A Feasibility Study for Usefulness of Preoperative Simulation of Medial Open-wedge High Tibial Osteotomy for Predicting Postoperative Realignment

Three-dimensional preoperative surgical realignment simulation of medial open-wedge high tibial osteotomy (OWHTO), in which simplified as the rigid rotation around the hinge axis, has been performed to predict the postoperative change and to develop a patient specific instrument for accurate osteotomy. However, the realistic practicality of this extremely simplified simulation method has not been verified. The purpose of this study was to investigate the usefulness of realignment simulation, in which medial OWHTO is simplified as a rotation around a hinge axis, in comparison with a postoperative CT model. Three-dimensional surface model of the tibia and femur was created from preoperative computed-tomography (CT) images (preoperative model) of three patients. Sixty computer simulation models of the medial OWHTO in each patient were created by realignment simulation, in which medial OWHTO is simplified as the rigid rotation of proximal part of tibia relative to the distal part from 1 degree to 20 degrees around three type of hinge axes. The simulation models were compared with the actual postoperative model created from postoperative CT images to assess the reality of the simulation model. After the distal parts of the tibia between each simulation model and postoperative CT model were aligned by a surface registration, average surface distance between two models was calculated as an index representing the similarity of the simulation model to the postoperative model. The minimum average surface distance between the simulation and postoperative CT models were almost 1mm in each patient. The rotation angles at which the minimum average surface distance was represented were almost identical to the actual correction angles. Overlaying the simulation and the postoperative CT models, we found that the posterior tibial tilt and the axial rotation of the proximal tibia of the simulation model well represented that of the postoperative CT model as well as the valgus correction. Therefore, the realignment simulation of medial OWHTO simplified as the rigid rotation around the hinge axis can generate the realistic candidates of postoperative realignment that includes the actual postoperative realignment, suggesting the usefulness for the preoperative simulation method.

Time-History Analysis of Composite Materials with Rectangular Microstructure under Shear Actions

It has been demonstrated that materials with microstructure, such as particle composites, show a peculiar mechanical behavior when discontinuities and heterogeneities are present. The use of non-local theories to solve this challenge, while preserving memory of the microstructure, particularly of internal length, is a challenging option. In the present work, composite materials made of rectangular rigid blocks and elastic interfaces are studied using a Cosserat formulation. Such materials are subjected to dynamic shear loads. For anisotropic media, the relative rotation between the local rigid rotation and the microrotation, which corresponds to the skewsymmetric part of strain, is crucial. The benefits of micropolar modeling are demonstrated, particularly for two orthotropic textures of different sizes.

The static response of axisymmetric conical shells exhibiting bistable behavior

Belleville springs are widely used in variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building-blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely a non-monotonous force-displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing to results of finite-element simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross-section of the spring rotates without bending, i.e. maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite-element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straight-forward to use, yet are significantly more accurate than existing analytical models.

Stretching and shearing contamination analysis for Liutex and other vortex identification methods

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, ∆, λ2, and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.

Stretching and Shearing Contamination Analysis for Liutex and Other Vortex Identification Methods

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, Δ, λ2 , and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.

Orbital period modulation in hot Jupiter systems

ABSTRACT We introduce a model for the orbital period modulation in systems with close-by giant planets based on a spin–orbit coupling that transfers angular momentum from the orbit to the rotation of the planet and vice versa. The coupling is produced by a permanent non-axisymmetric gravitational quadrupole moment assumed to be present in the solid core of the planet. We investigate two regimes of internal planetary rotation, that is, when the planet rotates rigidly and when the rotation of its deep interior is time-dependent as a consequence of a vacillating or intermittent convection in its outer shell. The model is applied to a sample of very hot Jupiters predicting maximum transit-time deviations from a constant-period ephemeris of approximately 50 s in the case of rigid rotation. The transit time variations of WASP-12, currently the only system showing evidence of a non-constant period, cannot be explained by assuming rigid rotation, but can be modelled in the time-dependent internal rotation regime, thus providing an alternative to their interpretation in terms of a tidal decay of the planet orbit.

Non-diffusive angular momentum transport in rotating -pinches

The stability of conducting Taylor–Couette flows under the presence of toroidal magnetic background fields is considered. For strong enough magnetic amplitudes such magnetohydrodynamic flows are unstable against non-axisymmetric perturbations which may also transport angular momentum. In accordance with the often used diffusion approximation, one expects the angular momentum transport to be vanishing for rigid rotation. In the sense of a non-diffusive $\unicode[STIX]{x1D6EC}$ effect, however, even for rigidly rotating $z$ -pinches, an axisymmetric angular momentum flux appears which is directed outward (inward) for large (small) magnetic Mach numbers. The internal rotation in a magnetized rotating tank can thus never be uniform. Those particular rotation laws are used to estimate the value of the instability-induced eddy viscosity for which the non-diffusive $\unicode[STIX]{x1D6EC}$ effect and the diffusive shear-induced transport compensate each other. The results provide the Shakura & Sunyaev viscosity ansatz leading to numerical values linearly growing with the applied magnetic field.

Study of vortex element method parameters and their effect on rigid rotation bodies aerodynamic computations

The purpose of this study was to implement a software package that allows non-stationary aerodynamic computations of fixed rotation bodies using the vortex element method. In the course of the work, we developed an algorithm for rigid rotation bodies aerodynamic computations by means of this method. Furthermore, we studied the influence of calculation parameters on the results obtained.