Constrained Plate Research Articles

Simultaneous optimal tri-directional distribution of material and porosity in functionally graded plates under free vibration

This paper for the first time attempts to find the simultaneously optimal three-dimensional distribution of porosity and material phases in functionally graded materials (FGMs) model that altogether maximize the natural frequency of porous FG plates. By using the same concept of non uniform rational B-splines (NURBS) based interpolation for the material distribution, the problem of finding the optimal porosity distribution is enabled. An upper bound of porosity is pointed out, which is necessary for considering the porosity design variables. Generalized shear deformation theory (GSDT) in the framework of isogeometric analysis (IGA) for free vibration analysis of the porous FG plates is verified with previous works. The findings are: in the optimal design of material only, the uniformly distributed pores have a neutral or detrimental effect on 4-side constrained plates but slightly increase the frequency for the cantilever plate; and with that same amount of porosity, the simultaneously optimal distributions of pores, similar to those in bio-materials or natural bones in the way that are most foam-like in the center or at the furthest from the boundaries, result in lighter yet of significantly elevated vibration frequency structures.

Hot tearing behavior of NZ30K Mg alloy under progressive solidification

Progressive solidification is usually considered an effective strategy to reduce the hot tearing susceptibility of a cast component. In this study, special constrained plate castings with progressive changes in cross-section were designed, which enabled progressive solidification. The hot tearing behavior of a newly developed NZ30K Mg alloy (Mg-3.0Nd-0.2Zn-Zr, wt.%) was studied under progressive solidification using various mold temperature distributions and constraint lengths. Of these, a homogeneous mold temperature distribution is found to be the best option to avoid hot tearing, followed by a local low mold temperature distribution (with a chiller), then a gradient mold temperature distribution. Unexpectedly, compared with the homogeneous mold temperature distribution, adding a chiller does not provide any further reduction in the hot tearing susceptibility of the NZ30K Mg alloy. A high mold temperature and a short constraint length increase the hot tearing resistance of cast Mg alloys. Progressive solidification is not a sufficient and necessary condition to avoid the formation of hot tearing. The two key factors that determine the occurrence of hot tearing under progressive solidification are the maximum cooling rate and the constraint length. Decreasing these values can reduce the incidence of hot tearing.

CFD-based study of the abrasive flow characteristics within constrained flow passage in polishing of complex titanium alloy surfaces

Study on the constrained abrasive flow polishing of complex titanium alloy surfaces is discussed both numerically and experimentally. The numerical simulation using Computational Fluid Dynamics method and Discrete Phase Model is first conducted to model the particle-laden fluid through the constrained flow passage by considering four types of constrained plate, including chevron-type, golf ball-type, fork-type and triangle-type. The triangle-type constrained plate is found to be the most optimized design than the other types of pattern for the polishing purpose because of increasing the dynamic pressure of water flow and resulting in a relatively uniform distribution of water flow velocity near the bottom surface of the constrained flow passage, as well as increasing the number of collisions between particles and the target surface. A set of experiments, including the rough and precision polishing procedures, is then conducted to evaluate the polishing performance by using the original and triangle-type constrained plates, respectively. It is found that the average material removal rate obtained from the triangle-type constrained abrasive polishing process is larger than the corresponding data taken from the original passage, and the surface roughness is found to be reduced after the triangle-type constrained abrasive polishing process. These experimental results are in a good agreement with the corresponding simulated results. Thus, both the polishing efficiency and quality have been improved by using the abrasive flow polishing of complex titanium alloy surfaces with the triangle-type constrained plate.

Seismic behavior of steel coupling beam with different buckling constraint materials

With constrained plates on both sides of steel coupling beam web, the continuous strengthening can be achieved in steel coupling beam subject to cyclic shear loading with web shear yielding failure. Compared to traditional steel coupling beam which sets stiffeners on the web, the local buckling of the new type of steel coupling beam with shear yielding will not occur, before the steel web reaches its ultimate shear strain, resulting in excellent energy dissipation capacity. Eight quasi-static tests on buckling constraint steel coupling beams with shear yielding had been carried out to study the impact of various constraint manners on seismic behavior of this type of steel coupling beam. Tests results showed that all the test specimens realized shear yielding and strengthening of bearing capacity, and major failure mode included weld joint fracture between flange and endplate and failure of constrained plate. Average over strength factor of the test specimens was 1.38, above 1.1, the minimum requirement of Code for Seismic Design of Building Structures. Among them, the over strength factor of test specimens which used 50mm-thick reinforced concrete constrained plates and 25mm-thick wooden constrained plates exceeded 1.5. Test specimens with different constraint methods showed similar yield shear strain. While test specimens without constrained plates showed the minimum ultimate shear strain, test specimens with 25mm-thick wooden constrained plates showed the maximum, approaching the ultimate shear strain of the web’s steel in material property test.

New Somali Basin magnetic anomalies and a plate model for the early Indian Ocean

The oldest portions of the Indian Ocean formed via the breakup of Gondwana and the subsequent fragmentation of East Gondwana. We present a constrained plate model for this early Indian Ocean development for the time period from Gondwana Breakup until the start of the Cretaceous Normal Superchron. The motions of the East Gondwana terranes are determined using new geophysical observations in the Somali Basin and existing geophysical interpretations from other coeval Indian Ocean basins. Within the Somali Basin, recent satellite gravity data clearly resolve traces of an east–west trending extinct spreading ridge and north–south oriented fracture zones. A thorough compilation of Somali Basin ship track magnetic data allows us to interpret magnetic anomalies M24Bn through M0r about this extinct ridge. Our magnetic interpretations from the Somali Basin are similar in age, spreading rate, and spreading directions to magnetic anomalies previously interpreted in the neighboring Mozambique Basin and Riiser Larsen Sea. The similarity between the two magnetic anomaly datasets allows us to match both basin's older magnetic anomaly picks by defining a pole of rotation for a single and cohesive East Gondwana plate. However, following magnetic anomaly M15n, we find it is no longer possible to match magnetic picks from both basins and maintain plausible plate motions. In order to match the post-M15n geophysical data we are forced to model the motions of Madagascar/India and East Antarctica/Australia as independent plates. The requirement to utilize two independent plates after anomaly M15n provides strong circumstantial evidence that suggests East Gondwana breakup began around 135Ma.

Dynamic characteristics analysis of active constrained layer damping plate with various boundary conditions

Considering the direct and converse piezoelectric effect, expressions of piezoelectric membrane internal forces in the piezoelectric constrained layer were given. The control equations of the piezoelectric constrained layer and host plate were obtained in according with the thin plate theory. Based on the layer wised principle, the integrated first order differential equation of an active constrained layer damping (ACLD) plate was derived for the simply supported boundary condition. Then, this method was expanded to the ACLD plate with cantilever boundary condition by virtue of geometric analogy method. Employing the extended homogeneous capacity precision integration approach, a high precision semi-analytical method was proposed to analyze the dynamic characteristics of the ACLD plate with various boundary conditions. The comparison with the literature results has verified the accuracy and effectiveness of the present method.

In vitro evaluation of stiffness and load sharing in a two-level corpectomy: comparison of static and dynamic cervical plates

Background context Anterior cervical plating has been accepted in corpectomy and fusion of the cervical spine. Constrained plates were criticized for stress shielding that may lead to subsidence and pseudarthrosis. A dynamic plate allows load sharing as the graft subsides. Ideally, the dynamic plate design should maintain adequate stiffness of the construct while providing a reasonable load sharing with the strut graft. Purpose The purpose of the study was to compare dynamic and static plate kinematics with graft subsidence. Study design/setting The study designed was an in vitro biomechanical study in a porcine cervical spine model. Methods Twelve spines were initially tested in intact condition with 20-N axial load in 15 degrees of flexion and extension range of motion (ROM). Then, a two-level corpectomy was created in all specimens with spines randomized to receive either a static or dynamic plate. The spines were retested under identical conditions with optimal length and undersized graft. Range of motion and graft loading were analyzed with a one-way analysis of variance (p<.05). Results Both plates significantly limited ROM compared with the intact spine in both graft length conditions. In extension graft, load was significantly higher (p=.001) in the static plate with optimal length, and in flexion, there was a significant loss of graft load (p=.0004). In flexion, the dynamic plate with undersized graft demonstrated significantly more load sustained (p=.0004). Conclusions Both plates reasonably limited the ROM of the corpectomy. The static plate had significantly higher graft loads in extension and significant loss of graft load in flexion, whereas the dynamic plate maintained a reasonable graft load in ROM even when graft contact was imperfect.

Implant Complications, Fusion, Loss of Lordosis, and Outcome After Anterior Cervical Plating With Dynamic or Rigid Plates

Prospective, controlled, randomized, multicenter study. To analyze implant complications and speed. Rigid plate designs, in which the screws are locked to the plate, are in common use and thought to provide more fixation than dynamic designs, in which the screws may glide when the graft is settling. The aim of the study is to analyze (1) implant complications, (2) speed of fusion, (3) loss of lordosis, and (4) clinical outcome in both types of plates. One hundred thirty-two patients were included and assigned by randomization to one of the groups in which they received a routine anterior cervical discectomy and autograft fusion with either a dynamic plate (ABC, study group) or a rigid plate (CSLP, control group). At discharge, after 3 and 6 months and finally after 2 years, implant complications, segmental mobility, absence of radiolucencies, absence of bone sclerosis, evidence of bridging trabecular bone, loss of lordosis, Visual Analog Scale (VAS) and Neck Disability Score were recorded. All radiographic measurements were performed by an independent radiologist. There have been 4 patients with implant complications within the control group and no implant complications within the study group, P = 0.045. Mean segmental mobility before discharge for the study group was 1.7 mm, 1.4 mm after 3 months, 0.8 mm after 6 months, and 0.4 mm after 2 years. For the control group, these values were 1.0, 1.8, 1.6, and 0.5 mm. The difference at 6 months between both groups was significant (P = 0.024). Neither absence of radiolucencies, nor absence of sclerosis, nor evidence of bridging bone showed significant differences between the 2 groups through the postoperative follow-up (P > 0.05). The loss of segmental lordosis for the study group with respect to intraoperative radiograph was 1.3 degrees at discharge and 4.3 degrees after 2 years. For the control group, these values were 0.9 degrees , 0.7 degrees . The difference at 2 years was significant (P = 0.003). Clinical postoperative outcome (VAS and ODI) was not different between the 2 groups through the postoperative follow-up (P > 0.05). Dynamic cervical plate designs provide less implant complications (no patient) compared with rigid plate designs (4 patients). Speed of fusion was faster in the presence of a dynamic plate. However, loss of segmental lordosis is significantly higher if dynamic plates are used, which did not result in differences regarding clinical outcome between dynamic and constrained plates after 2 years. Thus, dynamic plates should be considered to be the preferred treatment option because of the lower risk for implant failure-related revision surgery.

Anterior Cervical Discectomy and Fusion With a Locked Plate and Wedged Graft Effectively Stabilizes Flexion-Distraction Stage-3 Injury in the Lower Cervical Spine

An in vitro three-dimensional (3D) flexibility test of human C3-C7 cervical spine specimens. To test the hypothesis that anterior cervical fusion with a wedged graft and a locked plate can effectively stabilize the cervical spine after complete anterior and posterior segmental ligamentous release. Distraction-flexion Stage 3 injuries of the lower cervical spine (bilateral facet dislocations) are usually reduced under awake cranial traction. When the magnetic resonance imaging reveals a traumatic disc prolapse, anterior cervical discectomy and fusion (ACDF) is usually recommended. Most authors advise combining ACDF with posterior instrumentation to address the insufficiency of the posterior elements. However, there is clinical evidence that ACDF with a locked plate alone suffices for the treatment of these injuries, especially in young patients. Still, there are no biomechanical studies on the effect of a locked plate on the complete anterior and posterior ligamentous-deficient young cervical spine under physiologic preload. Eight fresh frozen human lower cervical spines (C3-C7) from young donors (age, 44.5 years; range, 21-63 years) were used. A 3D flexibility test was conducted using a moment of 0.8 Nm without preload. Flexion-extension was additionally tested using a moment of 1.5 Nm under 0 and 150 N follower preload. Spines were tested first intact, then after complete C5-C6 discectomy with posterior longitudinal ligament resection and ACDF with a wedged bone graft and a rigid locked plate, and finally after complete release of the supraspinous, interspinous, and intertransverse ligaments; the facet capsules; and ligamentum flavum. RESULTS.: When tested under 0.8 Nm moment without preload, complete posterior and anterior ligamentous release did not significantly increase the ROM of the ACDF construct in flexion-extension (P > 0.025), lateral bending (P > 0.025), and axial rotation (P > 0.025). When tested under 1.5 Nm moment with or without a compressive preload, the complete posterior and anterior ligamentous release did not significantly affect the ROM of the ACDF construct (P > 0.01). The application of preload significantly reduced the motion at the C5-C6 ACDF construct with ligamentous disruption in comparison with the motion in the absence of a preload (P < 0.01). Anterior cervical fusion with a wedged graft and a rigid constrained (locked) plate can effectively stabilize the nonosteoporotic cervical spine after complete posterior element injury when excessive ROM is prevented (for example, by the use of postoperative external immobilization). Even when the construct is subjected to higher moments, adequate stability can be achieved when physiologic preload is present. Osteoporosis and lack of sufficient preload due to poor neuromuscular control may affect long-term screw stability, and additional external immobilization may be needed until fusion matures.

Real‐time measurement of flow front kinematics using quantitative visualization in injection molding process

AbstractThis article presents an experimental method for measuring the kinematics of the melt flow front, during the filling stage of the plastic injection molding process. The three main steps were: (i) visualization of the flow front advancement, (ii) image processing of the recorded results, and (iii) calculation of the flow front kinematics. The designed visual mold was capable of monitoring the flow advancement in two different cases: (i) a simple (nonconstrained) plate and (ii) a constrained plate (with an obstacle pin). Variations in instant flow rate, melt front area (MFA), and average melt front velocity (MFV) during filling stage were measured as a function of time. The applied technique could clearly show the flow behavior from which the flow front parameters could be extracted. A particle tracking velocimetry (PTV) method was also applied to study the orientation behavior of the advancing melt front. The time history of the particle's velocity components at the flow front could be easily extracted using the method. POLYM. ENG SCI., 2008. © 2008 Society of Plastics Engineers

In vitro comparison of a translational anterior cervical plate with a constrained anterior cervical plate

In vitro comparison of a translational anterior cervical plate with a constrained anterior cervical plate

Closure to “Discussion of ‘Combinations for the Free-Vibration Behavior of Anisotropic Rectangular Plates Under General Edge Conditions’ ” (2001, ASME J. Appl. Mech. 68, p. 685)

Although the main idea of the paper is an introduction of the Polya counting theory to an engineering counting problem that may be encountered in applied mechanics, this author equally appreciates the interest shown by Professor Bert in the proposed Ritz method to calculate natural frequencies of anisotropic plates with arbitrary boundary conditions. Professor Bert raised two constructive comments that are answered in order.The first comment is that the present author took up only three classical boundary conditions (i.e., free, simply supported, and clamped edges) in numerical examples and did not consider the fourth boundary condition of a guided or sliding edge with zero effective shear force and bending moment. The function (20) in the x and y-direction (1) is not applicable in its direct form to the fourth boundary condition but it is widely accepted that the fourth condition is not as important as the first three ones. It may be possible to apply the present function to the fourth boundary condition by adding a constant term to give a constant displacement caused by the guided or sliding edge and also constraining the slope at the edge.The second comment, which is more important, is on convergence rates of the present solution applied to anisotropic plates. Before commenting on that, I have to make it clear that the caption in Table 2 of 1 was erroneous. The convergence result in the table was for a specially orthotropic square plate. (i.e., anisotropic plate with a fiber orientation angle θ=0 deg), not for skew orthotropic square plates (θ=30 deg). This was obvious that the converged values in Table 2 are in exact agreement with those of specially orthotropic plates in Table 5 of 1.Professor Bert stated that “it (Ritz method) converges rather slowly in the case of anisotropic plates.” I agree that the Ritz method tends to give slower convergence for anisotropic plates than for isotropic and specially orthotropic plates, but this tendency is also found for other methods and the important question is how slow the solution becomes. To see this, another test is conducted here to observe convergence rates of the present method for highly anisotropic material. Q11/Q22=25,Q12/Q22=0.25andQ66/Q22=0.5used in reference 2. This material has stronger anisotropy EL/ET=25 than that EL/ET=15.4 used in (1).Table 1 presents convergence test results of diagonally orthotropic square plates (θ=45 deg) with such material for boundary conditions of FFFF (free plate). SSSS (simply supported plate), CCCC (clamped plate), and CFFF (cantilever plate). Frequency parameters (1)Ω=ωa2ρh/D01/2withareferencestiffnessD0=ETh2/121−vLTvTLare presented with four significant figures for the number of terms M×N=6×6∼14×14(4×4∼16×16 for SSSS) in Eq. (15) of 1, and underlined figures are converged values within the range of our significant figures. It is seen that two extreme cases of the FFFF (totally free plate with only natural boundary conditions) and the CCCC (the most constrained plate with only geometrical boundary conditions) plates do yield fast convergence, while the SSSS plate with both natural and geometrical boundary conditions does slower convergence, particularly for the fundamental mode.The convergence behaviors of some different solutions are compared for the fundamental frequency of the SSSS plate in reference 2. The present values are converted to their frequency parameter (2)W=ωb2ρ/Q22h21/2and are shown in Fig. 1 with those presented in Fig. 4 of 2. It is observed that the present Ritz method gives much better upper bound than the Ritz result of Ashton and approaches closely to the lower bound of the Fourier analysis and DQ method. This figure therefore indicates that the convergence rate of the Ritz method is rather dependent on the choice of displacement functions.The present author has an opinion that use of the Ritz method with (modified) polynomial functions yields very accurate upper bounds with advantages in applying to arbitrary boundary conditions and in computation time, when it is used with the following points in mind (3).In summary, the Ritz method with modified polynomials is a valuable and recommendable approach. The only problem is that because it is very easy to use and guarantees good accuracy, one cannot escape this easiness and does not create new methodology.

Viscoelastic versus radiation damping in fluid‐loaded constrained plates

A hybrid model was developed for the analysis of constrained‐layer damping whereby the base plate is described by exact elasticity theory, while the elastomer and constraining layers are analogous to Kerwin's model [J. Acoust. Soc. Am. 31, 952–962 (1959)]. Under fluid loading, the success of the technique is measured by a damping efficiency, the ratio of loss in the elastomer to the total loss due to viscoelastic and radiation damping. This efficiency is usually evaluated by combining the viscoelastic loss from a composite plate in vacuum, for antisymmetric and symmetric waves separately with the radiation loss from a single fluid‐loaded plate. This assumes simple addition of the two effects for a fluid‐loaded constrained plate. Extension of the hybrid model to include fluid loading shows that at higher frequencies the presence of the two types of waves redistributes the energy across the plate, invalidating the presumed additive property. Thus it proves necessary to compute damping efficiency from analysis of the fluid‐loaded composite plate with inclusion of both antisymmetric and symmetric waves. [Work supported by the ONR.]