the heights and widths of the channel and bridge shape. Nine different microchannel cross-section shapes are evaluated to find effective microchannel cross-sections by combining three bridge shapes with three channel shapes. A three-dimensional fully coupled numerical model is used to calculate the fuel cell’s performance. Navier-Stokes, convection and diffusion, and Butler-Volmer equations are implemented using the numerical model. A narrow channel with a wide bridge shape shows the best performance among the tested nine cross-sectional shapes, which is increased by about 78% compared to the square channel with the square bridge shape.

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Kumar B., Varun, G. Manikandan, P. Kanna, Dawid Taler, Jan Taler, Marzena Nowak-Ocłoń, Karol Mzyk, and Hoong Toh. "A Performance Evaluation of a Solar Air Heater Using Different Shaped Ribs Mounted on the Absorber Plate—A Review." Energies 11, no. 11 (November 9, 2018): 3104. http://dx.doi.org/10.3390/en11113104.

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In this paper, the effect of various shapes of ribs used in Solar Air Heaters (SAHs) was discussed. The review is concentrated on the geometry of the rib and its location on the SAH panel. Both numerical and experimental works were considered for discussion with dry air and Nano fluids as a working fluid. The influence of various shapes, such as an L shape, W shape, V shape, Multiple V shape, V shape with a gap, detachable & attachable ribs etc., was analyzed. The common fact observed from this analysis is that the implementation of artificial roughness in the absorber plate results in a considerable increase in the rate of heat transfer. Further, it is observed that ‘Multiple V-shaped with open between the ribs’ results in the maximum thermal enhancement when compared to the other shapes.

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Ismail, Ikram K., and Abdennour Seibi. "Shape Factors for Irregular Glass Reinforced Plastic Pipes – An Analytical and Numerical Approach." Key Engineering Materials 471-472 (February 2011): 279–84. http://dx.doi.org/10.4028/www.scientific.net/kem.471-472.279.

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This paper presents the development of a mathematical model based on curved beam theory of composite pipes with irregular shapes under diametral loading. The analytical solution was validated through finite element models of the same pipe shapes under similar loading conditions. Four shapes (circular, elliptical, rectangular, and egg shaped pipes) were considered in this study. The analytical and finite element results were used to estimate the shape factor defined by the ratio of the maximum tangential stress of an irregular shape over the maximum tangential stress for a circular pipe. Comparison of the load-deflection curves for the four different shapes revealed that the egg pipe is the stiffest among the rest of the pipes while the square shape is the most flexible one. The analytical solution and finite element results were used to determine the shape factor for the four pipe shapes taking into account the circular pipe as the base shape. Both results were in good agreement and can be used as design guidelines for the irregular shapes without resorting to the conduct of any further testing.

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Tobushi, Hisaaki, Syunichi Hayashi, Kazumasa Hoshio, and Yoshihiro Ejiri. "OS16-1-2 Shape Recovery and Secondary-Shape Forming of Polyurethane-Shape Memory Polymer." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2007.6 (2007): _OS16–1–2——_OS16–1–2—. http://dx.doi.org/10.1299/jsmeatem.2007.6._os16-1-2-.

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Shim, H., and K. Son. "Optimal blank shape design by the iterative sensitivity method." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 216, no. 6 (June 1, 2002): 867–78. http://dx.doi.org/10.1243/095440502320192996.

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In order to realize net shape manufacturing of drawn parts, determination of the optimal blank shape plays a key role in the process development stage. The sensitivity method has many successful applications of the optimal blank design. In the method, the undeformed blank shape is modified iteratively by moving boundary nodes in the initial moving direction until the deformed shape satisfies a target shape. To determine the magnitude of the movement of the nodes, both the shape error measured at the deformed shape and the shape sensitivity defined by the effect of initial shape change on the final shape are utilized. To obtain shape sensitivity for each boundary node numerically, a couple of deformation processes has been analysed at each design stage with an original blank and offset blank. Drawings of the trapezoidal cup, cross-shaped cup and oil pan have been chosen as examples to verify the sensitivity method. Both the cross-shaped cup and oil pan are examples of complicated material flow during forming while the trapezoidal cup is of a simple flow. For every case the optimal blank shape has been obtained after only a few modifications without any predetermined deformation path. With the predicted optimal blank, a corresponding experiment has been carried out. The deformed shapes of the experiment almost exactly coincide with the desired target shape in every case. Through the investigation, the sensitivity method is found to be excellent in the blank design of arbitrary shaped drawing products.

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Xie, An-Xin, Nicole Rendine, and Hai-Feng Ji. "Anisotropic and Isotropic Shrinking of Candle Droplets in Cold Water and Warm Water." Micro 2, no. 3 (August 29, 2022): 508–12. http://dx.doi.org/10.3390/micro2030032.

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The effects of temperature and surfactant on the shape of candle droplets that solidify at air-water interfaces were investigated. In pure water, triangular or quadrangular shaped candle droplets were formed when the temperature was ≤6 °C and round shape droplets were observed when the temperature was ≥10 °C. In SDS/water solutions ≥ 0.5 mM, oval or concave bowl-shaped candle droplets were formed when the temperature was ≤6 °C and round shape droplets were observed when the temperature was ≥10 °C. The formation mechanisms of the different shapes were explored and discussed.

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Sakya, Pranay Ratna, Rinky Nyachhyon, Amita Pradhan, Ratina Tamrakar, and Sudeep Acharya. "MORPHOLOGY OF CONDYLE- A RADIOGRAPHIC STUDY." Journal of Chitwan Medical College 12, no. 1 (March 15, 2022): 17–20. http://dx.doi.org/10.54530/jcmc.636.

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Background: Mandibular condyle has a variety of morphology. The changes in their shape and size has been attributed to ageing process, developmental abnormalities, distinct diseases, trauma, endocrine shock, radio therapy etc. Panoramic radiographs remain the easiest, safest and most cost-effective screening modality for temporomandibular joint abnormalities. The study aimed to assess the different shapes of condyles using orthopantomograms from the archives of the hospital data. The variations among the sexes and between the right and left sides of an individual were also determined. Methods: This retrospective study was conducted at People’s Dental College and Hospital within the time period of 1 year (November 2019- November 2020). Orthopantomogram of patients falling within the inclusion criteria were studied. The different shapes of condylar process were traced using marker pencil for both right and left sides. Data collected was entered in Microsoft Office Excel sheet 2013-- and calculated in SPSS version 24 and analyzed using descriptive statistics. Results: Out of the 874 mandibular condyles of 437 patients, the most common was the oval shaped in both the right (275) and the left sides (277), followed by bird beak, diamond, flat and crooked finger respectively. The oval shaped condyle appeared to be predominant in both sexes. The flat shaped and diamond shaped condyle appeared to be a rarity. Conclusions: The most common shape of condyle was found to be oval shape bilaterally and in both genders. Least observed shapes of condyle were flat shape in female patients and diamond shape in male patients.

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Bender-Heine, Adam, Michelle Russell, Allen Rickards, J. Holmes, Mark Armeni, H. Lambert, and Matthew Zdilla. "Optimal Costal Cartilage Graft Selection According to Cartilage Shape: Anatomical Considerations for Rhinoplasty." Facial Plastic Surgery 33, no. 06 (December 2017): 670–74. http://dx.doi.org/10.1055/s-0037-1607972.

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AbstractCostal cartilage grafting is a commonly used reconstruction procedure, particularly in rhinoplasty. Although costal cartilage is broadly used in reconstructive surgery, there are differing opinions regarding which costal cartilage levels provide the most ideal grafts. Grafts are typically designed to match the shape of the recipient site. The shapes of costal cartilage grafts have been described as “boat-shaped,” “C-shaped,” “canoe-shaped,” “U-shaped,” “crescent-shaped,” “L-shaped,” “semilunar,” “straight,” and “Y-shaped.” The shapes of costal cartilages are thought to lend themselves to the shapes of certain grafts; however, there has been little study of the shapes of costal cartilages, and most reports have been anecdotal. Therefore, this study is aimed to detail the average shapes of the most commonly grafted cartilages (i.e., the fifth to seventh cartilages). A total of 96 cadaveric costal cartilages were analyzed through geometric morphometric analysis. The fifth costal cartilage was determined to have the straightest shape and would therefore be particularly suitable for nasal dorsum onlay grafting. The lateral portions of the sixth and, particularly, the seventh costal cartilages have the most acute curvature. Therefore, they would lend themselves to the construction of an en bloc “L”-shaped or hockey stick-shaped nasal dorsum-columellar strut graft.

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Maimun, Adi, Mehdi Nakisa, Ahmad Tarmizi, Yasser M. Ahmed, and Fatemeh Behrouzi. "Numerical Study on Hydrodynamic Resistance of New Hull Design for Multipurpose Amphibious Vehicle." Applied Mechanics and Materials 663 (October 2014): 522–31. http://dx.doi.org/10.4028/www.scientific.net/amm.663.522.

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MultipurposeAmphibiousVehicles(MAV)and other blunt-shaped floating vehicles encounter the problem of a large bow wave forming at high speeds. This wave formation is accompanied by higher resistance and at a critical speed results in bow submergence or swamping. Three new shapes of hull bow design for the multipurpose amphibious vehicle were conducted at several speeds to investigate the hydrodynamic phenomena using Computational Fluid Dynamics (CFD, RANS code) which is applied by Ansys-CFX14.0 and Maxsurf. The vehicle’s hydrodynamic bow shapes were able to break up induced waves and avoid swamping. Comparative results with the vehicle fitted with U-shape, V-shape and Flat-shape of hull bow, showed that the U-shape of the hull bow has reduced the total resistance to 20.3% and 13.6% compared with the V-shape and flat shape respectively. Though, the U-shape of hull bow is capable to increase the amphibious operating life and speed of vehicle. Also it has ability to reduce the vehicle’s required power, fossil fuel consumption and wetted hull surface.

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Lee, Sang-ik, Jin-Yong Choi, and Won Choi. "Effect of Groove Shape on Head Loss and Filtration Performance of Disc Filters." Water 13, no. 12 (June 17, 2021): 1683. http://dx.doi.org/10.3390/w13121683.

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To analyze the effect of a groove cross-sectional shape on disc filters, a head loss analysis and filtration performance test were conducted using disc filters with different groove shapes (semi-elliptical- and trapezoidal-shaped grooves). Furthermore, the groove shapes were analyzed using field emission scanning electron microscopy and the relationship between flow rate and head loss was derived from the head loss test. Even if the filters were designed with the same mesh standard, the sectional areas of the grooves were different depending on the shape. Therefore, the head loss was compared under the condition that the grooves have the same sectional area by applying the relationship between head loss and sectional area, and a smaller head loss was observed in the semi-elliptical-shaped groove. Additionally, the semi-elliptical-groove-shaped disc filter was evaluated to sufficiently filter the soil particles corresponding to the 120 mesh standard. Therefore, an optimum disc filter can be designed by considering the cross-sectional shape of the disc groove to reduce energy consumption and provide stable filtration. The elliptical groove shape, which is hydraulically advantageous, is preferred for the disc filter design.

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Drushel, R. F., D. M. Neustadter, L. L. Shallenberger, P. E. Crago, and H. J. Chiel. "The kinematics of swallowing in the buccal mass of Aplysia californica." Journal of Experimental Biology 200, no. 4 (February 1, 1997): 735–52. http://dx.doi.org/10.1242/jeb.200.4.735.

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Changes in the positions, shapes and movements of the feeding apparatus (buccal mass) of the marine mollusc Aplysia californica were studied in intact, transilluminated juveniles. The buccal mass assumes characteristic shapes as its internal structure, the radula/odontophore, moves anteriorly (protracts) or posteriorly (retracts). These shapes are especially distinctive when the radula/odontophore has protracted forwards fully, is close to its resting or neutral position, or has retracted backwards fully. We refer to the shapes that occur at full protraction, transition and full retraction as shape 1 (spherical), shape 2 (ovoid) and shape 3 (gamma-shaped), respectively. We introduce this shape nomenclature in order to avoid confusion with the existing terms protraction and retraction, which we reserve exclusively to describe the direction of movement of the radula/odontophore. The observed shape changes do not agree with those predicted on the basis of in vitro observations of a feeding head preparation, but are similar to shapes observed in vitro in the snail Lymnaea stagnalis. The buccal mass also rotates approximately 10 degrees dorsally during retraction, pivoting on the attachment to the mouth, before the subsequent protraction and return of the buccal mass to the transition shape. This rotation may be due to activation of the extrinsic muscles of the buccal mass. Plots of the buccal mass shape parameters eccentricity versus ellipticity create a two-dimensional shape space, which accurately quantifies the subtle transitions of shape between the different phases of the feeding cycle. Quantitative differences are observed between pure swallows and swallows with tearing behavior, but the qualitative shapes are similar. Hysteresis in the shape space plots of most swallows provides evidence for the hypothesis that protraction and retraction each have distinct 'active' and 'return' phases. The observed kinematic pattern imposes constraints on the internal structures of the buccal mass and may be used to infer the shape and positions of the radula and odontophore.

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Yu, Siyu, Lindred L. Greer, Nir Halevy, and Lisanne van Bunderen. "On Ladders and Pyramids: Hierarchy’s Shape Determines Relationships and Performance in Groups." Personality and Social Psychology Bulletin 45, no. 12 (April 22, 2019): 1717–33. http://dx.doi.org/10.1177/0146167219842867.

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Hierarchies take different forms, which individuals mentally represent using different geometric shapes. We propose and empirically demonstrate that individuals’ mental representations of the shape hierarchy takes affect its consequences. Five studies compared two common mental representations of hierarchy shapes—ladders and pyramids—to explore whether, why, and how individuals’ perceptions of hierarchy’s shape undermine constructive relationships within groups and group performance. Study 1 demonstrated that individuals commonly mentally represent hierarchies as ladders and pyramids. In Studies 2 and 3, employees who perceived their workplace hierarchies to be shaped like ladders (as compared with pyramids) experienced worse intragroup relationships. Finally, Studies 4 and 5 experimentally manipulated groups’ hierarchical shape in the lab and found that ladder-shaped hierarchies undermined social relationships and group performance relative to pyramid-shaped hierarchies. Taken together, these findings enhance our understanding of hierarchies’ multifaceted consequences and help shed light on the (dis)utility of hierarchy for group functioning.

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Koconis, David B., Låszló P. Kollår, and George S. Springer. "Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified." Journal of Composite Materials 28, no. 5 (March 1994): 459–82. http://dx.doi.org/10.1177/002199839402800504.

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The changes in shapes of fiber-reinforced composite beams, plates and shells affected by embedded piezoelectric actuators were investigated. An analytical method was developed to determine the voltages needed to achieve a specified desired shape. The method is formulated on the basis of mathematical models using two-dimensional, linear, shallow shell theory including transverse shear effects which are important in the case of sandwich construction. The solution technique is a minimization of an error function which is a measure of the difference between the deformed shape caused by the application of voltages and the desired shape. A computationally efficient, user-friendly computer code was written which is suitable for performing the numerical calculations. The code, designated as SHAPE2, gives the voltages needed to achieve specified changes in shape. To validate the method and the computer code, results generated by the code were compared to existing analytical and experimental results. The predictions provided by the SHAPE2 code were in excellent agreement with the results of the other analyses and data.

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Kumar, Raj. "Variations in the shape of foramen magnum at the base of human skulls among Indians in Rajasthan." Bioinformation 18, no. 5 (May 31, 2022): 488–91. http://dx.doi.org/10.6026/97320630018488.

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Variations in the shape of foramen magnum can affect the normal anatomy of vital structures passing through it. Therefore, it is of interest to evaluate the various shapes of foramen magnum by using CT scans performed in patients of Indian population to establish clinical correlation. A total of 314 CT images of human skull base obtained from the Department of Radio-diagnosis, Geetanjali Medical College and Hospital, Udaipur, Rajasthan were used in the present study. All the patients’ CT scans were observed to determine the shape of foramen magnum. They were classified into one of the following shapes: Oval, round, tetragonal, egg shaped, hexagonal, pentagonal and irregular. The shapes of the foramen magnum in CT scans were oval in 39.09%, round in 22.61%, tetragonal in 12.10%, hexagonal in 10.51%, irregular in 7.96%, pentagonal in 5.41% and egg shaped in 1.59% CT images. Data shows that it is easy to operate at the base of skull in case of round, oval and hexagonal shape foramen magnum, as the working space is more in these shapes.

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Covantev, Serghei, Rasul Uzdenov, Daria Turovets, and Olga Belic. "Spleen: an organ of multiple shapes." Iberoamerican Journal of Medicine 3, no. 4 (October 5, 2021): 326–31. http://dx.doi.org/10.53986/ibjm.2021.0052.

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Introduction: The spleen is located in the upper part of the abdominal cavity. As an organ, the spleen can have various shapes and size. Material and methods: The human spleen was studied in 273 cadavers (154 men and 119 women) who did not have diseases of the spleen. The shape of the spleen was analyzed based on splenic index, Michels classification. Results: The most common shape of the spleen in men is the elongated one. It was encountered in 79 (51.3%) cases out of 154. In women, the most common shape was the intermediate. It was encountered in 51 (42.9%) of the 119 cases. Based on Michels classification the clinoid (wedge) shape was encountered in 102 (37.74%) cases, triangular in 59 (21.83%) and tetrahedral in 30 (11.1%). In 30.26% the shape of the spleen couldn’t be classified according to Michels classification. In 21 cases (7.77%) the spleen had a flat shape; in 27 (9.99%) – dome-shaped; in 1 case (0,37%) – Z-shape; in 18 (6.66%) – round shape; in 6 (2.22%) – irregular shape; in 2 (0.66%) - shape with a node in the hilum; in 1 (0,37%) – rhomboid shape, in 2 (0,74%) – bilobed shape and in 4 cases (1,48%) – lobular shape. The splenic fissures located on the upper edge of the organ were found in 81 (29.91%) cases, and also on the lower edge - in 41 (14.02%) cases. In 13 (4.67%) cases fissures were encountered on both sides. In 148 (51.4%) cases the spleen had no fissures on its surface. Conclusions: The spleen has various shapes beyond the classical wedge, triangular and tetrahedral. All of these shapes do not represent a pathological finding but in certain situation may require further analysis and interpretation depending on the imaging technique and experience of the physician.

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LES, ZBIGNIEW. "SHAPE UNDERSTANDING: POSSIBLE CLASSES OF SHAPES." International Journal of Shape Modeling 07, no. 01 (June 2001): 75–109. http://dx.doi.org/10.1142/s0218654301000060.

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Yifeng Jiang, Jun Xie, and Hung-Tat Tsui. "Shape Registration by Optimally Coding Shapes." IEEE Transactions on Information Technology in Biomedicine 12, no. 5 (September 2008): 627–35. http://dx.doi.org/10.1109/titb.2008.920798.

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Horst, Kenneth E. "The shape of lamp shade shadows." Physics Teacher 39, no. 3 (March 2001): 139–40. http://dx.doi.org/10.1119/1.1364055.

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Jowers, Iestyn, Chris Earl, and George Stiny. "Shapes, structures and shape grammar implementation." Computer-Aided Design 111 (June 2019): 80–92. http://dx.doi.org/10.1016/j.cad.2019.02.001.

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Azis, Andy, Alchalil Alchalil, Adi Setiawan, and Nurul Islami. "STUDI EKSPERIMENTAL WIND TUNNEL TIPE SUBSONIC RANGKAIAN TERBUKA DENGAN VARIASI BENTUK HONYECOMB." Malikussaleh Journal of Mechanical Science and Technology 7, no. 2 (October 28, 2023): 105. http://dx.doi.org/10.29103/mjmst.v7i2.13491.

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Honeycomb is applied to the Open Series Subsonic Wind Tunnel which aims to obtain a unidirectional fluid flow shape with uniform (laminar) and stable fluid flow velocities. Honeycomb testing was carried out experimentally at a flow velocity of 3 m / s without honeycomb using a variety of shapes: hexagonal, square, and circular. Each honeycomb shaped to 8mm diameter. The results of the analysis on honeycomb testing with variations in shape obtained the value of turbulence intensity that occurs in the test section, namely for hexagonal shape variations the flow that occurs is better than circular shape, while in circular shape variations the value of turbulence intensity is better than square shape. The results of the Reynold's number calculation show that the flow that occurs is laminar with the following values, in the hexagonal shape variation the value is 787, circular shape 956.48, and square shape 1199.42. After calculating the turbulence intensity and Reynold's number, we can conclude that honeycomb with hexagonal shape variation is optimal than circular shape, and circular is optimal than square.

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Kang, Sung Koo, Inhee Choi, Jeongjin Lee, Younghun Kim, and Jongheop Yi. "Observation on Growth Process of Gold Y- and -shaped Nanoparticles in Solutions." Journal of Nanoscience and Nanotechnology 7, no. 11 (November 1, 2007): 3823–26. http://dx.doi.org/10.1166/jnn.2007.039.

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The morphological evolution of gold (Au) nanoparticles is demonstrated via TEM and UV-vis spectroscopy in a real-time basis. Y-shaped and -shaped Au nanoparticles were prepared by a seed mediated method at 0 °C. The evolution of shape ranging from spheres to Y- and -shapes was characterized by UV-vis spectroscopy. For the spherical particles, the corresponding transverse plasmon absorption (540 nm) was observed at the initial growth stage. As further growth proceeded, new peaks appeared at ca. 620 nm and ca. 700–1000 nm, which was to the characteristic peak of Y-shaped and -shaped nanoparticles, respectively. In addition, all intermediate steps were observed in the morphology change by TEM. At the initial step, spherical particles with 20 nm size were generated and the particles were gradually evolved from tiny triangular shape or I-shape to Y- and -shape. In this study, the growth mechanism of Au nanoparticles was investigated by the characterization of optical properties as well as morphologies with respect to reaction time.

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Milenkovic, Jovana, Milica Vasiljevic, Nemanja Jovicic, Dragan Milovanovic, Dragica Selakovic, and Gvozden Rosic. "Criteria for the Classification of the Interradicular Septum Shape in Maxillary Molars with Clinical Importance for Prosthetic-Driven Immediate Implant Placement." Diagnostics 12, no. 6 (June 10, 2022): 1432. http://dx.doi.org/10.3390/diagnostics12061432.

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The aim of this study was to use cone-beam computed tomography (CBCT) to evaluate the morphometric properties of the interradicular septum (IRS) in the maxillary molar region that may be indicative for prosthetic-driven implant placement. Following the repetitive algorithm based on the visual identification of IRS shapes, we described the following IRS shapes: arrow, boat, drop, and palatal and buccal convergence. The incidence of IRS shapes showed significant differences for the first and second maxillary molars (the highest frequency for the arrow shape, and the lowest for the drop shape) with no significant difference between the molars. The most prominent width indicative for implant placement was observed in the palatal convergence shape, whereas the height criteria were the most satisfying in the buccal convergence-shaped IRS for both molars. Apart from the parameters in the coronal view, the image analysis in the axial view revealed that IRS surface area, required for the implant placement, was the most prominent in the palatal convergence shape for the first, and boat shape for the second molars. Our results showed the benefits of CBCT diagnostics in posterior maxilla morphometric analysis. IRS shape classification may be helpful in achieving more rapid and accurate planning for interventions in this region.

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Velasco, Carlos, Andy T. Woods, Lawrence E. Marks, Adrian David Cheok, and Charles Spence. "The semantic basis of taste-shape associations." PeerJ 4 (February 4, 2016): e1644. http://dx.doi.org/10.7717/peerj.1644.

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Previous research shows that people systematically match tastes with shapes. Here, we assess the extent to which matched taste and shape stimuli share a common semantic space and whether semantically congruent versus incongruent taste/shape associations can influence the speed with which people respond to both shapes and taste words. In Experiment 1, semantic differentiation was used to assess the semantic space of both taste words and shapes. The results suggest a common semantic space containing two principal components (seemingly, intensity and hedonics) and two principal clusters, one including round shapes and the taste word “sweet,” and the other including angular shapes and the taste words “salty,” “sour,” and “bitter.” The former cluster appears more positively-valenced whilst less potent than the latter. In Experiment 2, two speeded classification tasks assessed whether congruent versus incongruent mappings of stimuli and responses (e.g., sweet with round versus sweet with angular) would influence the speed of participants’ responding, to both shapes and taste words. The results revealed an overall effect of congruence with congruent trials yielding faster responses than their incongruent counterparts. These results are consistent with previous evidence suggesting a close relation (or crossmodal correspondence) between tastes and shape curvature that may derive from common semantic coding, perhaps along the intensity and hedonic dimensions.

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MUHAMAD, ZULKIFLI, CHIK AIMAN, ZAHID BILAL, and YAHYA MOHAMAD. "Effects of impactors’ shape on three-dimensional woven fabric composites at low-velocity impacts." Industria Textila 73, no. 06 (December 20, 2022): 621–26. http://dx.doi.org/10.35530/it.073.06.202193.

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This study investigated the fabric resistance of three-dimensional (3D) woven fibreglass composites generated by impactors of three shapes, i.e., hemispherical, conical, and ogival, on four types of composite structures. Composites were fabricated using the hand lay-up technique. Crimp and mechanical impact resistance tests were carried out in accordance with ASTM D2444 standards and ASTM D3883-04, respectively. The four-floating interlocked (4FLL) yielded the strongest fabric damage tolerance for all the three types of impactors’ shapes with 6.3 kN for the hemispherical shape, 4 kN for the conically shaped, and 3.8 kN for the ogival shape. Additionally, the 4FLL generated a fabric crimp of 3.5% and 2.8% on both fabric directions. The post-impact damage showed that the ogival shape impactor penetrated samples of woven composites better than the conical and hemispherical shapes.

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Ohrn-McDaniel, Linda. "Shape creating shape." International Journal of Fashion Design, Technology and Education 6, no. 2 (July 2013): 82–88. http://dx.doi.org/10.1080/17543266.2013.793743.

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Su, Yuchen, Zhineng Chen, Zhiwen Shao, Yuning Du, Zhilong Ji, Jinfeng Bai, Yong Zhou, and Yu-Gang Jiang. "LRANet: Towards Accurate and Efficient Scene Text Detection with Low-Rank Approximation Network." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 5 (March 24, 2024): 4979–87. http://dx.doi.org/10.1609/aaai.v38i5.28302.

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Recently, regression-based methods, which predict parameterized text shapes for text localization, have gained popularity in scene text detection. However, the existing parameterized text shape methods still have limitations in modeling arbitrary-shaped texts due to ignoring the utilization of text-specific shape information. Moreover, the time consumption of the entire pipeline has been largely overlooked, leading to a suboptimal overall inference speed. To address these issues, we first propose a novel parameterized text shape method based on low-rank approximation. Unlike other shape representation methods that employ data-irrelevant parameterization, our approach utilizes singular value decomposition and reconstructs the text shape using a few eigenvectors learned from labeled text contours. By exploring the shape correlation among different text contours, our method achieves consistency, compactness, simplicity, and robustness in shape representation. Next, we propose a dual assignment scheme for speed acceleration. It adopts a sparse assignment branch to accelerate the inference speed, and meanwhile, provides ample supervised signals for training through a dense assignment branch. Building upon these designs, we implement an accurate and efficient arbitrary-shaped text detector named LRANet. Extensive experiments are conducted on several challenging benchmarks, demonstrating the superior accuracy and efficiency of LRANet compared to state-of-the-art methods. Code is available at: https://github.com/ychensu/LRANet.git

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Ho, Ching Yen, and Yu Hsiang Tsai. "Shape of Fusion Zone for the Welding Keyhole Induced by an Electron Beam." Materials Science Forum 773-774 (November 2013): 812–17. http://dx.doi.org/10.4028/www.scientific.net/msf.773-774.812.

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In this paper analytical predictions of the fusion zone shapes around the welding cavity produced by a moving electron beam are provided. A three-dimensional analytical model in the molten and heat-affected regions surrounding a paraboloid of revolution-shaped cavity is used to predict the shapes of the fusion zones. This work avoids the defect of the infinite temperature at the cavity base for the line-source model. Introducing a new image method, a new analytical solution is provided by satisfying exactly the adiabatic condition at the top surface. The shape of a fusion zone is governed by dimensionless parameters related to beam power per unit penetration, and the depth and shape of the cavity in this work. A three-dimensional shape of fusion zone is computed and presented in this paper. The effect of beam power per unit penetration on the shape of fusion is also discussed.

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Attard, Marie R. G., Emma Sherratt, Paul McDonald, Iain Young, Marta Vidal-García, and Stephen Wroe. "A new, three-dimensional geometric morphometric approach to assess egg shape." PeerJ 6 (June 27, 2018): e5052. http://dx.doi.org/10.7717/peerj.5052.

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This paper proposes a new methodology to quantify patterns of egg shape variation using geometric morphometrics of three-dimensional landmarks captured on digitally reconstructed eggshells and demonstrates its performance in capturing shape variation at multiple biological levels. This methodology offers unique benefits to complement established linear measurement or two-dimensional (2D) contour profiling techniques by (i) providing a more precise representation of eggshell curvature by accounting for variation across the entire surface of the egg; (ii) avoids the occurrence of correlations from combining multiple egg shape features; (iii) avoids error stemming from projecting a highly-curved three-dimensional (3D) object into 2D space; and (iv) enables integration into 3D workflows such as finite elements analysis. To demonstrate, we quantify patterns of egg shape variation and estimate morphological disparity at multiple biological levels, within and between clutches and among species of four passerine species of different lineages, using volumetric dataset obtained from micro computed tomography. The results indicate that species broadly have differently shaped eggs, but with extensive within-species variation so that all four-focal species occupy a range of shapes. Within-species variation is attributed to between-clutch differences in egg shape; within-clutch variation is surprisingly substantial. Recent comparative analyses that aim to explain shape variation among avian taxa have largely ignored potential biases due to within-species variation, or use methods limited to a narrow range of egg shapes. Through our approach, we suggest that there is appreciable variation in egg shape across clutches and that this variation needs to be accounted for in future research. The approach developed in this study to assess variation in shape is freely accessible and can be applied to any spherical-to-conical shaped object, including eggs of non-avian dinosaurs and reptiles through to other extant taxa such as poultry.

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Anilkumar, P. M., A. Haldar, S. Scheffler, B. N. Rao, and R. Rolfes. "Numerical Studies on the Design of Self-Resetting Active Bistable Cross-Shaped Structure for Morphing Applications." Proceedings 64, no. 1 (November 20, 2020): 16. http://dx.doi.org/10.3390/iecat2020-08482.

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Multistable structures that possess more than one elastically stable equilibrium state are highly attractive for advanced shape-changing (morphing) applications due to the nominal control effort required to maintain the structure in any of its specific stable shapes. The aim of the paper is to develop a bistable cross-shaped structure consisting of symmetric and unsymmetric laminate actuated using Macro Fibre Composite (MFC) actuators. The critical snap-through voltages required to change the shapes are investigated in a commercially available finite element package. The use of MFC actuators to snap the bistable laminate from one equilibrium shape to another and back again (self-resetting) is demonstrated. A new cross-shaped design of active bistable laminate with MFC actuators is proposed where the cross-shape consist of four rectangles on the four legs and a square on the middle portion. All the rectangles are made up of unsymmetric laminates, and the central portion is designed with a symmetric laminate. MFC actuators are bonded on both sides of the four legs to trigger snap-through and snap-back actions. An attempt is made to address the possible design difficulties arising from the additional stiffness contribution by MFC layers on the naturally cured equilibrium shapes of cross-shaped bistable laminates.

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Micheas, Athanasios C., and Dipak K. Dey. "Assessing shape differences in populations of shapes using the complex watson shape distribution." Journal of Applied Statistics 32, no. 2 (March 2005): 105–16. http://dx.doi.org/10.1080/02664760500054137.

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Shim, H. B., and K. C. Son. "Optimal Blank Design for the Drawings of Arbitrary Shapes by the Sensitivity Method." Journal of Engineering Materials and Technology 123, no. 4 (July 24, 2000): 468–75. http://dx.doi.org/10.1115/1.1398082.

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The sensitivity method is employed in this work in order to find initial blank shapes which result in desired shapes after deformation. By assuming the final deformation shape be the drawn cup with uniform trimming allowance at the flange, the corresponding initial blank which gives the desired final shape after deformation has been found. With the aid of a well-known dynamic explicit analysis code PAM-STAMP, shape sensitivity has been obtained. To get the shape sensitivity numerically, a couple of deformation processes have been analyzed. Drawings of trapezoidal cup, oil pan, and Audi front door panel, the benchmark test problem of Numisheet ’99, have been chosen as the examples. In every case the optimal blank shape has been obtained after only a few modifications without a predetermined deformation path. With the predicted optimal blank, both computer simulation and experiment are performed. Excellent agreements are obtained between simulation and experiment in every case. Through this investigation, the sensitivity method is found to be very effective in the design of arbitrary shaped drawing processes.

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Wach, Johannes, Johannes Naegeli, Martin Vychopen, Clemens Seidel, Alonso Barrantes-Freer, Ronny Grunert, Erdem Güresir, and Felix Arlt. "Impact of Shape Irregularity in Medial Sphenoid Wing Meningiomas on Postoperative Cranial Nerve Functioning, Proliferation, and Progression-Free Survival." Cancers 15, no. 12 (June 7, 2023): 3096. http://dx.doi.org/10.3390/cancers15123096.

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Medial sphenoid wing meningiomas (MSWM) are surgically challenging skull base tumors. Irregular tumor shapes are thought to be linked to histopathology. The present study aims to investigate the impact of tumor shape on postoperative functioning, progression-free survival, and neuropathology. This monocentric study included 74 patients who underwent surgery for primary sporadic MSWM (WHO grades 1 and 2) between 2010 and 2021. Furthermore, a systematic review of the literature regarding meningioma shape and the MIB-1 index was performed. Irregular MSWM shapes were identified in 31 patients (41.9%). Multivariable analysis revealed that irregular shape was associated with postoperative cranial nerve deficits (OR: 5.75, 95% CI: 1.15–28.63, p = 0.033). In multivariable Cox regression analysis, irregular MSWM shape was independently associated with tumor progression (HR:8.0, 95% CI: 1.04–62.10, p = 0.046). Multivariable regression analysis showed that irregular shape is independently associated with an increased MIB-1 index (OR: 7.59, 95% CI: 2.04–28.25, p = 0.003). A systematic review of the literature and pooled data analysis, including the present study, showed that irregularly shaped meningiomas had an increase of 1.98 (95% CI: 1.38–2.59, p < 0.001) in the MIB-1 index. Irregular MSWM shape is independently associated with an increased risk of postoperative cranial nerve deficits and a shortened time to tumor progression. Irregular MSWM shapes might be caused by highly proliferative tumors.

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Kumar, Pramod, Santanu Dwari, Shailendra Singh, Ashok Kumar, N. K. Agrawal, and Utkarsh Kumar. "Analysis and Optimization of Conformal Patch Excited Wideband DRA of Several Shapes." Frequenz 72, no. 5-6 (April 25, 2018): 197–208. http://dx.doi.org/10.1515/freq-2017-0039.

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AbstractIn this paper various shapes of DR antennas excited by common feed have been proposed and successfully implemented for wideband applications. Proposed structures are Hemispherical, Arrow-shaped and Triangular DRA, while common excited feed is inverted trapezoidal conformal patch. These shapes of DR offer significant optimization in several parameters such as impedance bandwidth, peak gain and bandwidth per unit volume of the antenna. By using inverted trapezoidal patch feed mechanism an impedance bandwidth (VSWR<2) of about 63 % for hemispherical shape, 66 % for arrow shape, and 72 % for triangular shape DRA has been achieved with maximum bandwidth per unit volume. Proposed wideband DRAs i. e. triangular, hemispherical, and arrow shapes of DR antennas cover almost complete C-band (4 GHz–8 GHz) frequency spectrum of microwave. The average peak gain within the operating band for hemispherical, arrow, and triangular shape DRA are about 5, 5.4, and 5.5 dB respectively. A comparative analysis of proposed structures for various antenna parameters has been analyzed by HFSS (High-Frequency Structure Simulator) and validated by experimental results.

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Hogendorn, Christiaan. "Niche Networks for New Entrants." Transportation Research Record: Journal of the Transportation Research Board 1567, no. 1 (January 1997): 17–25. http://dx.doi.org/10.3141/1567-03.

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How new entrant carriers may use returns to airline networks in competition is discussed. In addition to overall returns to scope and density, there are more localized returns that are based on network shape. A network shape index, which is a measure of airline network concentration based on the Herfindahl-Hirschman index, is described. Airlines have chosen many different shapes as measured by the network shape index, and new entrants tend to be shaped differently from major airlines. A model of new entrant profitability relative to the major airlines is developed. New entrants whose network shape indices are substantially different from the major airlines have niche networks, and the model indicates that niche networks are associated with higher profitability.

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Morishige, Koichi, Shingo Ishizuka, and Yoshimi Takeuchi. "Development of Tool Fabrication CAD/CAM for Conicoid End Mill." International Journal of Automation Technology 1, no. 2 (November 5, 2007): 128–35. http://dx.doi.org/10.20965/ijat.2007.p0128.

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This study deals with new practical fabrication of end mills based on 3D-CAD/CAM. End mills with arbitrary shapes generally difficult to produce are useful in upgrading machining accuracy and efficiency. Our tool fabrication CAD/CAM potentially produces end mills with arbitrarily shaped cutting edge. In order to make them practical, we developed a way to design the cutting edge shape and NC data generation for a 5-axis controlled tool grinding machine. The resulting system enables produces practical, arbitrarily shaped end mills with shape precision comparable to their commercially available counterparts.

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Zubkov, V. V. "Shape Formation of Stereometric Dome Shells." International Journal of Space Structures 7, no. 1 (March 1992): 39–60. http://dx.doi.org/10.1177/026635119200700104.

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Theoretical fundamentals of shape formation of stereometrical dome shells are revealed in this article. The genesis of shapes of shells consisting of plane elements of regular configuration in the form of truncated parts of regular polyhedrons is also considered. Principles of geometric formation of shell shapeil structures are touched upon and a brief description of each of them is given from the point of view of possible unification of shape forming elements. The author develops a methodology for designing stereometrical dome-shaped shells on the basis of regular crystals. He also describes methods of geometric calculation of stereometrical dome-shaped shells. Some methods of construction of shell surfaces and various kinds of compositions derived from them are demonstrated. Brief data on the peculiarities of material utilisation of stereometrical dome shells and some examples of their application in architecture are given.

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Bennett, David J. "Seeing Shape: Shape Appearances and Shape Constancy." British Journal for the Philosophy of Science 63, no. 3 (September 1, 2012): 487–518. http://dx.doi.org/10.1093/bjps/axr018.

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Raval, P. B., A. M. Butala, and N. S. Mehta. "Behavior study of precast pier of bridge for its various shape." IOP Conference Series: Earth and Environmental Science 1326, no. 1 (June 1, 2024): 012012. http://dx.doi.org/10.1088/1755-1315/1326/1/012012.

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Abstract This study presents the analysis and design of precast pier as per Indian standard codes. The analysis and design of pier is carried out by considering various loads as per Indian standers and IRC codes. The design of precast pier is carried out using the STAAD. Pro software. To study the effect of water pressure on precast pier various shapes of pier are considered like rectangular, circular, pier with triangular cut, pier with arch. The comparison of dis-placement, stresses, strength, and stiffness of different shapes are analysed to evaluate the behaviour of pier. The design of connection of the precast pier is done using IRC codal provisions. Looking to the results precast pier with circular shape is most suitable shape than other considered shape by having more stiffness in each direction, but to resist stresses the rectangle shaped with arc is good choice. And the displacement of pier having rectangular shape is less compared to circular pier.

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Xia, Fengfei, and Shanqing Li. "R-Function and variation method for bending problem of clamped thin plate with complex shape." Advances in Mechanical Engineering 13, no. 7 (July 2021): 168781402110348. http://dx.doi.org/10.1177/16878140211034832.

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Solving ordinary thin plate bending problem in engineering, only a few analytical solutions with simple boundary shapes have been proposed. When using numerical methods (e.g. the variational method) to solve the problem, the trial functions can be found only it exhibits a simple boundary shape. The R-functions can be applied to solve the problem with complex boundary shapes. In the paper, the R-function theory is combined with the variational method to study the thin plate bending problem with the complex boundary shape. The paper employs the R-function theory to express the complex area as the implicit function, so it is easily to build the trial function of the complex shape thin plate, which satisfies with the complex boundary conditions. The variational principle and the R-function theory are introduced, and the variational equation of thin plate bending problem is derived. The feasibility and correctness of this method are verified by five numerical examples of rectangular, I-shaped, T-shaped, U-shaped, and L-shaped thin plates, and the results of this method are compared with that of other literatures and ANSYS finite element method (FEM). The results of the method show a good agreement with the calculation results of literatures and FEM.

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Du, Shigui, Yunjin Hu, and Xiaofei Hu. "Generalized Models for Rock Joint Surface Shapes." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/171873.

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Generalized models of joint surface shapes are the foundation for mechanism studies on the mechanical effects of rock joint surface shapes. Based on extensive field investigations of rock joint surface shapes, generalized models for three level shapes named macroscopic outline, surface undulating shape, and microcosmic roughness were established through statistical analyses of 20,078 rock joint surface profiles. The relative amplitude of profile curves was used as a borderline for the division of different level shapes. The study results show that the macroscopic outline has three basic features such as planar, arc-shaped, and stepped; the surface undulating shape has three basic features such as planar, undulating, and stepped; and the microcosmic roughness has two basic features such as smooth and rough.

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KRSTIC, DJORDJE. "Shape decompositions and their algebras." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 19, no. 4 (November 2005): 261–76. http://dx.doi.org/10.1017/s0890060405050183.

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Shapes play an important role in many human activities, but are rarely seen in their natural form as raw and unanalyzed. Rather, shapes come analyzed, structured in terms of their certain parts, forming shape decompositions. Different kinds of shape decompositions are developed, the most interesting among which are the decompositions that could be used as shape approximations. Two kinds of such decompositions, discrete and bounded, are examined in greater detail. Computations with shapes conducted in the framework of shape grammars and related shape algebras have been standard for over 3 decades. Similar computations are possible with analyzed shapes or shape decompositions. Different algebras to compute with shape decompositions are developed and compared to the shape algebras. The measure of their agreement determines how well the shapes are approximated by their decompositions.

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Journal articles on the topic 'Shape'

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