Edge Loading Research Articles

Stability Performance of Perforated Stiffened Laminated Composite Plates Under the Influence of Environmental and Operational Loading Conditions Using FE Approach

Eccentrically stiffened plates are widely used as a structural component in many engineering applications. However, these structures are exposed to complex loading conditions, resulting in strength reduction leading to failure. This research aims to examine the stability performance of the perforated stiffened laminated composite plate subjected to non-uniform edge load under the influence of environmental conditions. Towards this, a robust and computationally efficient finite element (FE) formulation has been developed, where the plate is modeled using a 9-noded heterosis element to avoid the shear locking of the plate element and a 3-noded isoparametric beam element is adopted to model the stiffener by applying a displacement compatibility condition at the skin-stringer interface. A torsion correction factor is introduced in the beam formulation to account for the twisting of the stiffener. A unique dynamic technique is utilized to obtain the buckling load by employing two types of boundary conditions due to the non-uniform stress distribution in the perforated plate under environmental and operational loading conditions. An analysis is performed on the unstiffened plate to determine a suitable cutout shape, loading pattern and lamina scheme based on its improved stability performance. Unlike previous studies, several stiffener configurations are considered to comprehend the influence of temperature and moisture on the stability behavior of centrally placed cutout plates and obtain a stiffener configuration with improved performance. It is noticed that when the perforated stiffened plate is exposed to thermal or hygroscopic load close to a critical temperature or moisture, the buckling capacity drops suddenly in the plate attached to a stiffener of greater depth. Moreover, it is observed that when the stiffened plate is exposed to higher intensity of hygrothermal load, the plate’s buckling capacity drops significantly as the thickness of the plate reduces.

Nonlinear vibration characteristics of pre- and post-buckled FG-GRMMC laminated plates with in-plane auxeticity

The nonlinear vibration of a laminated plate constituting of graphene reinforced metal matrix composite (GRMMC) materials possessing in-plane negative Poisson’s ratio in pre- and post-buckled status is investigated in this work. The volume fraction of graphene remains constant in each layer but changes along the thickness direction of the plate to obtain functionally graded (FG) patterns. The plate rests on a Pasternak-type foundation and the post-buckling state of the plate is only caused by the thermal load or the compressive edge load. The nonlinear motion equations of the plate with the effect of the out-of-plane shear deformation are established and then solved by a two-step perturbation approach. The perturbation solutions provide a platform to study the influences of the FG arrangement, volume fraction of graphene and foundation stiffness on the post-buckled vibration of FG-GRMMC laminated plates. As the GRMMC material properties are dependent on temperature, the thermal effect on the linear and nonlinear frequencies of the plates for compressive post-buckling is also investigated. The numerical results of the linear and nonlinear frequencies of post-buckled FG GRMMC laminated plates under thermal and compressive loads are respectively illustrated and discussed in detail.

Combined kinematic cup alignment reduces the rate of impingement and edge loading compared to mechanical and anatomical alignment. An in-vitro case-control study

IntroductionIn recent years, different alignments have been described for acetabular components in total hip arthroplasty (THA), to reduce the risk of impingement and edge loading. Currently there are 3 main options: mechanical (40° inclination/15° anteversion relative to the anterior pelvic plane), anatomic (40° inclination/anteversion parallel to the transverse ligament) and combined kinematic (according to spinal-pelvic parameters). There are no studies comparing all three in terms of impingement and edge loading. We therefore performed a retrospective case-control in-vitro study comparing risk of impingement and edge loading between the three alignments. HypothesisThe study hypothesis was that combined kinematic alignment incurs significantly less risk of impingement and edge loading than do the other two types of alignment. MethodsUsing a THA planning system, we simulated the 3 alignments for 90 patients undergoing THA with a ceramic-on-ceramic bearing between November 2019 and January 2022; for each simulation, we recorded any prosthetic impingement or edge loading. The study endpoint was the rate of prosthetic impingement or edge loading between the 3 alignments. ResultsWith the mechanical alignment, 31% of patients (28/90) showed risk of impingement and 22% (20/90) risk of edge loading. With the anatomic alignment, 31% of patients (28/90) showed risk of impingement and 23.3% (21/90) risk of edge loading. With the combined kinematic alignment, 12.2% of patients (11/90) showed risk of impingement and 8.9% (8/90) risk of edge loading. Pairwise comparison showed that the combined kinematic alignment was associated with significantly less impingement and edge loading than the mechanical alignment (respectively, p=0.03 and p=0.022) or the anatomic alignment (respectively, p=0.03 and p=0.014), while the mechanical and anatomic alignments did not differ. ConclusionA combined kinematic cup alignment in THA significantly reduced the risk of impingement and edge loading compared to mechanical and anatomic alignments. Level of evidenceIII, retrospective case-control study.

Arthroscopic Femoral and Acetabular Osteoplasties Alter the In Vivo Hip Kinematics of Patients With Femoroacetabular Impingement

Three-dimensional (3D)-two-dimensional (2D) fluoroscopic image registration was used to measure 3D hip kinematics before and after hip arthroscopy in patients with femoroacetabular impingement (FAI). In total, 24 subjects diagnosed with FAI (21 unilateral, 3 bilateral) were prospectively recruited. A clinical impingement test was performed on both hips while the patient was awake and then while anaesthetized, and in the operative hip after arthroscopic osteoplasties and labral repair. Fluoroscopy was used to image the hip during the impingement tests. Images were analyzed using 3D-2D image registration to calculate joint kinematics. The examiner's hand was instrumented with a glove to measure internal rotation torque applied to the hip during each test. Internal rotation increased by 3.7° (standard error [SE] 0.95°) after surgery (P= .001). Maximum displacement of the femoral head out of the acetabulum was 4.0 mm (SE 0.5 mm) in the operative group before surgery and 1.8 mm (SE 0.3 mm) after surgery (P < .001). This was due to a decrease in lateral displacement by 1.3 mm (SE 0.4 mm, P= .002) and proximal displacement by 0.8 mm (SE 0.3 mm, P= .013). Internal rotation torque was greater in the operative hips when anaesthetized compared with when awake, by 5 Nm (SE 1.2 Nm, P < .001), and greater in the contralateral hips than the operative hips when awake by 8.4 Nm (SE 1.4 mm, P < .001). Arthroscopic osteoplasty and labral repair increased hip range of motion and reduced femoral head displacement from the acetabulum during the IR90 provocation test (i.e., hip flexion to 90°, maximum internal rotation) in patients with FAI. This suggests that the impinging acetabular rim acted as a fulcrum before surgery and may have caused edge loading that was reduced after surgery. Level IV case series, therapeutic study.

An experimental study of the stiffness and strength of cross-laminated timber wall-to-floor connections under compression perpendicular to the grain

In platform-type multi-story cross-laminated timber (CLT) buildings, gravity loads from upper floors, and vertical reaction forces from horizontal actions, like wind loads, cause substantial compressive forces in the CLT-floor elements. The combination of these high forces with a comparable low compression stiffness and strength perpendicular to the grain of timber, makes the compression perpendicular to the grain (CPG) verification of CLT an important design criterion. In this experimental study, CPG of CLT was investigated by means of typical wall-to-floor connections in CLT platform-type structures. CLT-wall elements were used for load application to transmit forces through the CLT-floor element by CPG. Compared to load application by steel elements, as it commonly is done in experiments, lower stiffness but similar strength were found for CLT walls. The study of different connection types showed the highest stiffness and strength for connections assembled with screws, followed by pure wood-to-wood contact, while connections with acoustic layers between the floor and wall elements showed the lowest stiffness and strength. In addition, these connections were tested for center and edge load position on the CLT-floor element. The strength for center and edge position compared to full surface loaded specimens increased linearly with the activated material volume, as determined by earlier proposed stress dispersion models. The stress dispersion effect was visualized by surface strain measurements using digital image correlation technique. Also, the stiffness increased with the activated material volume. Stress dispersion in the CLT-floor allowed to explain the increase in stiffness and strength with decreasing CLT-wall thickness. Strength values at different strain levels, and stiffness and strength increase factors suitable for the engineering design of CLT structures are provided.

Pre-buckling vibration and buckling analyses of composite skew plate: An analytical investigation

In this work, the analytical investigation for pre-buckling vibration and buckling analyses of a composite skew plate subjected to parabolically and linearly varying in-plane edge load are presented. When the composite skew plate is subjected to parabolic (non-uniform) in-plane edge loading, the pre-buckling stresses within the composite skew plate are not known a priori. To estimate the pre-buckling stresses within the composite skew plate for which the in-plane elasticity problem is solved by minimizing the membrane strain energy using the Ritz method. It is observed that the rate of diffusion of applied parabolic in-plane edge load within the skew plate to a state of uniform in-plane stress is faster in the case of isotropic material than composite material. Using estimated pre-buckling stresses, the total energy functional is derived from the total strain energy, potential energy, and kinetic energy. The total energy functional is reduced into sets of an ordinary differential equation and algebraic equation, respectively for pre-buckling vibration and buckling problems using the Ritz method in conjunction with BCOPs. The associated linear eigenvalue problems are solved to compute the pre-buckling vibration frequency and buckling load of the stressed skew plate. The outcome of the study may provide crucial inputs in the design of skewed bridge decks, ship structures, and aircraft wing design.

Collaborative Task Offloading and Service Caching Strategy for Mobile Edge Computing

Mobile edge computing (MEC), which sinks the functions of cloud servers, has become an emerging paradigm to solve the contradiction between delay-sensitive tasks and resource-constrained terminals. Task offloading assisted by service caching in a collaborative manner can reduce delay and balance the edge load in MEC. Due to the limited storage resources of edge servers, it is a significant issue to develop a dynamical service caching strategy according to the actual variable user demands in task offloading. Therefore, this paper investigates the collaborative task offloading problem assisted by a dynamical caching strategy in MEC. Furthermore, a two-level computing strategy called joint task offloading and service caching (JTOSC) is proposed to solve the optimized problem. The outer layer in JTOSC iteratively updates the service caching decisions based on the Gibbs sampling. The inner layer in JTOSC adopts the fairness-aware allocation algorithm and the offloading revenue preference-based bilateral matching algorithm to get a great computing resource allocation and task offloading scheme. The simulation results indicate that the proposed strategy outperforms the other four comparison strategies in terms of maximum offloading delay, service cache hit rate, and edge load balance.

Mid-term survivorship of fixed bearing unicondylar knee arthroplasty with no exclusion of early PFJ arthritis or ACL deficiency: Analysis of clinical and radiological predictors.

Fixed bearing (FB) UKA constituted 63.7% of unicondylar knee arthroplasties in 2020 Australian Registry with the longest UKA survivorship. The significance of patellofemoral joint (PFJ) arthritis, ACL deficiency, post-operative anteromedial pain, radiosclerosis or radiolucency on survivorship of FB UKA is not established. The aim of this study was to analyze the medium-term survivorship of fixed-bearing UKA with no exclusion of PFJ OA and ACL deficiency. Predictors for failure were analyzed. FB UKA performed in 2011-17 were reviewed. Cases with PFJ OA or ACL deficiency were not excluded. The effect on survivorship by ACL deficiency, PFJ arthritis, post-operative anteromedial pain and radiological abnormalities were analyzed. There were 96 UKA with follow-up time of 66 ± 18months (27-98). The mean age was 70 ± 9years, BMI 25.8 ± 2.6kg/m2. Alignment was varus 9° ± 4° pre-operatively and varus 3° ± 3° post-operatively. There were four revisions (4.2%) and 4 deaths (4.2%). Reasons for revisions were loosening (n = 1), persistent pain (n = 2) and lateral compartment disease (n = 1). Estimated survival at 8.3years was 94.7% (95% CI 91.6-97.7). BMI ≥30 was found to be a significant predictor for failure. The incidence of radiographic abnormalities was 75% for PFJ arthritis, 39% for tibial tray overhang, 14% for radiolucency or radiosclerosis, 5% for ACL deficiency and 5% for edge loading respectively but they were not significantly associated with lower survivorship or anteromedial knee pain. The presence of anteromedial pain after surgery in 36.5% was also not significantly associated with survivorship. FB UKA with no exclusion of early PFJ arthritis and ACL deficiency has satisfactory medium-term survivorship. BMI ≥30 could have higher risk of all-cause revision. Tibial tray overhang, non-progressive radiolucency or radiosclerosis do not seem to be associated with anteromedial knee pain or poorer medium term survivorship.

Numerical Solution of the Two-Dimensional Elasticity Problem in Strains

Usually, the boundary value problems of the theory of elasticity are formulated with respect to displacements, and are reduced to the well-known Lame equations. Strains and stresses can be calculated from displacements as a solution to Lame's equation. Also known are the Beltrami Mitchell equations, which make it possible to formulate the boundary value problem of the theory of elasticity with respect to stresses. Currently, the boundary value problems of the theory of elasticity in stresses are studied in more detail in the two-dimensional case, and usually solved numerically with the introduction of the Airy stress function. But, the direct solution of boundary value problems of elasticity theory with respect to stresses requires further researches. This work, similarly to the boundary value problem in stresses, is devoted to the formulation and numerical solution of boundary value problems of the theory of elasticity with respect to deformations. The proposed boundary value problem consists of six Beltrami-Mitchell-type equations depending on strains and three equations of the equilibrium equation expressed with respect to deformations. As boundary conditions, in addition to the usual conditions for surface forces, three additional conditions are also introduced based on the equilibrium equations. The boundary value problem is considered in detail for a rectangular area. The discrete analogue of the boundary value problem is composed by the finite difference method. The convergence of difference schemes and an iterative method for their solution are studied. Software has been developed in the C++ environment for solving boundary value problems in the theory of elasticity and deformation. A number of boundary value problems on the deformation of a rectangular plate are solved numerically under various boundary conditions. The reliability of the obtained results is substantiated by comparing the numerical results, with the exact solution, as well as with the known solutions of the plate tension problems with parabolic and uniformly distributed edge loads.

What Changes in Pelvic Sagittal Tilt Occur 20 Years After THA?

Cup orientation in THA in the supine, standing, and sitting positions is affected by pelvic sagittal tilt (PT). Patterns of PT shift between these positions may increase the risk of dislocation and edge loading. The PT has also been reported to change during the aging process; however, there is limited research regarding long-term changes in PT and PT shifts after THA. (1) What changes occur in PT in the supine, standing, and sitting positions during 20 years of follow-up after THA in patients who have not had revision or dislocation? (2) What factors are associated with the differences between preoperative supine PT and postoperative sitting or standing PT (Δ sitting and Δ standing, respectively) 20 years postoperatively? Between January 1998 and December 1999, 101 consecutive patients underwent THA for appropriate indications. AP radiographs of the pelvis in the supine, standing, and sitting positions preoperatively and at 1, 10, and 20 years after THA were longitudinally performed to evaluate changes in PT. Fifty-nine percent (60 of 101) of patients were lost before 20 years of follow-up or had incomplete sets of imaging tests, leaving 41% (41 of 101) eligible for analysis here. There were no patients who had recurrent dislocation or underwent revision arthroplasty in the cohort; therefore, this analysis regarding postoperative changes in PT indicates the natural course of the change in PT during follow-up of THA. PT was measured based on the anterior pelvic plane. PT shifts with positional changes, Δ standing, and Δ sitting during the follow-up period were calculated. Posterior changes and shifts are represented by negative values. To analyze the factors associated with Δ standing and Δ sitting after 20 years, the correlations between these parameters and preoperative factors (including sex, age, pelvic incidence [PI], lumbar lordosis [LL], preoperative PT, and preoperative PT shift) and postoperative factors (including the occurrence of new lumbar vertebral fractures, lumbar spondylolisthesis, contralateral THA performed during follow-up, and PI-LL 20 years after THA) were determined. Median (IQR) supine and standing PTs changed (moved posteriorly) by -5° (-11° to -2°; p < 0.01) and -10° (-15° to -7°; p < 0.01), respectively. Sitting PT did not change during the 20-year follow-up period. Median (IQR) PT shift from standing to sitting changed from -34° preoperatively (-40° to -28°) to -23° after 20 years (-28° to -20°). There were posterior changes in median (range) Δ standing (median -12° at 20 years [-19° to -7°]); Δ sitting did not change during the follow-up period (median -36° at 20 years [-40° to -29°]). Patients with a large preoperative posterior PT shift from supine to standing demonstrated larger posterior tilt of Δ standing at 20 years. Patients with lumbar vertebral fractures during follow-up demonstrated larger posterior tilt of Δ standing at 20 years. Patients who demonstrate a large preoperative posterior shift from supine to standing deserve special consideration when undergoing THA. In such circumstances, we recommend that the anteversion of the cup not be excessive, given that there is a relatively high risk of further posterior tilt in PT, which may lead to anterior dislocation and edge loading. Further longitudinal study in a larger cohort of patients with complications including postoperative dislocation and revision, as well as older patients, is needed to verify these assumptions on the potential risk for dislocation and edge loading after THA. Level III, therapeutic study.

Dynamic instability analysis of perforated stiffened laminated composite panels subjected to non-uniform in-plane edge load under hygrothermal condition

A robust and computationally efficient finite element (FE) formulation has been developed in an effort to understand the parametric instability behaviour of a perforated stiffened composite panel subjected to a pulsating non-uniform edge load under a hygrothermal environment. The panel is modelled using a 9-noded heterosis element to avoid shear locking, whereas the stringer uses a 3-noded isoparametric beam element with a displacement compatibility condition employed at the skin–stringer​ interface. Due to the non-uniform distribution of stress in the perforated panel as a result of exposure to environmental and mechanical loading conditions, a unique dynamic technique has been implemented to account for the instability performance by employing two types of boundary conditions. In the current investigation, an unstiffened panel is initially obtained based on the highest value of the dynamic instability opening (DIO) and the unstable excitation frequency of the panel for different lamina schemes, cutout shapes, and loading conditions. The obtained unstiffened panel is further investigated for various stiffener configurations to determine a highly unstable perforated stiffened panel based on the DIO value and instability zone frequency range. Detailed parametric studies are then carried out considering the cutout sizes, cutout orientation, panel’s aspect ratio, and stiffener depth to understand the parametric instability behaviour of the panel in a hygrothermal environment. It is found that moisture significantly influences the dynamic instability behaviour of the perforated stiffened panel compared to the temperature exposure by shifting the instability zone towards the lower frequency. The width of the instability region of the stiffened panel broadens abruptly as the magnitude of the applied static in-plane edge load enhances. Also, for certain combinations of the dynamic and static load factors, the lower bound of the instability region reduces to zero, resulting in fluttering. In general, it is observed that stiffer the panel, wider is the instability zone with a higher unstable excitation frequency range.

Decay Conditions for Antiplane Shear of a High-Contrast Multi-Layered Semi-Infinite Elastic Strip

The antiplane shear of a semi-infinite multi-layered elastic strip with traction free faces and edges subject to prescribed stress is studied. A high contrast is assumed in the stiffnesses of two types of homogeneous isotropic layers. Explicit conditions on the edge load are derived, ensuring the decay of stress components at the distance of order strip thickness. One of these conditions corresponds to the canonical Saint-Venant’s principle, manifesting the self-equilibrium of the load. The rest of the decay conditions consider the presence of high contrast and are of an asymptotic nature, in contrast to the exact former condition. The number of asymptotic conditions is the same as that of soft layers. An example of the implementation of the proposed decay conditions for calculating the solution for the interior (outside of a boundary layer zone) domain of a three-layered semi-strip, considering geometric asymmetry, is presented.

Influence of porosity and nonuniform in-plane edge loads on vibration and buckling response of power law and sigmoid function based FG sandwich plates with geometrical discontinuities

Porosity defects can emerge during the manufacturing process of Functionally Graded Sandwich Plates (FGSPs). In practice, FGSPs have geometric discontinuities/cutouts and are exposed to Nonuniform In-plane Edge Loads (NIELs). The presence of porosity, cutout and NIELs causes a significant reduction in the stiffness of the plate affecting its vibration and buckling behavior. Therefore, in this paper vibration and buckling results obtained using the Finite Element (FE) method hitherto not reported in the literature are presented for porous FGSPs with cutouts and subjected to NIELs. Four types of porosity distribution models are explored, and the porosity imperfections are modeled as the criteria of stiffness reduction. Porosity-dependent material properties of FGSPs are evaluated using modified power law and sigmoid function. The current study incorporates two distinct kinds of sandwich configuration in such a way that there is no material mismatch along the thickness direction. The application of different cases of NIELs on the plate with cutouts leads to the development of nonuniform stresses. Hence a novel dynamic approach has been proposed to evaluate buckling loads by implementing two sets of boundary conditions. The first set of boundary conditions calculates pre-buckling stress, while second set calculates critical buckling loads. The generated results from the current FE formulation are compared with existing results in the literature to ensure accuracy. Finally, the effect of porosity distribution, NIELs, cutout ratio and its positions, support conditions, volume fraction exponents and geometric parameters on the vibration and buckling response are studied and discussed to arrive at appropriate conclusion.

Model-Based Acetabular Cup Orientation Optimization Based on Minimizing the Risk of Edge-Loading and Implant Impingement Following Total Hip Arthroplasty.

In this paper, a computationally efficient model-based method for determining patient-specific optimal acetabular cup alignment for total hip arthroplasty (THA) is presented. The proposed algorithm minimizes the risk of implant impingement and edge-loading, which are reported as the major causes of hip dislocation following THA. First, by using motion capture data recorded from the patient performing different daily activities, the hip contact force and the relative orientation of the femur and pelvis are calculated by a musculoskeletal model. Then, by defining two quantitative indices, i.e., angular impingement distance and angular edge-loading distance (AED), the risk of impingement and edge-loading are assessed for a wide range of cup alignments. Finally, three optimization criteria are introduced to estimate the optimal cup alignment with a tradeoff between the risk of impingement and edge loading. The results show that patient-specific characteristics such as pelvic tilt could significantly change the optimal cup alignment, especially the value of cup anteversion. Therefore, in some cases, the well-known Lewinnek safe zone may not be optimal, or even safe. Unlike other dynamic model-based methods, in this work, the need for force plate measurements is eliminated by estimating the ground reaction forces and moments, which makes this method more practical and cost-efficient. Furthermore, the low computational complexity due to analytical formulas makes this method suitable for both pre-operative and intra-operative planning.

Third-gradient continua: nonstandard equilibrium equations and selection of work conjugate variables

This paper outlines the variational derivation of the Lagrangian equilibrium equations for the third-gradient materials, stemming from the minimization of the total potential energy functional, and the selection of suitable dual variables to represent the inner work in the Eulerian configuration. Volume, face, edge and wedge contributions were provided through integration by parts of the inner virtual work and by repeated applications of the divergence theorem extended to embedded submanifolds with codimension one and two. Detailed expressions were provided for the contact pressures and the edge loading, revealing the complex dependence on the face normals and on the mean curvature. Relationships were specified among the Lagrangian (hyper-)stress tensors of rank lower or equal to four, and their Eulerian counterparts.

A Effect of Radial Clearance, Corner Radius and Micro Lateralization on Contact Stress of Metallic and Ceramic Hip Prosthesis

Edge loading leads to high contact stress at the rim of the contact. This is due to less radial clearance and excessive lateral head displacement which potentially causes implant failure. The ceramic implants have a high possibility of fracture compared with metallic implants because of above-said reasons. The present study focuses on the investigation of contact stress for the combined effect of radial clearance (0.05-0.75 mm) and micro-lateralisation conditions (1-2.5 mm) for Metal-on-Metal (M-o-M) and Ceramic-on-Ceramic (C-o-C) pairs. The contact stresses are analysed for round corners of the acetabulum cup geometry for the above-said combinations with four different arc radii (1- 4mm). Finite element modeling (FEM) of femur head with half of the acetabulum cup is considered for the current study. Contact stress values obtained for 2 mm and 4 mm round corner geometry are quite low when compared with 1 and 3 mm round corners even for larger radial clearances and high lateral head displacements. The study also showed von Mises stress value obtained for M-o-M pair is quite low for 4 mm round corner for larger radial clearance and high lateral head displacements. Similarly, in C-o-C pair the compressive stress values are minimum for 4 mm round corner. Since the stress values were minimum for 4 mm round corner geometry, it clearly indicates that even edge loading occurs and the round corner geometry would be very helpful in reducing the stress for both M-o-M and C-o-C pairs.

Postbuckling and postbuckled vibration behaviour of imperfect trapezoidal sandwich plates with FG-CNTRC face sheets under nonuniform loadings

The present work investigates the postbuckling, and postbuckled vibration behaviour of initially imperfect trapezoidal sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets and FG porous metal foam core under the influence of non-uniform edge compression. The plate's kinematic assumptions are based on a refined higher order theory and the strain-displacement relations include von Karman assumptions for geometrical nonlinearity. The weak form of governing equations derived using Hamilton's principle is transformed into a discretized form of algebraic equations using the element free Galerkin (EFG) method in conjunction with moving kriging (MK) interpolation functions. The pre-buckling stresses are determined using static analysis to evaluate accurate critical buckling loads. Modified Riks technique is used to trace nonlinear equilibrium paths. Parametric studies include the effect of CNT distribution in face sheets, porosity distribution in the core layer and edge loading conditions on the nonlinear stability and vibration behaviour of sandwich plates. New results on trapezoidal sandwich plates with initial imperfections, hitherto not found in the literature, are presented for the first time, which can be used as benchmark solutions for further research.

A semi-analytical approach for instability analysis of composite cylindrical shells subjected to harmonic axial loading

In this article, nonlinear vibration and dynamic stability analyses of simply supported laminated composite circular cylindrical shells subjected to periodic edge loading are carried out. A third-order shear deformation shell theory that considers all the nonlinear terms in all five kinematic parameters and rotary inertia is used to develop the present mathematical model so that the model is also valid for thick cylindrical shells. Hamilton’s principle, an energy-based approach, is used to obtain the governing partial differential equations (PDEs) of motion of the cylindrical shell. Further, these equations are reduced into ordinary differential equations by employing Galerkin’s method. The incremental harmonic balance (IHB) method in conjunction with the pseudo-arc-length method is used to obtain the frequency-amplitude response of the system. For obtaining the zone of instability regions, Bolotin’s method is adopted. For more practical significance, analysis of results is also extended by considering damping into account for the composite cylindrical shells. Time history response and phase portrait are plotted by adopting Newmark-beta method. The effects of the static load factor, dynamic load factor, modal damping coefficient, and stacking sequence on nonlinear vibration, instability regions and time history responses are also examined.

Understanding the differences in wear testing method standards for total knee replacement

Preclinical evaluation of the wear of total knee replacements (TKR) is usually undertaken using International Standards Organization (ISO) test methods. Two international standards for the preclinical wear simulation of TKRs have been developed; using either force or displacement control. In addition, based on previously published measured kinematics of healthy subjects, a gait cycle (displacement control) was also developed at the University of Leeds, which pre-dates the ISO displacement control standard. Furthermore, different test methods have adopted different approaches to defining the centres of rotation and polarity (direction of application) of motions. However, the effects of using these different control regimes and input conditions on the kinematics, contact mechanics, and wear of any one TKR have not been fully investigated previously.The current study investigated the kinematics, contact mechanics, and wear performance of a TKR when running under ISO force and displacement control test methods as well as the Leeds gait cycle inputs using experimental and computational simulation methods, with the aim of understanding the mechanical and tribological outcomes predicted by the different test method standard conditions. Three ISO wear testing standards were investigated using a mid-size Sigma curved TKR (DePuy, UK), with moderately cross-linked UHMWPE curved inserts; ISO-14243-3-2004, ISO-14243-3-2014 and ISO-14243-1-2009. In addition, the Leeds displacement control gait cycle was also investigated.According to the computational simulation predictions, reversing the anterior-posterior (AP) displacement and tibial rotation polarities in the displacement control ISO-2014 standard compared to the ISO-2004 standard resulted in high stress, of more than 65 MPa, at the posterior edge of the inserts with more than 10% increase in wear rate for this TKR design. Although Leeds gait input kinematics produced femoral rollback, it did not result in high stress edge loading on the posterior lip of the insert. This was attributed to different test input kinematics and different centres of rotation of the femoral component adopted in the displacement control standard ISO-2014 and Leeds gait test methods. The predicted AP displacement and tibial rotation from the force control ISO-2009 had different polarities and magnitudes to the corresponding displacement control profiles. In addition, the predicted wear rate, from the computational model, under the force control ISO-2009 standard was more than double that predicted under displacement control ISO standards due to the increased AP displacement and tibial rotation motions predicted under the force control standard.These major differences, in the mechanics and wear, between different test methods imply that each standard must therefore be used with its own predicate control results from a device with proven clinical history and results across different standards should never be compared, as the choice of test method standard may well be dependent on the design solution for the knee. Clinically, the kinematics in the population are extremely variable, which results in highly variable wear rates. While a standard method is necessary, on its own it is not adequate and needs to be supported by tests under a portfolio of representative conditions with different kinematic conditions, different soft tissue constraints, as well as with different alignments, so that the variability and range of wear rates expected clinically might be determined. This study enables further progress towards the definition of such a portfolio of representative conditions, by deepening the understanding of the relationships between currently used input conditions and the resulting mechanical and wear outputs.

An approach to describe edge ductility

One of the challenges of utilizing advanced high-strength steels is their limited ability to withstand the forming of cut edges. Large production quantities of parts often lead to mechanical punching/shearing processes in blank preparation, providing a challenging starting point for forming processes. The most commonly used edge ductility test is the ISO 16630 hole-expansion test to describe stretch-flangeability properties. However, this method has been widely criticized for its large-scatter, unreliable results and the fact that it covers only a certain stress-strain state of cut edge forming. In addition, it does not provide enough data to be reliably used in forming simulations to predict edge failures. This paper presents an approach to create a more comprehensive way of describing overall edge ductility. Multiple edge forming test methods coupled with digital image correlation (DIC) were selected in order to investigate different edge loading scenarios in both open and closed trim line forming situations. Data regarding limiting local strain before cracking was collected for several steel grades, and results are gathered in 2D and 3D “Edge FLC”-figures. Attempts to utilize these results for simulation purposes are also presented. Results indicate that this approach can be useful to evaluate overall edge forming limits.