Elastic Flexure Research Articles

Enhancing and Decoding the Performance of Muscle Actuators with Flexures

Leveraging living muscle as an efficient and adaptive actuator for soft robots has been of increasing interest over the past decade, with a focus on proof‐of‐concept demonstrations of function. Reproducible design and scalable manufacturing of biohybrid machines requires methods to increase the stroke output of strain‐limited muscle actuators and enable accurate and precise quality control and performance monitoring. Compliant mechanical elements, termed flexures, are designed to enhance muscle contractile stroke to ≈5× previously reported values and decode contraction dynamics with high spatiotemporal resolution. Combining rigid and flexible elements within a linear elastic flexure enables us to outperform the sensitivity of gold standard elastomeric beam‐based measurements of muscle contraction at both low‐ and high‐frequency stimulations. Flexures are leveraged to make quantitative comparisons of force, work, and power outputs in muscle actuators, driving us to discover a new observation of frequency‐dependent fatigue in muscle, and also develop a novel method for tuning muscle contractile dynamics in a frequency‐independent manner. By enhancing the contractile stroke of muscle actuators and precisely tuning contractile dynamics and endurance with unprecedented precision, this study sets the stage for leveraging flexures to improve robust, reproducible, and predictive design and manufacturing of next‐generation biohybrid robots.

Explicit analytical solutions for the full plane-stress field in sandwich beams under flexure governed by zigzag warping

We provide analytical solutions for the full stress field of straight sandwich beams with identical skins subject to linear elastic flexure governed by zigzag warping, where all layers obey Timoshenko’s kinematics. As a main novelty, we make use of an equilibrium equation for the Cauchy continuum to recover of the through-the-thickness normal stress component, σy. The new estimates are accurate for a wide range of relative stiffness between skins and core and suitable boundary conditions, as it can be demonstrated through the comparison with detailed finite element simulations where the sandwich is modelled as a two-dimensional continuum. As a main practical result concerned with the study of delamination, we find that at a core–skin interface of a cantilever sandwich subjected to a uniformly distributed load, in a region close to the fully-clamped cross-section, σy is a tensile stress of magnitude larger than that of the shear stress. On this basis, we infer that the availability of good estimates for σy, along with those for the longitudinal and shear stresses, may be important for the accurate design of sandwich panels.

Asymptotic Analysis of Linearly Elastic Flexural Shells Subjected to an Obstacle in Absence of Friction

In this paper we identify a set of two-dimensional variational inequalities governing the displacement of a linearly elastic flexural shell subjected to a confinement condition, expressing that all the points of the admissible deformed configurations remain in a given half-space. The action of friction is neglected.

A corrected finite-difference scheme for the flexure equation with abrupt changes in coefficient

Abstract. The fourth-order differential equation describing elastic flexure of the lithosphere is one of the cornerstones of geodynamics that is key to understanding topography, gravity, glacial isostatic rebound, foreland basin evolution, and a host of other phenomena. Despite being fully formulated in the 1940s, a number of significant issues concerning the basic equation have remained overlooked to this day. We first explain the different fundamental forms the equation can take and their difference in meaning and solution procedures. We then show how numerical solutions to flexure problems as they are currently formulated are in general potentially unreliable in an unpredictable manner for cases in which the coefficient of rigidity varies in space due to variations of the elastic thickness parameter. This is due to fundamental issues related to the numerical discretisation scheme employed. We demonstrate an alternative discretisation that is stable and accurate across the broadest conceivable range of conditions and variations of elastic thickness, and we show how such a scheme can simulate conditions up to and including a completely broken lithosphere more usually modelled as an end-loaded, single, continuous plate. Importantly, our scheme will allow breaks in plate interiors, allowing, for instance, the creation of separate blocks of lithosphere which can also share the support of loads. The scheme we use has been known for many years but remains rarely applied or discussed. We show that it is generally the most suitable finite-difference discretisation of fourth-order, elliptic equations of the kind describing many phenomena in elasticity, including the problem of bending of elastic beams. We compare the earlier discretisation scheme to the new one in one-dimensional form and also give the two-dimensional discretisation based on the new scheme. We also describe a general issue concerning the numerical stability of any second-order finite-difference discretisation of a fourth-order differential equation like that describing flexure wherein contrasting magnitudes of coefficients of different summed terms lead to round-off problems, which in turn destroy matrix positivity. We explain the use of 128 bit floating-point storage for variables to mitigate this issue.

The Role of Isostasy in the Evolution and Architecture of Fold and Thrust Belts

Abstract Warmer conditions prevalent in the hinterland of orogenic systems facilitate local ductile flow underneath the surface load, making Airy-like local isostasy more prevalent in these domains. In contrast, flexural isostasy better describes the regional response to surface loading of more rigid lithospheres. Here, we explore how the interaction between horizontal tectonic mass transfer and vertical isostatic mass transfer, through either elastic flexure or viscous flow, impacts the overall architecture of fold and thrust belts. We compare numerical models of fold and thrust belts under either an Airy-like ductile isostasy boundary condition or a flexural-like regional isostasy boundary condition. Our experiments suggest that when ductile flow is involved in accommodating isostatic adjustment, subsidence is rather local, larger, and results in narrower, less elevated fold-thrust belts with a complex internal architecture consisting of prominent steeply dipping faults. When isostatic subsidence is controlled by lithospheric flexure, the tilting of the basement on 10 s of km scale facilitates the outward propagation of fold-thrust belts. The internal architecture is simpler and involves prominent basement-parallel décollements. The outcome is wider fold and thrust belts with higher topographies. A change in lithospheric elastic thickness does not significantly affect fold-thrust belt structural styles. Our results are compared to natural examples from the Subandean zone.

Total isostatic response to the complete unloading of the Greenland and Antarctic Ice Sheets

The land surface beneath the Greenland and Antarctic Ice Sheets is isostatically suppressed by the mass of the overlying ice. Accurate computation of the land elevation in the absence of ice is important when considering, for example, regional geodynamics, geomorphology, and ice sheet behaviour. Here, we use contemporary compilations of ice thickness and lithospheric effective elastic thickness to calculate the fully re-equilibrated isostatic response of the solid Earth to the complete removal of the Greenland and Antarctic Ice Sheets. We use an elastic plate flexure model to compute the isostatic response to the unloading of the modern ice sheet loads, and a self-gravitating viscoelastic Earth model to make an adjustment for the remaining isostatic disequilibrium driven by ice mass loss since the Last Glacial Maximum. Feedbacks arising from water loading in areas situated below sea level after ice sheet removal are also taken into account. In addition, we quantify the uncertainties in the total isostatic response associated with a range of elastic and viscoelastic Earth properties. We find that the maximum change in bed elevation following full re-equilibration occurs over the centre of the landmasses and is +783 m in Greenland and +936 m in Antarctica. By contrast, areas around the ice margins experience up to 123 m of lowering due to a combination of sea level rise, peripheral bulge collapse, and water loading. The computed isostatic response fields are openly accessible and have a number of applications for studying regional geodynamics, landscape evolution, cryosphere dynamics, and relative sea level change.

Mechanical, Dynamic-Mechanical, Thermal and Decomposition Behavior of 3D-Printed PLA Reinforced with CaCO3 Fillers from Natural Resources.

This study evaluates the effect of CaCO3 fillers extracted from waste eggshells on 3D-printed PLA performance. Samples of neat PLA and PLA reinforced with CaCO3 fillers embedded with different wt.% were prepared using an FDM (fused deposition modeling) technology. The samples were examined using mechanical, dynamic mechanical, thermal, and thermal decomposition analyses. The results revealed increasing elastic moduli, tensile strength, and flexure as the filler content increased. The rheological results from the MFR tests showed that the filler content did not influence the PLA-based samples’ processability. Further, the thermal degradation of neat and various CaCO3-wt.%-reinforced PLA specimens revealed relatively small discrepancies in their exposure to the temperature increase, mainly concerning the eggshell organic components and volatile components, from their processability up to 300 °C. By contrast, the increased filler content positively shifted the peaks along the temperature scale at the maximum degradation rate. Additionally, the weight content of the natural reinforcement strongly influenced the surface wettability and appearance of the samples. Further, the SEM analysis featured both the presence of interlayer disturbances and the interfacial compatibility the PLA with the selected fillers.

Optimization based Feedforward mitigation of Elastic Flexure of Distributed Parameter System due to Reference Tracking

If a large scale structure performs a rigid body motion, this motion is superposed by an elastic flexure due to its inherent elasticity. In order to mitigate the elastic motion feedforward and feedback laws can be applied. By minimizing the L2-norm of the elastic flexure subject to a reference trajectory and the elastic system description we derive a feedforward signal that attenuates elastic motions of the structure. A comparison to simplified solution approaches shows a major improvement for reference signals in the range of the system's natural frequencies.

Quantification of Moment–Rotation Relationship of Monolithic Precast Beam–Column Connections

The accurate prediction of nonlinear structural behaviors under different seismic intensities is an important basis for seismic resilience assessments of building structures. The moment–rotation relationship is often used to characterize the seismic performance of connections, and is widely used in high-efficiency nonlinear structural analysis. In this paper, a method of calculating the curve using a four-linear equivalent model is presented, aiming to quantify the characteristic point parameters of the moment–rotation curves of monolithic precast beam–column (MPBC) connections for engineering design purposes. The method considered the contribution of the elastic flexure of beams and columns, the relative slip of beam longitudinal bars in the core zone, and the formation of plastic hinges at beam ends to the total deflection. Due to the presence of local complex configurations in MPBC connections, the fine fiber section method was used for moment–curvature analysis of critical beam sections. The determination of the sectional analysis processes was controlled by the strain of steel bars or concrete or their coupling effect. In addition, a two-step method was proposed to construct the moment–rotation relationship of cruciform beam–column connections for solving the deformation compatibility of beams on both sides of the column caused by asymmetric reinforcement and the strength difference between new and old concrete. To reflect the current manufacturing level of MPBC connections, 58 representative specimens reported in recent years were analyzed and classified as type 1–5. All types of MPBC connections and their 18 cast-in situ counterparts were calculated using the proposed method for both verification and quantification. The verification showed that the proposed method had good applicability to both cast-in situ and precast beam–column connections. The quantification showed that the characteristic point parameters were slightly different between these two connections. Accordingly, modification coefficients were suggested for MPBC connections to facilitate design.

Explicit dynamics finite element analyses of asymmetrical roll bending process

In this article, results obtained from a preliminary study that contains a set of explicit dynamics finite element analyses of a metal plate bending process are presented through 3D asymmetrical three roller models. ANSYS Ls-Dyna explicit dynamics finite element (ED-FEA) preprocessor and solver were used to carry out dynamic simulations. Explicit dynamics of a low-velocity process such as the roll-bending of a metal plate is a computationally expensive method. Since plastic deformation occurs on the plate in addition to elastic flexure to eventually possess a circular geometry, the plate material is considered a non-linear material. In this particular study, an aluminum plate was modeled with the Bilinear Kinematic Hardening model including plasticity parameters such as the tangent modulus. A very significant parameter called the mass scaling factor was taken into account to be able to define a specific time-step that was used to determine the computation time interval and the total temporal cost. However, exaggerated reduction of the computation time results in unphysical consequences. The results were presented before and after redesigning the lower and side rolls having a convex geometry and the peripheral velocity of upper roll rotation was decreased to minimize the distortion that occurred on the pre-bent side walls of the aluminum plate.

Research of rational roll profiling during cold rolling of tapes from copper and yellow metal

It is shown that a main route of development of pressure treatment of non-ferrous metals is a heading of innovative designs in the manufacture, providing development of manufacture of new brands of alloys from brass metal and copper with demanded mechanical properties, including with high heat conductivity, and also the improved critical bucklings. Such properties tapes from brass metal and copper, and also their alloys with the improved critical bucklings possess. By manufacture of manufactured goods, and also by manufacture of the goods of mass demand (heat exchangers, pipes, radiators) are used cold rolling tapes from brass metal and copper. It is shown that questions of martempering of geometrical figures of merit of tapes from brass metal and copper, including formation of the transverse nonuniform thickness, a cross profile and the geometrical form of tapes, and also definition profiling rolls reversible four rolling mill and two rolling mill at cold rolling demand the development. It is installed that the major parametre of dimensional accuracy of tapes are nonflatness and the transverse nonuniform thickness, that is change of a thickness of a tape on its width. It is shown that on the form interstitial a positive allowance forming the transverse nonuniform thickness of tapes, following factors influence: an elastic bending flexure rolls, irregularity of flattening on length of the barrel rolls on work roll and hire contact, thermal convexity of barrels of shafts, deterioration of barrels rolls, a hydraulic bend rolling systems, the original transverse nonuniform thickness, profiling rolls. A traditional method of formation interstitial a positive allowance is profiling rolls which in huge extent influences a course of process of rolling and quality of metal products. Dependences for calculation rational profiling work rolls, and also an elastic bending flexure rolls on length of the barrel, equal width rolling tapes for the vacuum mill are presented. It is shown that at rolling of tapes from copper on the reversible two rolling mill 350×450 with use rational profiling rolls the deviation from planeness of ready tapes fulfils to acting specifications. At rolling of tapes from yellow metal on reversible four rolling a mils 150/500×400 with rational profiling rolls, the transverse nonuniform thickness of tapes of 1,00 mm matches in the thickness to the raised accuracy.

Evidence for a Locally Thinned Lithosphere Associated With Recent Volcanism at Aramaiti Corona, Venus

AbstractHeat flow estimates of terrestrial planets and icy satellites are important for exploring their thermal evolution. Topographic signatures of flexure can be used to estimate the effective elastic lithospheric thickness, he, and heat flow. Here, we use high resolution stereo topography and axisymmetric elastic flexure models to investigate lithospheric flexure around Narina Tholus, a steep‐sided volcanic dome ∼40 km across that superposes the tectonic annulus of Aramaiti Corona. Our results indicate a best‐fit elastic thickness he = 3.9–9.1 km, for values of Young's modulus, E, ranging from 65 to 5 GPa respectively. This suggests a thinned lithosphere locally around Narina Tholus, compared to regional estimates for he. The lower values of E are appropriate to the heavily fractured environment of the corona annulus, and we find that they predict flexural stresses compatible with the limited fracturing observed around Narina Tholus. A global survey yielded 13 additional tholi (or tholi groups) at coronae and with stereo coverage, none of which showed evidence for flexure. We find, that locally at Narina Tholus, the heat flow is elevated by a factor of 2–4 relative to that inferred from a previous study of flexure at Aramaiti, consistent with late‐stage, possibly recent, volcanism focused at, and facilitated by, the fracture annulus. Our results further strengthen arguments for a currently volcanically active planet and demonstrate the role that high‐resolution stereo topography can play in elucidating the current thermal state of Venus.

A new analytical solution for elastic flexure of thick multi-layered composite hybrid plates resting on Winkler elastic foundation in air and water

A new analytical flexural solution based on double finite integral Fourier transform and trigonometric series differentiation procedures was developed for thick multi-layered composite hybrid rectangular plates resting on Winkler elastic foundation in air and water. The effect of material anisotropy, coupled hydro-mechanical loads, and underwater floor inclination angle,which were overlooked in the literature, is considered in this study. Furthermore, the predetermination of the shape deformation function is not required in our proposed analytical solution, which offers more accurate results. For the particular cases where the plate made of isotropic material is in air, the analytical results are compared with, and verified by the literature. Literature is lacking to investigate thick multi-layered composite hybrid rectangular plates with free edges and under hydro-mechanical load; hence our analytical results are compared with, and verified by,numerical analysis employing finite element method (FEM). The analytical results provide excellent agreement with both literature and the proposed FEM. FEM is shown to be time-intensive since the results converge after 60 seconds runtime with definition of 12159 elements during mesh refinement, yet the proposed analytical method demonstrates that the convergence can easily be achieved after 5 seconds runtime through selecting small values for Fourier terms.

Quantifying Periodic Variations in Hotspot Melt Production

AbstractFluctuations in estimated mantle plume melt production rates suggest complex dynamics in the upper mantle including changes in plume upwelling, compositional heterogeneity within plume stems, entrainment of anomalous mantle, or other processes. Despite the implications for mantle dynamics, differences between previous studies including the methods, study areas, and types of melt volumes estimated, limit inter‐hotspot comparisons and assessment of global variability. Here, we use a consistent methodology to calculate igneous melt production through time across a suite of 12 hotspot chains located in the Pacific, Indian, and Atlantic Ocean basins. Using global data sets of topography, gravity, sediment cover, and seafloor age along with spectral methods for calculating elastic plate flexure and gravity anomalies, we estimate the total volume of igneous material at each hotspot in three components: (a) volcanic edifices, (b) flexural infill, and (c) intrusions (underplating) within the upper mantle and lower crust. Results indicate time‐averaged melt production rates across all studied hotspots range from 3.44 m3 s−1 (Cobb) to 14.75 m3 s−1 (Kerguelen), with underplating making up the largest component. Through time, melt production rates vary from 0.1 to 2.5 times average values with statistically significant periodic fluctuations of 1.1–71.5 Myr. Spectral analysis of estimated melt volumes shows total melt production varies periodically at all 12 hotspots. Excepting Galápagos, the studied hotspots exhibit multiple periodicities of melt production variability, implying complex dynamic, thermal, and/or chemical processes within the plume conduit. Moreover, we find several groups of hotspots exhibiting similar periods of melt production variability.

Evidence of paleoseismic activity recorded in glaciolacustrine sediments predating the Weichselian glacial maximum in East Lithuania

AbstractSoft-sediment deformation structures (SSDS) were identified in proglacial lacustrine (glaciolacustrine) sediments dated to 25–24 ka in the Buivydžiai outcrop, situated 30 km north of Vilnius in east Lithuania. These sediments accumulated in front of the last Weichselian glaciation maximum. The SSDS originated due to sandy silt liquefaction that disrupted the decimeter-thick silty sand interlayer. A NW-SE trending Buivydžiai fault was mapped in the proximity (8 km) of the Buivydžiai outcrop. The fault is well traced by a dense drilling in the sediments of the preglacial Daumantai Formation in the basal part of the Quaternary cover and attributed to the earliest Pleistocene. Depth difference of the formation along the fault is ~5–8 m; the northern flank is relatively uplifted with respect to the southern flank. The Buivydžiai earthquake was most likely induced by formation of an elastic forebulge flexure of the Earth's crust in front of the ice sheet. The magnitude was evaluated ~M = 6.0–6.5 and was most likely of shallow hypocenter depth. Furthermore, the Bystritsa (Belarus) earthquake of magnitude M = 3.5–4.0 was registered in December 1908 to the east (12 km) of the Buivydžiai outcrop along the Buivydžiai fault, which points to recurrent seismic activity of this fault.

Design of an electrostatic balance mechanism to measure optical power of 100 kW.

A new instrument is required to accommodate the need for increased portability and accuracy in laser power measurement above 100 W. Reflection and absorption of laser light provide a measurable force from photon momentum exchange that is directly proportional to laser power, which can be measured with an electrostatic balance traceable to the SI. We aim for a relative uncertainty of 10-3 with coverage factor k = 2. For this purpose, we have designed a monolithic parallelogram 4-bar linkage incorporating elastic circular notch flexure hinges. The design is optimized to address the main factors driving force measurement uncertainty from the balance mechanism: corner loading errors, balance stiffness, stress in the flexure hinges, sensitivity to vibration, and sensitivity to thermal gradients. Parasitic rotations in the free end of the 4-bar linkage during arcuate motion are constrained by machining tolerances. An analytical model shows this affects the force measurement less than 0.01 percent. Incorporating an inverted pendulum reduces the stiffness of the system without unduly increasing tilt sensitivity. Finite element modeling of the flexures is used to determine the hinge orientation that minimizes stress which is therefore expected to minimize hysteresis. Thermal effects are mitigated using an external enclosure to minimize temperature gradients, although a quantitative analysis of this effect is not carried out. These analyses show the optimized mechanism is expected to contribute less than 1 × 10-3 relative uncertainty in the final laser power measurement.

Towards stratigraphic-thermo-mechanical numerical modelling: Integrated analysis of asymmetric extensional basins

Abstract Subsidence and uplift patterns and thermal history of sedimentary basins are controlled by tectonics, mantle dynamics and surface processes, such as erosion, sediment transport and deposition and their links to climatic variations. We use combined thermo-mechanical and stratigraphic numerical modelling techniques to quantify the links between tectonic and surface processes. We aim to assess the thermal evolution and subsidence rates of asymmetric extensional basins during the syn- and post-rift times by simulating different erosion and sedimentation rates. We analyse the 3D sedimentary architecture and facies distribution of the depocenters. Model results are validated by observations in the Pannonian Basin of Central Europe. Extensional reactivation of inherited suture zones creates asymmetric basin systems controlled by large-scale detachments or low-angle normal faults, where crustal and lithospheric mantle thinning are often rheologically decoupled. Subsidence rates and basement heat flow in the depocenters show large variabilities during asymmetric extension and post-rift evolution controlled by their initial position from the suture zone and migration of deformation. Transient heat flow anomalies mirror crustal exhumation of footwalls, sediment blanketing and erosion effects in the basins. Enhanced erosion and sedimentation facilitate lower crustal deformation and elastic flexure of the weak, extended lithosphere leading to accentuated differential uplift and subsidence during the syn- and post-rift basin evolution. Tectonics, climate and autogenic processes control transgressive-regressive cycles at different timescales together with the overall sedimentary facies distribution. In our models assuming wet climate the high subsidence rate often outpaces moments of eustatic water-level fall preventing relative base-level fall and enhances the effects of autogenic processes, such as lobe switching processes.

A fault-bounded palaeo-lake basin preserved beneath the Greenland Ice Sheet

Subglacial topography not only exerts strong controls on contemporary ice sheet dynamics, but also provides an important long-term record of landscape evolution pertaining to past glacial and interglacial conditions. In particular, the bed topography beneath the Greenland Ice Sheet bears the signatures of past processes of landscape evolution that record the development of the ice sheet since its inception. Here we present evidence from airborne radio-echo sounding, gravity, and magnetic data for an enclosed palaeo-lake basin situated beneath the ice sheet in northwest Greenland. Geomorphological analysis and hydrological modelling indicate that the basin once hosted a lake with a surface area of up to ∼7,100 km2 and a volume of up to ∼580 km3. The basin and associated topography control the organisation of a preserved palaeo-fluvial channel network, suggesting that the basin pre-dates widespread glaciation in northwest Greenland. We use flexural modelling to show that the morphology of the basin and surrounding topography is consistent with elastic plate flexure driven by mechanical displacement along a normal fault bounding the basin margin. Analysis of gravity and magnetic anomalies indicates that the basin contains a sedimentary infill up to ∼1.2 km thick, which may contain valuable records of past ice sheet extent and environmental conditions in northwest Greenland. We therefore propose that this newly identified palaeo-lake basin may be a promising target for future acquisition of ground-based active source seismic data and potential recovery of subglacial material by sub-ice drilling programs.

Straightening of Shafts by Surface Plastic Deformation with Elastic Flexure of the Workpiece

A method is proposed for straightening nonrigid parts by surface plastic deformation. This method is based on the change in the stress–strain state of the workpiece in finishing.

Elastic Flexure of Young, Overlapping Basaltic Lava Flows Offshore the Galápagos and Hawaiian Islands: Observations, Modeling, and Thermal/Chronological Analysis

AbstractA recent multibeam bathymetry survey in the Galápagos archipelago revealed a novel observation between the islands of Santa Cruz and Santiago: a steep flexural moat formed between two volcanic flows, nearly 50 m deep and about 500 m wide. Submarine observations and elastic plate modeling are consistent with this feature forming after one inflationary flow overlapped another young flow, deflecting the underlying lava flow in what appears to be a classical elastic flexural pattern. We present a flexural analysis of this moat feature using a thin‐plate approximation to determine the effective elastic thickness of the underlying flow. Moreover, we propose that this elastic thickness serves as a proxy for the thickness of the cooling, solidifying upper crust of the lava flow at the time of deflection, a time‐dependent thermal property. This approach offers a chronological tool to put bounds on the elapsed time between two overlapping lava flows. We applied this method to the Galápagos moat to constrain the time history of its formation. Additionally, we identified and modeled seven additional flexural moat candidates in the Hawaiian archipelago and in the Galápagos using multibeam bathymetry. Elastic/thermal history analysis of these features yields relative time intervals between submarine lava flows ranging from a few years to about 600 years, which suggests that there is a critical time interval during which elastic deflection of the underlying lava flow may become “frozen in.” This methodology may provide helpful constraints on the temporal relations between overlapping lava flows wherever they form in relatively rapid succession.