Hybrid Shape Research Articles

Traversable wormhole models in modified theories of gravity

In this paper, we explore traversable wormhole solutions in different cases of modified [Formula: see text] theories of gravity. We have taken the functional form [Formula: see text], where [Formula: see text] is Ricci scalar and [Formula: see text] is the trace of energy momentum tensor, while [Formula: see text] and [Formula: see text] are constants. The different forms of [Formula: see text]-gravity in [Formula: see text], [Formula: see text] frameworks and [Formula: see text] gravity are analyzed with its geometric behavior. The energy conditions are also discussed in the isotropic scenario using EoS [Formula: see text] and hybrid shape function [Formula: see text], where [Formula: see text] is the throat radius. In this investigation, we found that quadratic geometric term and linear trace term of [Formula: see text] gravity and hybrid shape function play a significant contribution to validate the energy conditions for nonexotic wormhole solutions.

Processing of hybrid shape memory alloy coupled with P(VDF-TrFE) piezoelectric polymer composite for energy harvesting application

Small-scale energy harvesting to power self-powered electronic devices is tremendously increasing. In this context, the ability to combine thermal and mechanical energy harvesting using smart materials deserves more attention for further study. We have presented the feasibility of using P(VDF-TrFE) piezoelectric polymer coupled with NiTi shape memory alloy (SMA) to harvest both mechanical and thermal energy in simple scalable devices. A novel hybrid composite consisting of SMA, and P(VDF-TrFE) has been developed without any complex composites or patterned structures, which couples the piezoelectric effect of the poly(vinylidene fluoride-co-trifluoroethylene) (P(VDF-TrFE)) and the shape memory effects of NiTi SMA. We have also fabricated a multi-layer SMA/PEN/P(VDF-TrFE) device using epoxy as an interface and bonding layer. During bending, the P(VDF-TrFE) device with an active area of 3.68 cm2 generated an output voltage of 8 V and an output power of 6.25 µW. When coupled with NiTi SMA to create a hybrid composite thermoelectric material, the device can convert the phase change associated with SMA, and thus thermal energy is converted to mechanical energy and finally into electrical energy. The SMA/P(VDF-TrFE) hybrid composite produced an output voltage of ∼2 V for one cyclic heating and cooling of the device. This is a promising approach for the further development of coupled hybrid energy harvester devices for the powering of small-scale electronic devices such as sensors, MEMS, or biomedical devices.

Hybrid Shape Optimization of Automotive Spring Seat

Hybrid Shape Optimization of Automotive Spring Seat

A hybrid shape memory polymer filled metallic foam composite: shape restoring, strain sensing, Joule heating, strengthening, and toughening

In this paper, an open-cell metallic foam was filled in by a tough shape memory polymer (SMP), to form a hybrid metal/polymer composite with multifunctionalities and enhanced mechanical properties. This work aims to study the positive composite actions between the metallic skeleton and the SMP filler. Mechanical, thermal, and conductive properties of the resulting hybrid composite were evaluated and compared to the individual components. Uniaxial compression tests and shape memory effect tests were conducted. Results demonstrated an improvement in the compressive strength and toughness. The hybrid composite also exhibited excellent shape recovery and high recovery stress of 1.76 MPa. Infrared thermography has been used to verify the free shape recovery by Joule heating. Sandwich structures with the hybrid composite as the core were studied through low velocity impact test and three-point bending test. The sandwich structures with the composite foam core showed significant performance improvement in both tests. Electrical resistivity study during the three-point bending test validates the possible application of this multifunctional polymer-aluminum open cell foam composite as strain sensor. This type of hybrid composites can be beneficial in many industrial sectors that search for an ideal combination of high strength, high toughness, low weight, damage sensing, and excellent energy absorption capabilities.

Stochastic vibration and buckling analysis of functionally graded microplates with a unified higher-order shear deformation theory

Based on equations of the elasticity, this paper proposes a unified higher-order shear deformation theory for stochastic vibration and buckling analysis of the functionally graded (FG) microplates. The governing equations of motions are derived from Hamilton’s principle. The solutions are approximated by bi-directional series in which hybrid shape functions are proposed, then the stiffness and mass matrix are explicitly derived. In order to investigate the stochastic responses of the FG microplates, the polynomial chaos expansion (PCE) is used. The multiple uncertain material properties are randomly changed via the lognormal distributions. Numerical results are presented for different configurations of the FG microplates such as the power-law index, material length scale parameter, length-to-thickness ratio and boundary conditions on their critical buckling loads and natural frequencies. The results from PCE are evaluated by comparing with those from Monte Carlo simulation to show the efficiency and accuracy of the present approach. Some new results for stochastic analysis of the FG microplates are presented and can be used for future references.

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams is proposed in this paper. It is based on a unified nonlinear variation of shear strains in the wall thickness and then theoretical formulation is derived in the general form which can recover the previous conventional theories such as classical and first-order thin-walled beam theory. Series-type solutions with hybrid shape functions are developed for different boundary conditions. Numerical examples are performed on laminated thin-walled composite I-beams with arbitrary lay-ups. Effects of transverse shear strains, fiber angles and slenderness ratio on the critical buckling loads and natural frequencies of the beams are reported.

Shape Matters in Magnetic-Field-Assisted Assembly of Prolate Colloids.

An anisotropic colloidal shape in combination with an externally tunable interaction potential results in a plethora of self-assembled structures with potential applications toward the fabrication of smart materials. Here we present our investigation on the influence of an external magnetic field on the self-assembly of hematite-silica core–shell prolate colloids for two aspect ratios ρ = 2.9 and 3.69. Our study shows a rather counterintuitive but interesting phenomenon, where prolate colloids self-assemble into oblate liquid crystalline (LC) phases. With increasing concentration, particles with smaller ρ reveal a sequence of LC phases involving para-nematic, nematic, smectic, and oriented glass phases. The occurrence of a smectic phase for colloidal ellipsoids has been neither predicted nor reported before. Quantitative shape analysis of the particles together with extensive computer simulations indicate that in addition to ρ, a subtle deviation from the ideal ellipsoidal shape dictates the formation of this unusual sequence of field-induced structures. Particles with ρ = 2.9 exhibit a hybrid shape containing features from both spherocylinders and ellipsoids, which make their self-assembly behavior richer than that observed for either of the “pure” shapes. The shape of the particles with higher ρ matches closely with the ideal ellipsoids, as a result their phase behavior follows the one expected for a “pure” ellipsoidal shape. Using anisotropic building blocks and external fields, our study demonstrates the ramifications of the subtle changes in the particle shape on the field-directed self-assembled structures with externally tunable properties.

Controlling Resonator Nonlinearities and Modes through Geometry Optimization.

Controlling the nonlinearities of MEMS resonators is critical for their successful implementation in a wide range of sensing, signal conditioning, and filtering applications. Here, we utilize a passive technique based on geometry optimization to control the nonlinearities and the dynamical response of MEMS resonators. Also, we explored active technique i.e., tuning the axial stress of the resonator. To achieve this, we propose a new hybrid shape combining a straight and initially curved microbeam. The Galerkin method is employed to solve the beam equation and study the effect of the different design parameters on the ratios of the frequencies and the nonlinearities of the structure. We show by adequately selecting the parameters of the structure; we can realize systems with strong quadratic or cubic effective nonlinearities. Also, we investigate the resonator shape effect on symmetry breaking and study different linear coupling phenomena: crossing, veering, and mode hybridization. We demonstrate the possibility of tuning the frequencies of the different modes of vibrations to achieve commensurate ratios necessary for activating internal resonance. The proposed method is simple in principle, easy to fabricate, and offers a wide range of controllability on the sensor nonlinearities and response.

Design, validation, and application of a hybrid shape memory alloy-magnetorheological fluid-based core bracing system under tension and compression

Civil infrastructures are vulnerable to catastrophic failures when exceeding the limit loading, requiring a reliable structural control mechanism, such as bracing systems, to enhance the integrity and stability of the structure. Bracing systems improve the performance of the structures by increasing the stiffness/strength of structures, the damping coefficient, and/or the energy absorption capacity. However, the functionality of these bracing systems is not controllable and may be altered after strong seismic events. Recently, the smart bracing systems based on multifunctional materials, particularly the shape memory alloy (SMA) and the magnetorheological fluid (MRF) have been developed. The superelasticity properties of SMA give the capability of recovering the original state after remarkable deformation. Furthermore, the SMA dissipates the energy of the applied load in the loading-unloading mechanism. The viscosity of MRF is variable and depends on the intensity of the applied magnetic fields. In the present study, a state-of-art hybrid SMA-MRF-based core bracing system is designed and in-house fabricated to enhance the structural behavior of the bracing system, including energy dissipation capacity and equivalent damping coefficient. Experimental tests have been conducted to illustrate the functionality of the system and the benefits of the SMA and the MRF systems. Finally, the seismic performance of the three-, six- and nine-story buildings equipped with the proposed SMA-MRF damping system is numerically assessed using nonlinear response history analyses. The results reveal that the proposed damping system significantly improves the seismic performance of the archetype buildings.

Thermodynamic and viscoelastic constitutive model of TPI/HDPE hybrid shape memory polymer

In recent years, shape memory smart materials have developed rapidly, and more and more novel shape memory polymers have been developed and applied. In sharp contrast to the rapid development of shape memory smart materials, its theoretical research is obviously lagging behind. Therefore, it is necessary to clearly understand and master the thermodynamic dynamic response mechanism of shape memory polymers. In view of the fact that the influence of thermodynamic properties of hybrid shape memory polymer under the coupling effect of multiple factors is still very vague, a novel hybrid shape memory polymer composites (SMPC) thermodynamic viscoelastic constitutive model is proposed for the first time by combining the macroscopic phenomenological viscoelastic theory with the microscopic phenomenological phase transition model, and a microstructure composed of two parts of reversible phase and stationary phase in parallel is constructed. At the same time, a three-dimensional parameter equation with temperature effect and capable of describing the coordinated changes of various parameters in the phase transition process is established. Through the validation of the model, it can be found that the variation trend of the simulation curve is in good agreement with the experimental curve during the whole static loading process, and the error of the fracture stress is less than 2%. Through the dynamic evolution of multi-content and wide-temperature range, the consistency between the simulation results and the experimental results is successfully proved, and the microscopic mechanism of the macroscopic static mechanical behavior of the hybrid SMPC is revealed. The model established in this paper can accurately describe the internal phase change of the mixed matrix, and realize the effective prediction of the stress-strain response under the coupling effect of the matrix composition and the external environment. The proposal of this model provides a new idea for the exploration of hybrid SMPC thermodynamic viscoelastic theory, and also provides an important theoretical reference for the development and application of novel hybrid shape memory materials in the future.

Modelling of mid-rise concrete shear walls reinforced with superelastic shape memory alloys: Nonlinear analysis

The response of hybrid Shape Memory Alloy (SMA)-steel reinforced concrete shear walls containing Nickel-Titanium superelastic SMA as alternative reinforcement in the plastic hinge region was investigated using nonlinear finite element modelling. The hybrid wall system promotes self-centering and significant reduction of permanent deformations. Two types of conventional steel-reinforced concrete shear walls were designed for a prototype 10-storey office building according to the current Canadian concrete design standard, assuming two distinct seismic design scenarios. A moderately ductile shear wall was designed for a moderate seismic zone in eastern Canada, whereas a ductile shear wall was designed for a high seismic zone in western Canada. Equivalent, hybrid SMA-steel reinforced concrete shear walls were defined following the design of the two conventional shear walls, in terms of geometry and reinforcement layout. Full-scale, two-dimensional finite element models were developed to assess the pushover and hysteretic responses of the walls. Similarities in wall cross-section and yield force capacity of the steel and SMA reinforcement permitted a comparison between the walls, including strength, stiffness, self-centering, and energy dissipation capacities. The results indicate similar lateral strength and displacement capacities, and superior restoring capacity of the SMA-reinforced walls in comparison to the steel-reinforced walls. Furthermore, a preliminary study was conducted to investigate the effect of the SMA-bar length in the ductile wall due to concentration of damage near the base of the wall. Lengths corresponding to approximately 50% and 20% of the original SMA length were considered. Based on the analyses, a satisfactory response could be achieved with shorter SMA reinforcing bars, which reduces the quantity of SMA reinforcement without significant loss in self-centering capacity.

Augmentation of low frequency damping via hydrogen-doping in a hybrid shape memory alloy composite

Carbon fiber reinforced polymer (CFRP) composites hybridized with hydrogen-doped NiTi wires can be used to design structures requiring high stiffness and high damping in the low frequency range, such as helicopter blades. The current work investigates aging and hydrogen-doping for high damping without hydrogen embrittlement. We establish a hydrogenation treatment that (i) results in a response that is repeatable in the martensitic phase and after exposure to composite processing temperatures and (ii) increases the loss factor in NiTi wires by nearly 470%. By embedding H-doped wires exhibiting the highest damping into the interlayers of a [0/±45]s carbon/epoxy laminate at a volume fraction of 0.1, the hybrid NiTi-CFRP composite loss factor increases by 170%. The measured dynamic properties were found to be close to micromechanical predictions based on the properties of the NiTi and CFRP.

Oblong formaten en liedboeken in de zestiende eeuw

Abstract This article examines the earliest example of a Dutch printed songbook without musical notation in oblong format: Een Schoon Liedekensboeck (Antwerp, 1544), commonly known as the Antwerp Songbook. Its oblong format was probably inspired by music books, even if the advantages attached to this format only partially applied to songbooks without scores and notes. Even so, the Antwerp Songbook’s typography and lay-out do facilitate performance of the songs to some degree. Additionally, unlike contemporary books in oblong, this songbook’s title page is rotated 90 degrees to portrait orientation. This article contends that this hybrid shape underlines the book’s hybrid function: it was a music book intended for those who cannot or have no inclination to read music. Similarly, Een devoot ende profitelijck boecxken (Antwerp, 1539) stands out for having a comparable hybrid shape: it combines elements of music books (such as notes and the oblong format) with elements of vernacular song tradition and a title page in portrait orientation.

Morris–Thorne wormholes in modified f(R, T) gravity

Wormhole solutions obtained by Morris and Thorne (MT) in general relativity (GR) is investigated in a modified theory of gravity. In the gravitational action, we consider f(R, T) which is a function of the Ricci scalar (R) and the trace of the energy-momentum tensor (T). In the framework of a modified gravity described by $$f(R,T)=R+\alpha R^{2}+\lambda T^{\beta }$$ , where $$\alpha $$ , $$\beta $$ and $$\lambda $$ are coupling constants, MT wormhole (WH) solutions with normal matter are obtained for a relevant shape function. We have considered two different values of $$\beta $$ leading to two forms of f(R, T)-gravity. The energy conditions are probed at the throat and away from the throat of the WH. It is found that the coupling parameters, $$\alpha $$ and $$\lambda $$ in the gravitational action play an important role in deciding the matter composition in the wormholes. It is found that for a given $$\lambda $$ , WH exists in the presence of exotic matter at the throat when $$\alpha <0$$ . It is demonstrated here that WH exists even without exotic matter for $$\alpha >0$$ in the modified gravity. Two different shape functions are considered to obtain WH solutions that are permitted with or without exotic matter. It is noted that in a modified f(R, T) gravity MT WH is permitted with normal matter which is not possible in GR. It is demonstrated that a class of WH solutions exist with anisotropic fluid for $$\lambda \ne -8\pi $$ . However, for flat asymptotic regions with anisotropic fluids WH solutions cannot be realized when $$\lambda =-8\pi $$ . All the energy conditions are found consistent with the hybrid shape function indicating existence of WH even with normal matter for $$\lambda \rightarrow 0$$ .

Development of novel TPI/HDPE/CNTs ternary hybrid shape memory nanocomposites

In order to make up for the defects of trans-1,4-polyisoprene (TPI) shape memory polymer, TPI/high density polyethylene (HDPE) hybrid shape memory matrix was prepared from the perspective of matrix composition. The carbon nanotubes (CNTs) with excellent mechanical properties were introduced into the hybrid shape memory matrix. Due to the difference of the inherent properties and geometry of nano-fillers, the change of the content of nano-fillers directly affects the bonding state within the composites. Therefore, it is very important to choose the appropriate content. In order to give full play to the potential of thermodynamics of nano-filler, the TPI/HDPE/CNTs ternary hybrid shape memory nanocomposites were prepared by mechanical melt blending technology combined with dynamic vulcanization and hot-pressing forming technology. The addition of CNTs promotes the formation of the crystal structure of TPI and HDPE, and facilitates the energy transfer between different interface, which greatly improves the thermal conductivity and mechanical properties of the nanocomposites at the same time. The effect of the changes of filler content on the thermodynamic properties of the composite materials were revealed by series of tests. The results show that the CNTs act as nucleating agents in the crystallization region of TPI and HDPE. However, the excessive addition of CNTs can inhibit the formation of HDPE crystal structure. Meanwhile, the crystallinity of nanocomposites is also an important factor affecting its thermal conductivity. The specimens with the CNTs content of 0.5 wt% have excellent tensile resistance and cyclic recovery ability, and it can improve the shape recovery properties. Therefore, the nanocomposite with the CNTs content of 0.5 wt% has the best thermodynamic and shape memory properties.

Magnetically Levitated Linear Drive Using an Active Gravity Compensation Based on Hybrid Shape Memory Actuators

This article presents a magnetically levitated linear drive for precision engineering with integrated active gravity compensation. The gravity compensation combines permanent magnets with novel hybrid shape memory actuators. The magnetically levitated system uses a homopolar linear drive as well as nine reluctance actuators to levitate a passive armature with no mechanical connection between the stator and armature. The mechanical design is based on geometrically decoupled horizontal and vertical guidance axes. A decoupled Cartesian control scheme is developed, which compensates for the actuator and system nonlinearities in order to achieve high bandwidths. The active gravity compensation adjusts the air gap between the permanent magnets and armature to the required gravity compensation force. This helps to keep the dissipated power and temperature increase in the magnetically levitated drive low (and thus, system precision high). To avoid the generation of particles in clean room applications, the actuators positioning the permanent magnets are solely based on solid-state effects: thermal shape memory alloys actively generate motion, while passive magnetic shape memory alloy elements realize a multistable behavior based on their internal twinning force. The resulting actuator is compact, energy efficient, and abrasion-free. The implementation of the gravity compensation in the levitated linear drive is verified and the functionality of the system is demonstrated in experiments.

Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions.

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

Wormhole models in R2-gravity for f(R, T) theory with a hybrid shape function

In the present paper, we explore wormholes in R2-gravity within the f(R, T) formalism by using [Formula: see text] (hybrid shape function). The functional form f(R, T) = R + αR2 + λT is considered where R and T are the Ricci scalar and trace of the energy–momentum tensor, respectively, and α and λ are controlling parameters. With the help of the EoS, ω = pr/ρ, geometric behavior is analyzed and energy conditions are discussed in the anisotropic scenario. In this investigation, significant contribution of the quadratic geometric term (R2) and linear trace term (T) are shown to validate energy conditions for the specific shape function and analyze wormhole solutions in the absence of exotic matter. Also, we observe that the energy conditions are valid in the whole range (r ≥ r0) in the case of constant redshift function with this shape function.

Wormhole structures and energy conditions in f(ℛ) gravity with hybrid shape functions

This paper discusses the possible wormhole solutions in modified [Formula: see text] gravity by employing the two hybrid shape functions i.e. [Formula: see text] and [Formula: see text], where [Formula: see text] is constant. The solutions are accomplished by implementing the modified-gravity functions [Formula: see text] and [Formula: see text], where [Formula: see text]. It is presented by investigating the energy constraints through the graphical analysis that the null energy conditions for the energy–momentum tensor are largely violated for our both models. Energy constraints connected to the matter source threading the possible wormhole structures are in general worked out, supporting the null energy constraints in the neighborhood of the wormhole neck. This concludes that threaded by the matter, the existence of the non-exotic wormhole geometries have been found in this gravity. Subsequently, it is shown that violation of the null energy condition may be accredited to the collective effects of the [Formula: see text] gravity and owing to the non-commutative geometry.

Thermoelastic and vibration response analysis of shape memory alloy reinforced active bimorph composites

In this paper, thermoelastic and free vibration responses of hybrid Shape Memory Alloy (SMA) and E-glass fiber-reinforced composites are investigated using finite element analysis. We consider four composites for analysis and comparison of performances, (1) single layer SMA fiber-reinforced hybrid composite (unimorph SMAHC), (2) a two-layer (cross-ply) SMA fiber-reinforced hybrid composite (bimorph SMAHC), (3) single layer SMA fiber-reinforced with a honeycomb core, and (4) single layer SMA fiber-reinforced with reentrant-honeycomb or auxetic core. We analyze the bending response of all the aforementioned composite structures, focusing on the bimorph anticlastic and synclastic bending with negative and positive Gaussian curvatures, respectively. The uniqueness of this work is utilizing the shape memory effect of the SMA fibers to achieve active shape control of low-stiffness and lightweight auxetic composite structures. We investigated the free vibration response and analyzed the effect of the fiber volume fraction and the fiber orientation angle on the natural frequency of the system. Further, the role of the reentrant angle and stiffness of honeycomb struts on the overall effective mechanical properties of the ply is also studied. Results confirm the non-linearity of the parametric combination and the importance of optimization of these parameters for improved Gaussian curvature. The findings are envisaged to be useful for the design of lightweight rigidizable space structures and tensairity structures.