Initial Shape Research Articles

Bursting oscillation of simply supported fluid-conveying pipes

ABSTRACT The main purpose of this article is to explore an originality multiple-frequency bursting of simply-supported fluid-conveying pipes with initial micro-bending shape under different low-frequency excitation conditions. Based on the Galerkin's method and the fast-slow dynamics analysis method, rich vibration phenomena are observed with different excitation conditions, and the multi-valued characteristics are verified by the domain of attraction. The results demonstrate that low-frequency excitation can cause complex dynamical phenomena of the fluid-conveying pipes.

4D printing of recoverable buckling-induced architected iron-based shape memory alloys

Architected materials exhibit extraordinary properties in comparison with conventional materials and structures, resulting in additional functionality and efficiency by engineering the geometry in harmony with the base material. Buckling-induced architected materials (BIAMs) are a class of architected materials that exhibit a significant potential to absorb and dissipate energy owing to their local instabilities. Previous studies have shown a trade-off between energy dissipation and geometrical recoverability in metallic BIAM, which limits their use in applications that require both of these features. This study, for the first time, presents 4D printing of buckling-induced architected iron-based shape memory alloys (BIA Fe-SMAs) using laser powder bed fusion (LPBF). The results show that 4D printing of BIA Fe-SMAs can offer both energy dissipation and geometrical recoverability (i.e., recentring). The study was conducted on two different alloy compositions of Fe-17Mn-5Si-10Cr-4Ni. Quasi-static cyclic tests were performed on the two BIA Fe-SMAs, and the samples were subsequently heated to 200 °C to activate the shape memory effect (SME) of the base material. The samples could recover the residual deformations accumulated during the cyclic load owing to the SME of the base material, which led to shape-recovery ratios of 96.8 and 98.7% for the studied BIA Fe-SMAs. The results of this study demonstrate that 4D printing of BIA Fe-SMAs can yield an enhanced multi-functional behavior by combining the material's inherent functional behavior with the functionalities of the architected structure. Notably, BIA Fe-SMA samples could reconfigure their initial shape without damage after densification, which sets them apart from conventional crushable lattices.

Analysis and tests of non-uniform wrapping process of tape spring

A tape spring, which has a high ratio of retraction and deployment, is a type of basic deployable member that plays an important role in deployable structures. This paper is focused on the non-uniform wrapping process of a tape spring that the fixed end section preserves the initial shape. A theoretical method is presented to predict the non-uniform wrapping process of a metallic tape spring based on classical theories about the bending behavior of this type of tape spring. There are two possible shapes for a tape spring after the non-uniform wrapping process, namely a polygon or a continuous curve. The boundary lines of the two possible shapes are studied, and it is shown that the shape depends on the radius of the central cylindrical hub. A finite element model is built using the commercial software ABAQUS to verify the reliability of the theoretical model. Experimental measurement is also conducted to record the shape change process of a tape spring. The comparisons of the results of the three different methods show that they are in good agreement with each other, which means that the theoretical model can be used to predict the non-uniform wrapping behavior of the tape spring. Additionally, the behavior of four tape springs during the non-uniform wrapping process is studied, and the results show that the shapes of multiple tape springs in a coiled state correspond to that of a single tape spring.

What long-period comets tell us about the Oort Cloud

Context. The Oort Cloud is located in the farthest outskirts of the Solar System, extending to a heliocentric distance of several tens of thousands of au, and remains the last region of the Solar System where no object has been detected. Thus, all our knowledge of the Oort Cloud has been deduced from the observed long-period comets that are thought to originate from it. Aims. We aimed to retrieve valuable information that might be hidden in the orbital distributions of the observed long-period comets. Such information will allow us to impose constraints not only on the present shape of the Oort Cloud but also on its initial shape 4.5 Gyr ago. This has direct implications for the scenario proposed for its formation. Methods. We used two different databases of long-period comets. First, we calculated the distribution of orbital elements that might carry valuable information about the shape of the Oort Cloud. Then, we compared the distribution with that obtained from two synthetic samples of observable comets. These samples correspond to two considerably different initial configurations: one is a disk model, where we consider a swarm of comets with orbits aligned to the ecliptic plane and with a cometary perihelion close to the giant planets. The other is an isotropic model, where we consider a fully isotropic and thermalized initial distribution of comets. Results. The comparison revealed that the databases contained several features that were in better agreement with the disk model than with the isotropic model. The Oort Cloud contained an initial disk of objects with perihelia close to the planetary region of the Solar System and aphelia extending out to roughly 20 000 au. Some parts of this disk likely remain in the present Solar System. However, the fit to the disk model is poor. The discrepancy between the observational and synthetic results indicates that some dynamical processes in the current Oort Cloud were not included in either model. Conclusions. This initial shape of the Oort Cloud implies that planetary scattering was crucial during its formation. In addition, the fact that some dynamical features are still detec table 4.5 Gyr after the cloud formation imposes constraints on the role of exosolar effects, such as giant molecular clouds, Galactic tides, and the stellar cluster surrounding the Solar System at the time of its formation.

Positive effects of Pycnogenol®-Centellicum® on venous elasticity: an ex-vivo concept study.

The aim of this ex-vivo study was to evaluate the efficacy of Pycnogenol®-Centellicum® oral supplementation on vein segments, retrieved from graft harvesting or from vein surgery. The parameters assessed were elasticity and recovery after dynamic tests: 1) an enlargement stress; 2) an elongation stress; and 3) elasticity after torsion. The tests were made in standardized conditions, less than 3 hours after explant, at 22 °C by the same operator with surgical and microsurgical experience. Veins of 59 subjects were included in the study: 17 subjects with normal veins with a planned bypass graft and 42 subjects with varicose veins. Of the subjects with normal veins, 8 subjects followed standard management (group 1) and 9 took Pycnogenol®-Centellicum® for 4 weeks before surgery (group 2). In the group with varicose veins, 22 subjects served as controls (group 3) and 20 were supplemented with Pycnogenol®-Centellicum® for 4 weeks before surgery (group 4). No side effects or tolerability problems were observed in the supplementation period before surgery and veins harvesting. The full return to initial shape/sizes after dynamic stress was evaluated in 1 min after removing the stress. In group 1, 4 out of 8 vein segments recovered their size after forced enlargement vs. 7/9 in the Pycnogenol®-Centellicum® group 2 (P<0.05). In the elongation test, 3/8 normal control vein segments recovered their length (group 1) vs. 7/9 in the supplement group (group 2) (P<0.05). In the torsion test, 4/8 (group 1) veins recovered their shape after torsion vs. 9/9 veins in Pycnogenol®-Centellicum®-pretreated segments (group 2) (P<0.05). Only 45.8% of normal, control vein segments (group 1) recovered their shape/size in comparison with 85.2% of normal vein segments in the supplement group (group 2) (P<0.05). In group 3 and 4 (segments of varicose veins), the proportion of vein segments with enlargements, elongation and torsion were significantly lower at the end of the test (P<0.05) in the Pycnogenol®-Centellicum® group 4 with 51.7% of the vein segments recovering their shape in the Pycnogenol®-Centellicum® vs. 16.6% of the vein segments recovering their shape in control segments (P<0.05). Results show that Pycnogenol®-Centellicum® supplementation allows vein segments to better return to their original shape/size after a morphological alteration of shape (in different directions). This could be an expression of an improved wall tone and elasticity of the veins. No vein was teared or damaged during the 59 tests indicating that all stresses were well within the normal wall tensile characteristics of the veins. In this study, Pycnogenol®-Centellicum® improved vein elasticity in subjects with normal and varicose veins as vein segments were more elastic (able to recover length and shape) and less passively dilated by high pressure or dynamic stresses. This study indicates that the protective effects of Pycnogenol®-Centellicum® may partially stop passive dilatation of veins to varicose veins over time by improving vein elasticity. Pycnogenol®-Centellicum® managed vein segments return more rapidly back to the initial dimensions, shapes and diameters after a dynamic stress.

Topology optimization of rib patterns for a freeform composite structure

This paper presents an algorithm for the design of efficient and stable composite freeform shell structures. The design workflow combines form-finding, structural analysis, and optimization techniques. To illustrate it, the paper provides a case study of the design and optimization of carbon fiber-reinforced polymer shell. After form-finding of the the initial structural shape, topology optimization was conducted to develop the reinforcing rib pattern to increase its buckling resistance. The use of optimized rib layouts greatly increased the rigidity of the shell, which was confirmed by finite element simulations.[copyright information to be updated in production process]

Topology Optimization Using a Normalized Gaussian Network of Iron Yoke for Magnetic Field Design of an Accelerator Superconducting Magnet

Field quality in the order of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-4}$</tex-math></inline-formula> is required for a superconducting dipole magnet to keep the beam stable in an accelerator. An iron yoke usually is employed to enhance the magnetic field and reduce the fringe field. As the superconducting magnet provides a field that is higher than 2 T, the field quality is distorted by the saturation effect of the iron yoke during the beam acceleration. Field tuning holes are adopted to the iron yoke to adjust the magnetic flux so as to keep the field error variation flat in the region from the injection field to the top field. It is time costly in terms of computing to determine the initial shape and search for the best solution that satisfies design requirements. This paper presents a topology optimization method using a non-dominated sorting genetic algorithm for the iron yoke design of an accelerator superconducting magnet. The shape of the iron yoke is represented by using the normalized Gaussian network to achieve smoothness of the material distribution. This method is applied to a superconducting bending magnet for a compact heavy-ion synchrotron in which the field errors are required to be lower than 2.5 unit and 3.5 unit at the point of injection field and the top field, respectively. As a result, a smooth shape of the iron yoke is obtained by this method; both field error at the top field and the field error variation are mitigated by the method.

Development and evaluation of a bulk three-moment parameterization scheme incorporating the processes of sedimentation and collision-coalescence

There are a few three-moment schemes that consider other processes besides sedimentation. Thus, a performance assessment of these types of schemes due to the combined effect of sedimentation and other microphysical processes is a matter of interest. In this study, a warm rain bulk three-moment parameterized scheme was developed and evaluated through a detailed comparison with a bin microphysical scheme. To evaluate the impact of sedimentation and the combined effect of sedimentation and collision-coalescence on the droplet size distribution (DSD), a rain shaft model was applied to the DSD with different initial values of the shape parameter. For pure sedimentation, a good correspondence was obtained between the three-moment scheme and the explicit model, with a practically perfect coincidence of bulk quantities for larger values of the gamma distribution’s initial shape parameter and, in general, the three-moment parameterization scheme performing much better than the two-moment scheme. The simulations performed for this case confirm (as reported in previous studies) that for pure sedimentation, the three-moment parameterization schemes deliver a physically more complete representation of the evolution of droplet size distribution. The impact of the combined effect of sedimentation and collision-coalescence processes on DSD was also assessed. We could observe that certain differences arise between the parameterized scheme and the spectral model when the collision-coalescence process is incorporated, as the onset of precipitation occurs earlier in the three-moment parameterized scheme. It can be concluded that, in general, the three-moment warm rain bulk microphysics scheme is able to reproduce the results of the reference bin microphysical model.

Analysis and prestress optimisation of membrane structures with optimal fabric alignment using modified energy minimisation

The use of light-weight tensile membrane structures (TMS) has become popular, particularly for covering vast areas. The behaviour of these structures when subjected to external actions is dependent on the initial shape, prestress and material property. The load analysis and optimisation of TMS are still challenging due to different factors including membrane wrinkling, choice of material fibre orientation and practical design considerations. This paper formulates the load analysis process by defining a modified energy functional with respect to the material fibre basis direction. The energy functional is directly minimised using a quasi-Newton solver addressing convergence issues. Improved algorithms to find the wrinkling criteria and direction are proposed. The choice of the material fibre direction and optimal seam partitioning based on the principal curvature are also developed. A practical optimisation framework for TMS is formulated based on available guidelines. The integrated methodology is successfully tested and demonstrated on a wide variety of case studies and benchmark problems. The optimal material fibre basis provides a stiffer (hence, more stable) structure and reduces the induced shear. The integrated solution along with the optimisation framework provide the end user with an effective method and tool for the design of TMS.

The Physics of Electric Saroj Veena: A Folk Musical Instrument from India's North Eastern Region

Saroj Veena is known as a famous Folk musical Instrument in the North eastern part of India. We will discuss about the Shape and Size, Structure, body mechanism of Saroj Veena. In our lab studies, we look at the harmonic structure of standing waves in Saroj Veena strings. Using a digital oscilloscope with a Fast Fourier transform and a magnetic pickup from a Saroj Veena, the experimental data was gathered. Depending on where the string is plucked, the harmonic amplitudes in the measured signal vary, giving the sound a distinct timbre. The relative amplitudes of transverse standing waves in a string were determined from experimental data and predicted by the wave equation when the boundary and beginning circumstances matched the initial shape of the string.

Innovative Materials with Possible Applications in the Wound Dressings Field: Alginate-Based Films with Moringa oleifera Extract.

For a long time, biopolymers have proven their effectiveness in the development of materials with various applications, lately those intended for the biomedical and pharmaceutical industries, due to their high biocompatibility and non-toxic, non-allergenic, and non-immunogenic nature. The ability to incorporate various active substances in this matrix has yielded materials with characteristics that are far superior to those of classic, conventional ones. The beneficial effects of consuming Moringa oleifera have promoted the use of this plant, from Ayurvedic to classical medicine. The addition of such compounds in the materials intended for the treatment of surface wounds may represent the future of the development of innovative dressings. This study followed the development of materials based on sodium alginate and moringa powder or essential oil for use as dressings, pads, or sheets. Thus, three materials with the addition of 10-30% moringa powder and three materials with the addition of 10-30% essential oil were obtained. The data were compared with those of the control sample, with sodium alginate and plasticizer. The microtopography indicated that the materials have a homogeneous matrix that allows them to incorporate and maintain natural compounds with prolonged release. For example, the sample with 30% moringa essential oil kept its initial shape and did not disintegrate, although the swelling ratio value reached 4800% after 20 min. After testing the mechanical properties, the same sample had the best tensile strength (TS = 0.248 MPa) and elongation (31.41%), which is important for the flexibility of the dressing. The same sample exhibited a very high antioxidant capacity (60.78% inhibition). The materials obtained with moringa powder added presented good values of physical and mechanical properties, which supports their use as wound dressings for short-term application and the release of embedded compounds. According to the obtained results, all the biopolymeric materials with moringa added can be used as dressings for different wound types.

Effect of initial morphology on particle growth in an undercooled melt

The effect of initial morphology on particle growth in an undercooled melt is studied in terms of an analytical approach. The growth of the particle is formulated as a dynamics model for the particle with different initial morphologies of concave and convex deformations. By using the asymptotic method, we solve the asymptotic solution of the dynamics model of the particle. The asymptotic solution reveals the effect of convexity and concavity of the initial shapes of the non-spherical particle on the temperature, concentration, and growth rate of the particle in an undercooled melt. The interface temperature in the concave part of the interface becomes higher than that in the convex part. The solutes are enriched near the concave part of the interface more than near the convex part of the interface. Compared with the convex part of the interface, the local undercooling and solute enrichment in the concave part of the interface facilitate the particle growth. The convexity of the particle depresses the particle growth, and the concavity of the particle promotes the particle growth. As the particle grows, the effect of initial morphology of non-spherical particles on particle growth attenuates, and the non-spherical particle tends to evolve into a spherical particle.

Recent trends in thermo‐responsive elastomeric shape memory polymer nanocomposites

AbstractShape memory polymers (SMPs) are polymeric smart materials, a class of stimuli‐responsive polymers that can return to their initial shape from a programmed temporary shape under the application of external stimuli, such as light, heat, magnetism, and electricity. Because of these unique features, SMPs can find applications in many fields, like aerospace, biomedical devices, flexible electronics, soft robotics, shape memory arrays, and 4D printing. The comparatively low density, low cost, easy biodegradability, and biocompatibility make SMPs a better candidate for shape memory applications. Among them, thermo‐responsive SMPs can revert to their permanent shape depending on a temperature greater than their polymer transition temperature. Thermo‐responsive SMPs combine semi‐crystalline or elastomeric polymers with improved mechanical and electrical properties. Integrating nanofillers into the polymer elastomer matrices can further enhance these properties, forming shape‐memory polymer nanocomposites (SMPNCs). This review focuses on the basics, design, and classifications of thermo‐responsive SMPs and the characteristics of elastomers and blends of polymers used. Incorporating various nanofillers to get SMPNCs to have improved properties over SMPs is also presented. The importance of Tg (glass transition temperature) and Tm (melting temperature) based SMPs and SMPNCs, various elastomers used, and the methods for preparation like solution casting, melt compounding, in situ polymerization, and their possible future applications are also discussed.

ВІДНОВЛЕННЯ ШТОКІВ СИЛОВИХ ГІДРОЦИЛІНДРІВ АВТОМОБІЛІВ ЛЕКТРОЛІТИЧНИМ ХРОМУВАННЯМ

The quality of the repair of parts of military equipment and the increase of their service life largely depends on how it is organized and in what ways the restoration of malfunctioning or damaged parts is carried out. To restore the full functionality of the damaged parts, it is necessary to return them to their initial dimensions, geometric shape, hardness, corrosion resistance and other properties. One of the progressive methods of restoring the working rods of hydraulic cylinders is the application of electrolytic coatings on their working surface. The purpose of the study is to improve the method of restoration of hydraulic cylinder rods by electrolytic chroming with the aim of intensifying the process, improving operational properties and obtaining electrolytic chromium deposits of uniform thickness on the restored rods. The scientific and practical direction of the work consists in the fact that for the first time the technology of process intensification, improvement of the quality of coatings and obtaining of electrolytic chromium deposits uniform in length with the use of an ejector anode design has been considered. The research methodology is to identify the influence of the chrome plating process parameters on the uniformity, microhardness and microcracking of chrome coatings made of universal (250 г/л – СrO3; 2,5 г/л – H2SO4) та кріолітового (10 г/л – Na3AlF6; 250 г/л – СrO3; 2,5 г/л – H2SO4) of electrolytes by the ejector method. The results of the study are the establishment of the dependence of uniformity, microhardness and microcracking on the parameters of the ejector chromium plating process in standard and cryolite electrolytes and the determination of the optimal temperature and current density for use in restoring the rods of hydraulic cylinders of military equipment. The value of the conducted research is that for the first time an ejector anode is used as a positive electrode, which ensures obtaining high-quality and uniform electrolytic coatings directly in the chrome plating bath. Anode-ejector provides height-adjustable suspension suction of gaseous products of electrolysis and renewal of electrolyte in the interelectrode space due to the ejector effect in the anode tubes when the electrolyte is passed under pressure in the jet tubes. Keywords: stom density, anode-cathode distance, uniformity, cracking, microhardness, electrolyte temperature, anode-ejector.

Harnessing chiral buckling structure to design tunable local resonance metamaterial for low-frequency vibration isolation

This paper proposes a tunable local resonance metamaterial with chiral buckling structures for low-frequency vibration isolation. The unit cell consists of the inner and outer buckling stiffness structure, basic structure, and local resonator. The bistability of three kinds of unit cells with different initial shapes of beams is investigated and compared via the elliptic integral method and finite element analysis. Then, their axial stiffness in different states is studied. The dynamic responses of the metamaterial with simple unit cells and hybrid supercells are theoretically derived and analyzed by Bloch's theorem and transfer coefficient method. Theoretical, numerical, and experimental results demonstrate that the unit cell with initially convex downward beams has strong bistability and determinate deformation modes. The axial stiffness of the unit cell in two stable states differs by an order of magnitude. Changing some specific parameters broadens the gap in the axial stiffness between the two stable states. The axial negative stiffness characteristics and rotation effect of the unit cell have the potential for energy dissipation and tensile-torsion material. The metamaterial with simple unit cells has tunable and wide band gap and low-frequency vibration isolation via the stable states switching of the inner and outer buckling stiffness structures. The metamaterial with hybrid supercells can further broaden the band gap width and lower the band gap frequency, which has up to 16 different band gap characteristics.

Initial shape reconstruction of a volcanic island as a tool for quantifying long-term coastal erosion: the case of Corvo Island (Azores)

Abstract. Long-term coastal erosion is not yet well studied given that it is difficult to quantify. The quantification of long-term coastal erosion requires reconstruction of the coast's initial geometry and the determination of where and when the erosion started. Volcanic islands fulfill these two conditions: their initial shape is roughly conical and the age of the lavas that generated this geometry is easily measured. We have developed a method to reconstruct the initial shape of simple volcanic edifices from aerial and submarine topographic data. The reconstructed initial shape and associated uncertainties allow us to spatially quantify the coastal erosion since the building of the island. This method is applied to Corvo Island in the Azores archipelago. We calculated that, due to coastal erosion, the island has lost a volume of 6.5 ± 2.7 km3 and roughly 80 % of its surface area since it first came into being. Taking the large uncertainty in the age of the topmost lava flows (0.43 ± 0.34 Myr) into account, we have estimated that Corvo Island has lost an average of 5000 to 100 000 m3 yr−1 of its volume due to coastal erosion. Lastly, we show a strong correlation between long-term coastal erosion and the spatial distribution of the waves. Specifically, we highlight a stronger control on erosion by smaller and more frequent waves than by storm waves. The next step will be to apply this method to other volcanic islands in order to (i) streamline and improve the method and (ii) verify the correlations observed in the present study.

Surface generating mechanism in surface shape error control for thin copper plate with large-diameter based on chemical mechanical lapping

As metal plane flyer, pure copper thin plate is required with extremely low surface shape error. To achieve this goal, some researchers make a significant attempt to develop a deterministic full-aperture polishing/lapping process. However, the detail relationship of surface shape error and vital machining parameter such as machining time which benefits machining efficiency promotion is not given. Besides, the error rate of surface shape error prediction is high. To solve this problem, the surface shape prediction model considering the influence of pressure and relative velocity distribution on material removal amount is established for thin copper plate. Through the product of pressure distribution, relative velocity distribution, Preston coefficient k and machining time T, material removal distribution is obtained. According to initial surface shape characteristic, through targeted adjustment of eccentricity, lapping pad rotation speed, workpiece rotation speed to control pressure and relative velocity distribution, suitable material removal distribution is formed to smooth surface radial profile, realizing deterministic control of surface shape error. By above method, the flatness of pure copper thin plate (Φ200 mm × 2.2 mm) decreases from PV 54.8 μm to PV 1.9 μm with mean error rate of surface shape error prediction <10 %, realizing deterministic control of surface shape error.

A reinforcement learning approach to airfoil shape optimization

Shape optimization is an indispensable step in any aerodynamic design. However, the inherent complexity and non-linearity associated with fluid mechanics as well as the high-dimensional design space intrinsic to such problems make airfoil shape optimization a challenging task. Current approaches relying on gradient-based or gradient-free optimizers are data-inefficient in that they do not leverage accumulated knowledge, and are computationally expensive when integrating Computational Fluid Dynamics (CFD) simulation tools. Supervised learning approaches have addressed these limitations but are constrained by user-provided data. Reinforcement learning (RL) provides a data-driven approach bearing generative capabilities. We formulate the airfoil design as a Markov decision process (MDP) and investigate a Deep Reinforcement Learning (DRL) approach to airfoil shape optimization. A custom RL environment is developed allowing the agent to successively modify the shape of an initially provided 2D airfoil and to observe the associated changes in aerodynamic metrics such as lift-to-drag (L/D), lift coefficient (Cl) and drag coefficient (Cd). The learning abilities of the DRL agent are demonstrated through various experiments in which the agent’s objective-maximizing L/D, maximizing Cl or minimizing Cd-as well as the initial airfoil shape are varied. Results show that the DRL agent is able to generate high performing airfoils within a limited number of learning iterations. The strong resemblance between the artificially produced shapes and those found in the literature highlights the rationality of the decision-making policy learned by the agent. Overall, the presented approach demonstrates the relevance of DRL to airfoil shape optimization and brings forward a successful application of DRL to a physics-based aerodynamics problem.

Extensional flow of a free film of nematic liquid crystal with moderate elasticity

The human tear film is a multilayer structure in which the dynamics are often strongly affected by a floating lipid layer. That layer has liquid crystalline characteristics and plays important roles in the health of the tear film. Previous models have treated the lipid layer as a Newtonian fluid in extensional flow. Motivated to develop a more realistic treatment, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to the rheology. We rescale a weakly elastic model due to Cummings et al. [“Extensional flow of nematic liquid crystal with an applied electric field,” Eur. J. Appl. Math. 25, 397–423 (2014).] to describe a lipid layer of moderate elasticity. The resulting system of two nonlinear partial differential equations for sheet thickness and axial velocity is fourth order in space, but still represents a significant reduction of the full system. We analyze solutions arising from several different boundary conditions, motivated by the underlying application, with particular focus on dynamics and underlying mechanisms under stretching. We solve the system numerically, via collocation with either finite difference or Chebyshev spectral discretization in space, together with implicit time stepping. At early times, depending on the initial film shape, pressure either aids or opposes extensional flow, which changes the free surface dynamics of the sheet and can lead to patterns reminiscent of those observed in tear films. We contrast this finding with the cases of weak elasticity and Newtonian flow, where the sheet retains the same qualitative shape throughout time.

Application of power algorithm optimization for optimal placement of BRB in 3D shear wall frame building structure

This paper examines the optimal placement, optimal numbers, and the optimal shape of Buckling Restrained Braces (BRB) for a 3D shear-wall frame building structure based on linear static analysis utilizing ETABS software. The total amount of BRBs referred to as the number of BRBs are considered as design variables and the objective function to be minimized is the maximum story displacement and inter-story drift. The diagonal shape (D), X-shape (X), V-shape (V), and Inverted V-shape (Inv-V) of BRBs are installed between shear walls simultaneously with initial stiffnesses of 1K0, 2K0, 4K0, and 8K0, respectively. Then, the performance efficiency analysis is carried out to identify the effectiveness of initial stiffness, BRB shapes, and optimal stories. Based on the results of the optimization procedure and efficiency analysis, it is found that the performance of the structure can be improved by optimizing BRB placement within the optimal stories rather than using the maximum amount of BRBs in all stories. The most optimal location to install BRBs is the middle stories and the BRB placement at the upper and lower stories is shown to have minor or no effects on reducing story responses of the structure. Furthermore, the model with Inv-V, V, and X shapes of BRB have almost the same maximum efficiency performance, while the model with diagonal shapes has the lowest performance efficiency. Additionally, the maximum performance of the structure can be achieved by using larger initial stiffness. The proposed method is further validated by comparing the results of ETABS with MATLAB programming. It concludes that the method proposed in this study saves 40% of the total amount of BRBs used in the structure by optimal placement of BRBs within the height of the structure. This method of optimization allows the structural designer to decide the optimal placement, optimal shape, and optimal stiffness of BRBs either by the predetermined performance level of the structure or based on experiences in RC shear wall-frame building structures.