Fold Lines Research Articles

Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry

Dynamic responses of a linear oscillator coupled to a nonlinear energy sink (NES) under harmonic forcing in the regime of 1:1:1 resonance are investigated. Primary attention is paid to the detailed investigation of the so-called strongly modulated response (SMR), which is not related to the fixed points of average modulation equations of the system. Essential mass asymmetry allows a global analysis of the responses despite strong nonlinearity. It is demonstrated that the strongly modulated response is related to a relaxation-type motion and its description in the limit of small mass ratio maybe reduced to the 1D return map of a subset at a fold line of slow invariant manifold. The SMR exists in the O ( ε ) -vicinity of the exact resonance, where ε ≪ 1 characterizes the mass asymmetry. It is also shown that the SMR appears in the system as a result of global fold bifurcation of limit cycles and exhibits some properties pertinent to generic 1D nonlinear maps, such as period doubling. Transient responses with finite number of relaxation cycles and subsequent attraction to stable periodic attractor are revealed. Analytic results are compared to numeric simulations and a good agreement is observed.

Heterogeneous systems of extractive rectification with one high-boiling component

The behavior of fold lines in the scalar fields of equilibrium temperatures and univolatility lines for the extractive rectification of azeotropic two-phase binary systems by one high-boiling agent is analyzed.

NURBS Strands Modeling of Prestressed Concrete Bridges

AbstractTo establish the unified description of strands in prestressed concrete girder bridge, NURBS strands model is presented with introducing Non-Uniform Rational Basic Spline (NURBS). Prestressed strands in design and construction are analyzed, with reasons for selection of NURBS as the strands model. Compared with Fold Line Approximation Model (FLAM), NURBS needs less parameters for preprocessor with higher accuracy in calculation of prestress equivalent load and loss of tendon force. The example testified the NURBS is fit to be as unified description method for strands in all kinds of prestressed structures.

Evidence from folding and functional lines of wings on inter-ordinal relationships in Pterygota

Insects fold their hind wings because of quite simple reasons. With fl exed and folded wings, it is easier to hide, to use small crevices and shelters against the impact of weather, e.g. wind and rain, and to escape predators, to name just a few reasons. The fi tness advantage is so great that wing folding convergently evolved in many separate insect ʻordersʼ (Heteroptera, Hymenoptera, Lepidoptera amongst others), using superfi cially different mechanisms. The Dermaptera, Blattodea and Coleoptera were examined in more detail. Included in the comparative study were other, technical and ornamental folded structures such as Origami models. The comparison showed despite very many differences some common features: almost all fold structures consist of Basic Mechanisms, an arrangement of four plates and four folding lines intersecting in one point. In hind wings, resilin is ample; energy is needed to unfold and/or fold the wings and prevents wear at critical locations in the wing. Often the folding lines in the wing are not morphologically differentiated (at least at LM and SEM level), but some specialised structures, typical for taxonomic families and orders do occur. The actual mechanics used in folding and unfolding, respectively, are fundamentally different: Coleoptera use their thoracic muscle to unfold the wing, but the elytra and the abdomen to fold it again. In Dermaptera, the wing is unfolded with the cerci, and folded with intrinsic elasticity stored in the many, strategically placed resilin patches. In Blattodea the wing unfolding is a simple by-product of wing promotion. Technical folded structure such as airplanesʼ wings are comparatively simple, and take advantage of the option to have additional tools & mechanisms for (un-)folding, as well interrupting the structural integrity for a short period of time. So they become unfunctional for a spell, which is no option for biological structures.

Variations in Form and Stress Behaviour of a V-shaped Membrane in a Foldable Structure

Adaptable tensile structures are often considered to be either completely opened or completely closed. The current study is part of a research project studying adaptable tensile structures which demonstrate stable behaviour within a wide range of opened positions. In this paper a simple V-shaped membrane is studied during the unfolding process. Starting from an initially flat folded membrane, which is not pre-tensioned, a slight curvature is obtained when it is unfolded due to the fact that along the folding line a curved section is cut out of the fabric. The tension introduced in the transverse direction implies a tension in the longitudinal direction too. Two cases are analysed: one with a high curvature in the diagonal cable (~5% sag) and one with a low curvature (~1.3% sag). Based on computer simulations the form and the tensions are verified for different opening angles. The deformation under loading is checked for the shape with a low curvature of the diagonal cable at an opening angle of 70o. The results indicate that the membrane could be used as a fabric roof. Further refined analysis is needed to be able to implement the presented concept for real applications.

In situ monitoring and analysis of rock mass behavior prior to collapse of the main transport roadway in Linglong Gold Mine, China

An extra-deep multiple-point borehole extensometer, applicable up to 300 m depth of cover, is introduced for the deformation monitoring of the deep rock masses (i.e., the rock mass below the ground surface) in the eastern area of Jinshandian Iron-ore Mine, and the in situ monitoring results collected over eight years are analysed. Combined with the deformation monitoring results on the ground surface collected by using a Global Positioning System (GPS), Level Monitoring Technique, and a three-dimensional Laser Scanning System (Leica HDS 880), the ground movement mechanism of the deep rock masses induced by underground mining is investigated. Results show that the extra-deep multiple-point borehole extensometer can capture the deformation information pertaining to deep rock masses in metal mines with complex geological conditions such as Jinshandian Iron-ore Mine. The moment that the deformation of the monitoring point starts to increase significantly can be used to determine whether the major deformation has transferred to the deep rock mass at the monitoring points, or not: the monitoring results from such critical moments indicate that the major deformation of the overburden strata gradually develops from the lower part to the upper part, consistent with the results from a physical modelling experiment. In Jingshandian Iron-ore Mine, the second caving of the deep rock masses reaches the ground surface above the centre of the mined-out area, and then causes the ground collapse; under the combined effect of the underground mining in Jinshandian Iron-ore Mine and the remaining private mined-out areas, large-scale ground surface collapses and cracks can be observed in mining-affected areas. The deep rock masses surrounding the mined-out areas are in a state of global deformation, and the boundary line of the deep break zone is a fold line. Currently, the rock masses in the major deformation zone move downwards under gravity on the shear surfaces in Jingshandian Iron-ore Mine.

Kinematics of a sigmoidal fold and vertical axis rotation in the east of the Zagros–Makran syntaxis (southern Iran): Paleomagnetic, magnetic fabric and microtectonic approaches

The Zagros Simple Fold Belt is characterized by elongated, curved, or sigmoidal folds. The trend of these structures together with the structural style, change suddenly across the Zagros–Makran syntaxis which separates the continental collision domain of Zagros from the oceanic subduction one in Makran. This work focuses on the Minab anticline, outcropping in the easternmost part of Zagros. In order to understand the kinematics of a sigmoidal fold and underscore possible vertical axis rotations in the eastern side of the syntaxis, we performed a joint study of magnetic fabric, microtectonics and paleomagnetism of the northern termination of this fold. The two limbs have been sampled (7 sites, 134 samples) along three cross-sections corresponding to three different orientations of the fold axis. The rocks are weakly deformed fine-grained Mio-Pliocene reddish siltstones. The shortening directions deduced from both magnetic fabric analysis and microtectonic observations are consistent with each other, they are horizontal and roughly perpendicular to the local fold axis, following the torsion of the fold hinge line, and indicating a tectonic origin of the magnetic fabric. Rockmagnetic analyses (thermomagnetic curves, hysteresis loops) point to the presence of magnetite in the PSD and MD ranges as the main magnetic carriers, together with a minor contribution from hematite. Apart from a post-tilting sub-actual VRM and/or CRM (component A), paleomagnetic analyses yield mainly two pre-tilting magnetization components: Component B is carried by magnetite, spanning the intermediate to high unblocking temperature range (300 °C ≤ T ubs ≤ 580 °C). Component C has unblocking temperatures characteristic of hematite (580 °C ≤ T ubs ≤ 680 °C). Both are ante-folding, based on positive reversal and fold tests, inside each of the cross-section but also for the three sections together. However, because component C is biased by some inclination flattening, only component B is taken into account afterwards. After full tectonic correction, the site mean direction of component B calculated for 6 out of the 7 sites is not statistically different from the individual site mean directions. The intersection direction determined by small circle analysis in these six sites is: D = 18.0° I = 33.7° k = 482 alpha 95 = 2.6°. Compared to the Mio-Pliocene direction expected in this area for Africa, it corresponds to an overall clockwise rotation of the whole structure of some 18.3° ± 5.1°, consistent with the regional geodynamic context. The absence of differential paleomagnetic rotation from one cross-section to the other, and the fact that the magnetic lineation together with the shortening direction deduced from microtectonic analysis follows the fold curvature demonstrate that the torsion of this fold is not secondary but rather coeval with the fold amplification. The torsion of the fold would stem from underlying inherited Mesozoic structures and the rheological response, during the deformation, of two incompetent décollement layers undergoing differential velocities and a change of thickness, in a constant stress field direction.

725 アルキメデスのらせん状折り線を用いた円形膜の巻き取り収納法の一般化

Wrapping method of thin circular flat membranes was newly developed by using fold lines of Archimedean spiral configurations. The angle relations in mesh pattern of fold lines constituting the spiral were formulated in a generalized form.

The structures of higher boron halides B8X12(X = F, Cl, Br and I) by gas-phase electron diffraction and ab initio calculations

The structure of B8F12 has been shown by gas electron diffraction and computational methods (up to MP2/6-31+G*) to have the same highly asymmetric form observed in crystalline phases. The structure can be regarded as derived from a central B2 group, bridged by two BF2 groups to give a central B4 core that is folded, not planar, and with a very short bond [164.3 pm calculated, 164.2(19) pm experimental] along the fold line. There are also four terminal BF2 groups. One of the other four bonds in the core is consistently 20-30 pm longer than the others. This asymmetry has been attributed to many intra-molecular B...F interactions, particularly those between core boron atoms and fluorines of the terminal BF2 groups. Calculations for the chloro analogue lead to a structure similar to that for B8F12, but with the long core bond extended so that one of the bridging BCl2 groups may now be regarded as terminal. With bromine as the halogen the structure changes again, with one bromine atom taking up a bridging position. With iodine, this process continues further, and there are three bridging iodine atoms. However, in this case this is not the lowest energy structure, and instead a loosely associated dimer of B4I6 is preferred. In all these cases, and particularly with the heavier halogens, there are huge differences between the results obtained with different computational methods.

Fatigue of web-flange weld of corrugated web girders: 1. Influence of web corrugation geometry and flange geometry on web-flange weld toe stresses

The fatigue performance of the web-flange weld of steel girders with trapezoidal corrugated webs was examined experimentally, using large-scale girder specimens, and analytically. The focus was on a region of constant bending moment. Fatigue cracks initiated at many points along the inclined folds, and then propagated perpendicular to the principal stress direction. Propagation of cracks initiating near the end of the inclined folds led to failure. Parametric FEM analyses indicated that the corrugation angle and the bend radius at the fold lines of the corrugations are the parameters that most influence the stress at the web-flange weld toe.

Luxation irréductible du genou par incarcération du plan capsulo-ligamentaire médial: À propos de quatre cas

Purpose of the study Irreducible dislocation of the knee is exceptional. Incarceration of the capsulo-ligamentary elements in the inter-condylar notch is a particular causal mechanism. We report four new cases and review the literature to describe the diagnostic and therapeutic approach. Material and methods Between January 2001 and January 2002, four patients underwent surgery after trauma (wind surf, ski accidents) producing an irreducible knee dislocation. Mean patient age was 53 years and mean follow-up was 16 months. The IKDC classification was used to assess outcome. Results Physical examination revealed characteristic signs: a groove facing the medial joint line with signs of cutaneous suffering just above and a fold line behind the medial condyle. Orthopedic reduction failed. Surgery was performed in all cases and revealed incarceration of the entire capsulo-ligamentary structure in the intercondylar notch with the medial condyle in an extra-articular position. After surgical reduction, healing was achieved in all cases without cutaneous necrosis. The mean subjective IKDC score was 53.9. Discussion Orthopedic reduction is impossible in about 4% of all cases of knee dislocation. Clinical signs are characteristic when the medial capsulo-ligamentary structures are incarcerated in the intercondylar notch; the anatomic injury is almost always the same. Vasculonervous complications are exceptional but an emergency arteriography should be obtained to rule out an infra-clinical intimal lesion. Cutaneous necrosis is a specific complication of irreducible dislocation. Early and complete reduction is required to prevent necrosis. Arthroscopic management raises the risk of compartment syndrome since peripheral lesions are not healed. Satisfactory functional recovery requires associated repair of the cruciate ligaments. Conclusion This type of irreducible dislocation of the knee is a specific clinical entity. It usually results from postero-lateral rotation but may exceptionally occur after lateral dislocation. A groove associated with a fold line indicates the need for rapid surgical reduction to avoid the risk of cutaneous necrosis.

Measurement protocol of women?s nude breasts using a 3D scanning technique

It has been difficult to obtain accurate surface data for women’s breasts, since the borderline of the breast is ambiguous at the skin surface. In this paper, we scanned 37 women’s nude breasts using 3D phase shifting moiré and explored a measurement protocol to get a reliable boundary of the breast and thereby provided new shape parameters for breasts. The folding line method was useful for finding a continuous and natural boundary for the breasts, so that the breasts base and volume could be measured more accurately. The global average radius of the curvature of the bottom breast line was suggested as a useful shape parameter for the design of a comfortable and form-fitting brassiere, especially for those who have a skewed bottom breast curve. It is also expected that data on breast volume based on natural anatomy would be a useful reference for surgical operation on the breast.

EVALUATION OF THE FOLD LINE BY ASYMPTOTIC EXTRAPOLATION FOR STRUCTURAL ANALYSIS

A technique for imperfection sensitivity analysis with reference to the geometrically nonlinear analysis of structures is presented. The paper discusses how detailed information on structural behavior can be obtained with less computational cost. The imperfection sensitivity analysis of structures is carried out by detecting the critical states on the equilibrium path relating to the various imperfections. In fact we can investigate the behavior of imperfect structures without considering the imperfect equilibrium curve. In this work we obtained the fold line, the one-dimensional equilibrium subset of limit points relating to different values of imperfection, by asymptotic extrapolation from a known singular point. The evaluation of this singular point on the perfect equilibrium curve is carried out by a path-following algorithm. A procedure that overcomes the ill-conditioning of the systems defined in the critical points is described. This proves to be highly advantageous in terms of computational cost in comparison with classical methods of analysis. The paper investigates the behavior of cylindrical shell. In particular the sensitivity analysis for load imperfections is carried out. The asymptotic extrapolation algorithm is also compared with continuation methods for the analysis of imperfect cylindrical shell.

Measurement protocol of women’s nude breasts using a 3D scanning technique

It has been difficult to obtain accurate surface data for women’s breasts, since the borderline of the breast is ambiguous at the skin surface. In this paper, we scanned 37 women’s nude breasts using 3D phase shifting moiré and explored a measurement protocol to get a reliable boundary of the breast and thereby provided new shape parameters for breasts. The folding line method was useful for finding a continuous and natural boundary for the breasts, so that the breasts base and volume could be measured more accurately. The global average radius of the curvature of the bottom breast line was suggested as a useful shape parameter for the design of a comfortable and form-fitting brassiere, especially for those who have a skewed bottom breast curve. It is also expected that data on breast volume based on natural anatomy would be a useful reference for surgical operation on the breast.

Evolution of vertical faults at an extensional plate boundary, southwest Iceland

Vertical faults having both opening and vertical displacements are common in southwest Iceland, and hypotheses vary regarding whether they propagated to the surface from below or from the surface downward. We address this issue through a study of vertical faults and associated surface fracture zones in regions of both oblique and normal spreading in southwest Iceland. Individual fracture segments are commonly rotated out of the general trend of the fracture zone, suggesting oblique motion along subsurface normal faults. These faults commonly breach the upper hinge lines of narrow monoclinal folds that flank many fault traces on the hanging wall side. Based on these field observations and the results of numerical models, we propose that 60–75° dipping normal faults in the subsurface propagated to the surface from below. Vertical fractures formed at the upper tips of the faults at depths of between 250 and 500 m (25–50% of the fault length) in response to stress concentrations along the tip line. Model results indicate that narrow monoclinal folds develop at the surface above these vertical fractures, which subsequently breach the monoclines along the upper hinge line, forming vertical fault scarps and open fissures at the surface. If vertical fractures utilize pre-existing cooling joints in basalt to connect directly to the surface, the hanging wall is able to pull apart from the footwall without the development of a surface monocline along the fault trace.

A new conceptual fold-fracture model including prefolding joints, based on the Emigrant Gap anticline, Wyoming

Symmetric relations between synfolding fractures and fold geometry have been used to explain the formation of fractures in folded sedimentary rocks. Based on field observations at the Emigrant Gap, a Laramide anticline located near Casper, Wyoming, we propose that the orientation of synfolding fractures was influenced dominantly by two tectonic joint sets, J1 and J2, which developed prior to folding. Rotations appropriate for unfolding the strata reorient most fractures such that they strike sub-parallel to one or the other of the two joint sets and oblique to the fold hinge line. On the fold limbs, these prefolding joints apparently propagated along strike and infilled during folding to form a denser network of joints bedding perpendicularly with spacing ∼1/5 to 1/10 that of the same joint set in nearby unfolded outcrops of the same formation. With proximity to the hinge line of the anticline, where bending of strata and surface curvature are elevated, the style of deformation is different. Whereas most J2-parallel fractures still are joints, fractures in the J1 orientation include sheared prefolding joints and bedding-inclined shear fractures. Apparent normal offsets of bedding by these shear fractures are an order of magnitude larger than offsets observed across sheared joints on the fold limbs. The proposed model of fracture-fold relationships differs from existing conceptual models because it postulates that folding-related fracture orientations are controlled by the orientations of prefolding fractures. For the Emigrant Gap anticline, these fractures are not oriented symmetrically with respect to the fold hinge line.

The puzzle of axis-normal magnetic lineations in folded low-grade sediments (Bude Formation, SW England)

Abstract A single upright, open anticline from sub-greenschist facies sedimentary rocks of the Bude Formation (Cornwall, UK) was sampled in order to investigate the kinematic relationships between fold development and anisotropy of magnetic susceptibility (AMS). The mean magnetic susceptibility of these samples is 0.25 × 10 −3 SI, suggesting low concentrations of ferromagnetic phases. AMS ellipsoids have a mean corrected anisotropy degree of 1.03 and a mean shape parameter of −0.54 (prolate). K min and K int define a girdle distribution striking sub-parallel to the fold axial plane, with K min tending to cluster around the fold axis. K max axes from both limbs of the fold define a cluster with a mean azimuth perpendicular to the fold axis. This arrangement of K max and K min could represent an inverse magnetic fabric of composite primary/tectonic origin. This is discounted, however, on the basis of broad correlation between the orientation of AMS and AIRM (anisotropy of isothermal remanence) ellipsoids. The prolate shapes and axis-normal orientation of K max axes contrast markedly with the widely observed relationship of AMS ellipsoids in folds, which are typically oblate and have K max parallel to the fold axis. This relationship is interpreted to represent progressive overprinting of primary depositional/compactional fabrics ( K min perpendicular to bedding) by a tectonic fabric ( K min perpendicular to cleavage). Consistency of K max orientations irrespective of position within the fold clearly points to a fabric of tectonic origin. Prolate ellipsoids with long axes perpendicular to the fold hinge line are indicative of superimposed sub-horizontal stretching at a late stage or post-dating fold formation. Such a situation is not inconsistent with superimposed southward-directed thrusting simple shear that has been suggested in this area to account for variations in fold attitude on a regional scale. It is more likely, however, that the fabric reflects post-orogenic extension, with the fold occupying a position in the immediate hanging-wall of a major northward dipping normal fault. In either case, the AMS fabrics around the fold record only the last increments of deformation in this area, with earlier primary and fold-related fabrics being entirely obliterated.

Optimization for Crush Characteristics of Cylindrical Origami Structure Using Reversed Spiral Model

It has been clearly shown that a can or PET bottle made by origami technique can be crushed with much smaller force. Furthermore, this structure is desirable to absorb more crash energy during automobile light collision or vehicles-pedestrian accidents. Thus, in this research, to minimize average crash force of the origami structure, the shape of the structure and the angle of polygonal folding lines are optimized by the method of MPOD, one kind of Response Surface Methods based on Holographic Neural Network (HNN).

Folding/Wrapping Methods of Circular Membranes Easily Deployable

The aim of the present paper is to develop compact folding/wrapping method of circular and conical shaped membranes facilely deployable. By using folding condition at nodes and generalized continuous condition of fold lines in the membranes, various kinds of folding methods have been newly devised by prescribing two groups of equiangular spirals, e.g., stowing method of circular membrane wrapped downwards round its central axis. Subsequently, modified fold patterns consisting of arbitrary type spirals are newly developed, which are available when the thickness of the membrane is taken into account. Finally, fold pattern of conical shaped mambranes has been newly developed. The availability of prescribed models has been checked by making origami samples.

折り紙構造物の圧潰特性の最適化

It has been clearly shown that a can or PET bottle made by origami technique can be crushed with much smaller force. Furthermore, this structure is desirable to absorb more crash energy during automobile light collision or vehicles-pedestrian accidents. Thus, in this research, to minimize average crash force of the origami structure, the shape of the structure and the angle of polygonal folding lines are optimized by the method of MPOD, one kind of Response Surface Methods based on Holographic Neural Network (HNN).