Stability state evaluation of composite three-layered annular plates with asymmetrical damage

The paper presents the response of a three-layered annular plate with damaged laminated facings to the loads acting in their planes. The presented problem concerns the analysis of the combination of global plate failure in the form of buckling with the local micro defects, like fibre or matrix cracks, located in the laminas. The plate structure consists of thin laminated, fibre-reinforced composite facings and a thicker foam core. The matrix and fibre cracks of facings laminas can be transversally symmetrically or asymmetrically located in plate structure. Critical static and dynamic stability analyses were carried out solving the problem numerically and analytically. The numerical results show the static and dynamic stability state of the composite plate with different combinations of damages. The final results are compared with those for undamaged structure of the plate and treated as quasi-isotropic ones. The analysed problem makes it possible to evaluate the use of the non-ideal composite plate structure in practical applications

Influence of Parameters of Core Bingham Material on Critical Behaviour of Three-Layered Annular Plate

The paper presents the dynamic response of annular three-layered plate subjected to loads variable in time. The plate is loaded in the plane of outer layers. The plate core has the electrorheological properties expressed by the Bingham body model. The dynamic stability loss of plate with elastic core is determined by the critical state parameters, particularly by the critical stresses. Numerous numerical observations show the influence of the values of viscosity constant and critical shear stresses, being the Bingham body parameters, on the supercritical viscous fluid plate behaviour. The problem has been solved analytically and numerically using the orthogonalization method and finite difference method. The solution includes both axisymmetric and asymmetric plate dynamic modes

Dynamic Response of Three-Layered Annular Plate with Imperfections

This paper presents the imperfection sensitivity of annular plate with three-layered structure. The plate composed of thin elastic facings and a thicker elastic core is loaded in facing plane. The classical issue of a three-layered plate was solved for dynamic deflection problem using the approximation methods: orthogonalization and finite difference. The solution includes the axisymmetric and asymmetric plate modes of the dynamic stability loss. The evaluation of the rate of plate sensitivity to imperfection of plate preliminary geometry has been enriched by the analysis of plate models built of finite elements. The ABAQUS program has been used. The numerous calculation results in the form of deflection characteristics, buckling modes, values of critical parameters create the view of response of dynamic plate structure with different rate of imperfection and linear in time loading growth, too

Dynamic stability of three-layered annular plates with viscoelastic core

Rozwiązanie zagadnienia ugięć warstwowych, w tym trójwarstwowych, przekładkowych płyt pierścieniowych prowadzące do oceny ich obciążeń krytycznych jest bardzo często ograniczone do rozwiązania szczególnego przypadku płyt, których postać wyboczenia jest obrotowo symetryczna. Możliwość utraty stateczności płyty poddanej obciążeniom działającym zwłaszcza na jej zewnętrzny brzeg, w postaci kilku lub nawet kilkunastu fal obwodowych odpowiadających minimalnym wartościom obciążenia krytycznego, wymaga przeprowadzenia złożonego, ogólnego rozwiązania problemu i wykorzystania metod numerycznych.The solution of the layered, in this work three-layered, annular plates leading to the evaluation of their critical loads is very often limited to the solution of the special case of plates with the axially-symmetrical form of buckling. The possibility of the loss of plate stability, particularly for plates loaded on the outer perimeter, in the form of several or even a dozen or so circumferential waves corresponding to the minimal value of plate critical load requires realization of the complex, general solution of the problem with using the numeric methods. The solution based on the approximate methods: orthogonalization and discretization with finite differences for three-layered plate structure composed of geometrically nonlinear, thin outer layers and soft, thicker core with viscoelastic properties is presented in this work. Obtained values of critical, static loads of plates and the time histories of maximum plate deflections are the results of calculations. The critical values of time, load and deflection, which determine the dynamic response of examined plate have been denoted for the accepted criterion of the loss of plate dynamic stability. The detailed analysis of plates critical behaviours have been conducted for various plate parameters, like: geometrical, material, connected with the load and initial shape imperfections. Among other things, one can take notice of the observed cases of decrease in the values of critical, dynamic loads below the values of critical static loads of plates

Temperature Effect on Stability of Clamped–Clamped Composite Annular Plate with Damages

The paper presents the response of a three-layered annular plate with different damaged laminate facings to the action of the static or dynamic temperature field model. Various damages of laminate, composite facings change the plate structure reaction under the temperature fields. Obtained results indicate practical meaning of analyses in failure diagnostic process. The thermal sensitivity of two kinds of plate structures, undamaged and damaged, offers both new practical and scientific possibilities in evaluation of the plate behavior. The relations between macro-damage, i.e., the buckling of the plate structure and micro-damages of plate layers subjected to temperature gradient, are shown. The numerical solution is proposed as the most effective in examinations of the various transversally symmetrical and asymmetrical plate structures with a different rate of damages. The graphical distribution of changes in values of static and dynamic critical loads illustrate the process of structural damaging during its exploitation. They have practical importance in the evaluation of the structure capacity. The knowledge of the effect of laminate degradation process on plate buckling phenomenon located in thermal environment complements previous investigations and designates complex, multi-parameter problems as having scientifically new elements

Static Stability of Composite Annular Plates with Auxetic Properties

This paper presents an evaluation of the static stability of complex, composite annular plates with layers having auxetic properties. The main objective of the numerical investigations is the development of a plate model, which uses an approximate solution based on orthogonalization and finite difference methods. The three-layered plate is composed of auxetic facings and a soft, foam core. The material properties of the facings are characterized by Poisson’s ratio, the values of which are variously positive and negative. The results obtained for an auxetic plate were compared on the basis of the results for a plate with traditional facings and a plate model built of finite elements. Additionally, in order to verify the calculation results, an analysis of the homogeneous plate was performed. Two plate models built of finite differences and finite elements were compared. The wide image of buckling responses of the examined plates was created on the basis of the calculation results of both compressed and radially stretched plates. An increase in the values of the critical static loads with increasing absolute value of Poisson’s ratio of auxetic facings is one of the observations

Dynamic stability of mechanically and thermally loaded three-layered annular plate with viscoelastic core

The problem of dynamic stability of composite three-layered annular plate with viscoelastic core is the subject of the consideration. Plate composed of thin outer layers and soft core is loaded quickly in time with forces compressing facings and with temperature gradient in radial direction. Two kinds of plate support system are analysed: plate slideably clamped in thermo-mechanical problem and plate clamped on both edges in thermal analysis. The analytical and numerical solution, which is based on the orthogonalization and finite difference methods includes axisymmetric and asymmetric forms of buckling and rheological properties of plate core

Dynamic behaviour of three-layered annular plates with viscoelastic core under lateral loads

This paper presents the dynamic behaviour of three-layered, annular plates with a linear viscoelastic core. The annular plate is loaded in plane of facings with variable in time forces acting on the inner or outer plate edges. The analysed plate structure is symmetric and composed of three-layers: thin facings and a thicker, soft core. The core material is considered as linear with viscoelastic properties. Analytical and numerical solution will be presented including the wavy forms of dynamic loss of plate stability. In the analytical and numerical solution, two approximation methods: orthogonalization and finite difference have been applied to obtain the system of differential equations for the analysed problem of dynamic deflections of the examined plate with the viscoelastic core. Additionally, the suitable plate model using the finite element method has been built. The numerical calculations carried out in ABAQUS system show the results which are compatible with those obtained for the analytical and numerical solution. Presented in figures time histories of plate deflections and velocity of deflections as well as buckling forms of the plate model show the dynamic response of the examined plate on time-dependent loads and core material propertie

Impact of Vitamin D Supplementation during Lactation on Vitamin D Status and Body Composition of Mother-Infant Pairs: A MAVID Randomized Controlled Trial

<div><p>Objective</p><p>The optimal vitamin D intake for nursing women is controversial. Deterioration, at least in bone mass, is reported during lactation. This study evaluated whether vitamin D supplementation during lactation enhances the maternal and infant’s vitamin D status, bone mass and body composition.</p><p>Design and Methods</p><p>After term delivery, 174 healthy mothers were randomized to receive 1200 IU/d (800 IU/d+400 IU/d from multivitamins) or 400 IU/d (placebo+400 IU/d from multivitamins) of cholecalciferol for 6 months while breastfeeding. All infants received 400 IU/d of cholecalciferol. Serum 25-hydroxyvitamin D [25(OH)D], iPTH, calcium, urinary calcium, and densitometry were performed in mother-offspring pairs after delivery, and at 3 and 6 months later.</p><p>Results</p><p>A total of 137 (79%) (n = 70; 1200 IU/d, n = 67; 400 IU/d) completed the study. 25(OH)D was similar in both groups at baseline (13.7 ng/ml vs. 16.1 ng/ml; <i>P = </i>0.09) and at 3 months (25.7 ng/ml vs. 24.5 ng/ml; <i>P</i> = 0.09), but appeared higher in the 1200 IU/d group at 6 months of supplementation (25.6 ng/ml vs. 23.1 ng/ml; <i>P</i> = 0.009). The prevalence of 25(OH)D <20 ng/ml was comparable between groups at baseline (71% vs. 64%, <i>P</i> = 0.36) but lower in the 1200 IU/d group after 3 months (9% vs. 25%, <i>P</i> = 0.009) and 6 months (14% vs. 30%, <i>P</i> = 0.03). Maternal and infants’ iPTH, calciuria, bone mass and body composition as well as infants’ 25(OH)D levels were not significantly different between groups during the study. Significant negative correlations were noted between maternal 25(OH)D and fat mass (R = −0.49, <i>P</i> = 0.00001), android fat mass (R = −0.53, <i>P</i> = 0.00001), and gynoid fat mass (R = −0.43, <i>P</i> = 0.00001) after 6 months of supplementation.</p><p>Conclusions</p><p>Vitamin D supplementation at a dose of 400 IU/d was not sufficient to maintain 25(OH)D >20 ng/ml in nursing women, while 1200 IU/d appeared more effective, but had no effect on breastfed offspring vitamin D status, or changes in the bone mass and the body composition observed in both during breastfeeding.</p><p>Trial Registration</p><p>ClinicalTrials.gov <a href="http://clinicaltrials.gov/" target="_blank">NCT01506557</a></p></div