A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

Energy absorption behaviours of CSM-based GFRC plates with hemispherical features

In the present study, the mechanical behaviour of CSM (chopped strand mat)-based GFRC (glass fibre-reinforced composite) plates with single and multiple hemispheres under compressive loads has been investigated both experimentally and numerically. The basic stress-strain behaviours arc identified with quasi-static tests on two-ply coupon laminates and short cylinders, and these are followed up with compressive tests in a UTM (universal testing machine) on single- and multiple-hemisphere plates. The ability of an explicit LS-DYNA solver in predicting the complex material behaviour of composite hemispheres, including failure, is demonstrated. The relevance and scalability of the present class of structural components as `force-multipliers' and `energy-multipliers' have been justified by virtue of findings that as the number of hemispheres in a panel increased from one to four, peak load and average absorbed energy rose by factors of approximately four and six, respectively. The performance of a composite hemisphere has been compared to similar-sized steel and aluminium hemispheres, and the former is found to be of distinctly higher specific energy than the steel specimen. A simulation-based study has also been carried out on a composite 2 x 2-hemisphere panel under impact loads and its behaviour approaching that of an ideal energy absorber has been predicted. In summary, the present investigation has established the efficacy of composite plates with hemispherical force multipliers as potential energy-absorbing countermeasures and the suitability of CAE (computer-aided engineering) for their design.

VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

A note on the inverse mode shape problem for bars, beams, and plates

Motivated by the idea of designing a structure for a desired mode shape, intended towards applications such as resonant sensors, actuators and vibration confinement, we present the inverse mode shape problem for bars, beams and plates in this work. The objective is to determine the cross-sectional profile of these structures, given a mode shape, boundary condition and the mass. The contribution of this article is twofold: (i) A numerical method to solve this problem when a valid mode shape is provided in the finite element framework for both linear and nonlinear versions of the problem. (ii) An analytical result to prove the uniqueness and existence of the solution in the case of bars. This article also highlights a very important question of the validity of a mode shape for any structure of given boundary conditions.

Improvement in Bone Properties by Using Risedronate Adsorbed Hydroxyapatite Novel Nanoparticle Based Formulation in a Rat Model of Osteoporosis

A superior drug formulation capable of achieving efficient osteogenesis is in imperative demand for the treatment of osteoporosis. In the present study we investigated the potential of using novel risedronate-hydroxyapatite (HA) nanoparticle based formulation in an animal model of established osteoporosis. Nanoparticles of HA loaded with risedronate (NHLR) of various sizes (80-130 nm) were generated for bone targeted drug delivery. Three months after ovariectomy, 36 ovariectomized (OVX) rats were divided into 6 equal groups and treated with various doses of NHLR (500,350 and 250 mu g/kg intravenous single dose) and sodium risedronate (500 mu g/kg, intravenous single dose). Untreated OVX and sham OVX served as controls. One month after drug administration, the left tibia and femur were tested for bone mechanical properties and histology, respectively. In the right femur, bone density was measured by method based on Archimedes principle and bone porosity analyses were performed using X-ray imaging. NHLR (250 mu g/kg) showed a significant increase in bone density and reduced bone porosity when compared with OVX control. Moreover, NHLR (250 mu g/kg) significantly increased bone mechanical properties and bone quality when compared with OVX control. The results strongly suggest that the NHLR, which is a novel nanoparticle based formulation, has a therapeutic advantage over risedronate sodium monotherapy for the treatment of osteoporosis in a rat model of postmenopausal osteoporosis.

Homocysteine alters the osteoprotegerin/RANKL system in the osteoblast to promote bone loss: pivotal role of the redox regulator forkhead O1

In this study we determined the molecular mechanisms of how homocysteine differentially affects receptor activator of nuclear factor-kappa B ligand (RANKL) and osteoprotegerin (OPG) synthesis in the bone. The results showed that oxidative stress induced by homocysteine deranges insulin-sensitive FOXO1 and MAP kinase signaling cascades to decrease OPG and increase RANKL synthesis in osteoblast cultures. We observed that downregulation of insulin/FOXO1 and p38 MAP kinase signaling mechanisms due to phosphorylation of protein phosphatase 2 A (PP2A) was the key event that inhibited OPG synthesis in homocysteine-treated osteoblast cultures. siRNA knockdown experiments confirmed that FOXO1 is integral to OPG and p38 synthesis. Conversely homocysteine increased RANKL synthesis in osteoblasts through c-Jun/JNK MAP kinase signaling mechanisms independent of FOXO1. In the rat bone milieu, high-methionine diet-induced hyperhomocysteinemia lowered FOXO1 and OPG expression and increased synthesis of proresorptive and inflammatory cytokines such as RANKL, M-CSF, IL-1 alpha, IL-1 beta, G-CSF, GM-CSF, MIP-1 alpha, IFN-gamma, IL-17, and TNF-alpha. Such pathophysiological conditions were exacerbated by ovariectomy. Lowering the serum homocysteine level by a simultaneous supplementation with N-acetylcysteine improved OPG and FOXO1 expression and partially antagonized RANKL and proresorptive cytokine synthesis in the bone milieu. These results emphasize that hyperhomocysteinemia alters the redox regulatory mechanism in the osteoblast by activating PP2A and deranging FOXO1 and MAPK signaling cascades, eventually shifting the OPG:RANKL ratio toward increased osteoclast activity and decreased bone quality (C) 2013 Elsevier Inc. All rights reserved.

Scaffolds for bone tissue engineering: role of surface patterning on osteoblast response

The fabrication of tissue engineering scaffolds necessitates amalgamation of a multitude of attributes including a desirable porosity to encourage vascular invasion, desired surface chemistry for controlled deposition of calcium phosphate-based mineral as well as ability to support attachment, proliferation, and differentiation of lineage specific progenitor cells. Scaffold fabrication often includes additional surface treatments to bring about desired changes in the surface chemistry. In this perspective, this review documents the important natural and synthetic scaffolds fabricated for bone tissue engineering applications in tandem with the surface treatment techniques to maneuver the biocompatibility of engineered scaffolds. This review begins with a discussion on the fundamental concepts related to biocompatibility as well as the characteristics of the biological micro-environment. The primary focus is to discuss the effects of surface micro/nano patterning on the modulation of bone cell response. Apart from reviewing a host of experimental studies reporting the functionality of osteoblast-like bone cells and stem cells on surface modified or textured bioceramic/biopolymer scaffolds, theoretical insights to predict cell behavior on a scaffold with different topographical features are also briefly analyzed.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

Methionine down-regulates TLR4/MyD88/NF-kappa B signalling in osteoclast precursors to reduce bone loss during osteoporosis

Background and PurposeStudies have demonstrated that a moderate intake of amino acids is associated with development of bone health. Methionine, a sulphur-containing essential amino acid, has been largely implicated for improving cartilage formation, however its physiological significance on bone integrity and functionality have not been elucidated. We investigated whether methionine can prevent osteoporotic bone loss. Experimental ApproachThe anti-resorptive effect of methionine, (250mgkg(-1) body wt administered in drinking water for 10 weeks), was evaluated in ovariectomized (OVX) rats by monitoring changes in bone turnover, formation of osteoclasts from blood-derived mononuclear cells and changes in the synthesis of pro-osteoclastogenic cytokines. Key resultsMethionine improved bone density and significantly decreased the degree of osteoclast development from blood mononuclear cells in OVX rats, as indicated by decreased production of osteoclast markers tartarate resistant acid phosphatase b (TRAP5b) and MIP-1. siRNA-mediated knockdown of myeloid differentiation primary response 88 MyD88], a signalling molecule in the toll-like receptor (TLR) signalling cascade, abolished the synthesis of both TRAP5b and MIP-1 in developing osteoclasts. Methionine supplementation disrupted osteoclast development by inhibiting TLR-4/MyD88/NF-B pathway. Conclusions and ImplicationsTLR-4/MyD88/NF-B signalling pathway is integral for osteoclast development and this is down-regulated in osteoporotic system on methionine treatment. Methionine treatment could be beneficial for the treatment of postmenopausal osteoporosis.

Multifunctional Properties of Multistage Spark Plasma Sintered HA-BaTiO3-Based Piezobiocomposites for Bone Replacement Applications

This work reports the processing-microstructure-property correlation of novel HA-BaTiO3-based piezobiocomposites, which demonstrated the bone-mimicking functional properties. A series of composites of hydroxyapatite (HA) with varying amounts of piezoelectric BaTiO3 (BT) were optimally processed using uniquely designed multistage spark plasma sintering (SPS) route. Transmission electron microscopy imaging during in situ heating provides complementary information on the real-time observation of sintering behavior. Ultrafine grains (0.50m) of HA and BT phases were predominantly retained in the SPSed samples. The experimental results revealed that dielectric constant, AC conductivity, piezoelectric strain coefficient, compressive strength, and modulus values of HA-40wt% BT closely resembles with that of the natural bone. The addition of 40wt% BT enhances the long-crack fracture toughness, compressive strength, and modulus by 132%, 200%, and 165%, respectively, with respect to HA. The above-mentioned exceptional combination of functional properties potentially establishes HA-40wt% BT piezocomposite as a new-generation composite for orthopedic implant applications.

Detonation-driven-shock wave interactions with perforated plates

The study of detonations and their interactions is vital for the understanding of the high-speed flow physics involved and the ultimate goal of controlling their detrimental effects. However, producing safe and repeatable detonations within the laboratory can be quite challenging, leading to the use of computational studies which ultimately require experimental data for their validation. The objective of this study is to examine the induced flow field from the interaction of a shock front and accompanying products of combustion, produced from the detonation taking place within a non-electrical tube lined with explosive material, with porous plates with varying porosities, 0.7-9.7%. State of the art high-speed schlieren photography alongside high-resolution pressure measurements is used to visualise the induced flow field and examine the attenuation effects which occur at different porosities. The detonation tube is placed at different distances from the plates' surface, 0-30 mm, and the pressure at the rear of the plate is recorded and compared. The results indicate that depending on the level of porosity and the Mach number of the precursor shock front secondary reflected and transmitted shock waves are formed through the coalescence of compression waves. With reduced porosity, the plates act almost as a solid surface, therefore the shock propagates faster along its surface.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition. (C) 2013 Elsevier Masson SAS. All rights reserved.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.