Parthasarathi Mandal

Lateral-torsional buckling of beams and the Southwell plot

The Southwell plot is a well-known technique for determining experimentally the elastic critical load of a structure, without having to subject the structure to loading in the vicinity of critical. But several authors have suggested that when the structure is a beam which undergoes lateral-torsional buckling, a modified version of the Southwell plot is called for. In this paper we demonstrate that the modified form of the Southwell plot is not needed, and that the standard version is indeed satisfactory. We do this by plotting and re-plotting some experimental data; by drawing attention to some very clear work by Meck; and by explaining the practical coupling between the variables describing the lateral deflection and the rotation when lateral-torsional buckling occurs. Finally, we examine an argument based on symmetry which appears to support the idea that a modification of the standard Southwell plot is needed in the case of lateral-torsional buckling: but we show that a correct deployment of the argument from symmetry leads to the conclusion that the modified form of the Southwell plot is valid only for special, unrealistic cases.

Optimization of the position of the acetabulum in a ganz periacetabular osteotomy by finite element analysis

Periacetabular osteotomy (PAO) is a surgical procedure to correct acetabular orientation in developmental dysplasia of the hip (DDH). It changes the position of the acetabulum to increase femoral head coverage and distribute the contact pressure over the cartilage surface. The success of PAO depends significantly on the surgeons experience. Using computed tomography data from patients with DDH, we developed a 3D finite element (FE) model to investigate the optimal position of the acetabulum following PAO. A virtual PAO was performed with the acetabulum rotated in increments from the original center edge (CE) angle. Contact area, contact pressure, and Von Mises stress in the femoral and pelvic cartilage were analyzed. Five dysplastic hips from four patients were modeled. Contact area, contact pressure, and Von Mises stress in the cartilage all varied according to the change of CE angle through virtual PAO. An optimal position could be achieved for the acetabulum that maximizes the contact area while minimizing the contact pressure and von Mises stress in the pelvic and femoral cartilage. The optimal position of the acetabulum was patient dependent and did not always correspond to what would be considered a “normal” CE angle. We demonstrated for the first time the interrelation of correction angle, contact area, and contact pressure between the pelvic and femoral cartilage in PAO surgery.

Changes in the stress in the femoral head neck junction after osteochondroplasty for hip impingement: A finite element study

The surgical treatment of femoroacetabular impingement (FAI) often involves femoral osteochondroplasty. One risk of this procedure is fracture of the femoral neck. We developed a finite element (FE) model to investigate the relationship between depth of resection and femoral neck stress. CT data were used to obtain the geometry of a typical cam‐type hip, and a 3D FE model was constructed to predict stress in the head–neck after resection surgery. The model accounted for the forces acting on the head and abductor muscular forces. Bone resection was performed virtually to incremental resection depths. The stresses were calculated for five resection depths and for five different activities (i) standing on one leg (static case); (ii) two‐to‐one‐to‐two leg standing; (iii) normal walking; (iv) walking down stairs; and (v) a knee bend. In general, both the average Von Mises stresses and the area of bone that yielded significantly increased at a resection depth of ≥10 mm. The knee bend and walking down stairs demonstrated the highest stresses. The FE model predicts that fracture is likely to occur in the resection area first following removal of a third (10 mm) or more of the diameter of the femoral neck. We suggest that when surgeons perform osteochondroplasty for hip impingement, the depth of resection should be limited to 10 mm.

Buckling of thin cylindrical shells: an attempt to resolve a paradox

Abstract The classical theory of buckling of axially loaded thin cylindrical shells predicts that the buckling stress is directly proportional to the thickness t , other things being equal. But empirical data show clearly that the buckling stress is actually proportional to t 1.5 , other things being equal. As is well known, there is wide scatter in the buckling-stress data, going from one half to twice the mean value for a given ratio R / t . Current theories of shell buckling explain the low buckling stress—in comparison with the classical—and the experimental scatter in terms of “imperfection-sensitive”, non-linear behaviour. But those theories always take the classical analysis of an ideal, perfect shell as their point of reference. Our present principal aim is to explain the observed t 1.5 law. So far as we know, no previous attack has been made on this particular aspect of thin-shell buckling. Our work is thus breaking new ground, and we shall deliberately avoid taking the classical analysis as our starting point. We first point out that experiments on self-weight buckling of open-topped cylindrical shells agree well with the mean experimental data mentioned above; and then we associate those results with a well-defined post-buckling “plateau” in load/deflection space, that is revealed by finite-element studies. This plateau is linked with the appearance of a characteristic “dimple” of a mainly inextensional character in the deformed shell wall. A somewhat similar post-buckling dimple is also found by quite separate finite-element studies when a thin cylindrical shell is loaded axially at an edge by a localised force; and it turns out that such a dimple grows under a more-or-less constant force that is proportional to t 2.5 , other things being equal. This 2.5-power law can be explained by analogy with the inversion of a thin spherical shell by an inward-directed force. Thus, the deformation of such a shell is generally inextensional except for a narrow “knuckle” or boundary layer in which the combined local elastic energy of bending and stretching is proportional to t 2.5 , other things being equal. Similarly, the modes of deformation in the post-buckling dimples in a cylindrical shell are practically independent of thickness, except in the highly deformed boundary-layer regions which separate the inextensionally distorted portions of the shell. These ideas lead in turn to an explanation of the t 1.5 law for the post-buckling stress of open-topped cylindrical shells loaded by their own weight. We attribute the absence of experimental scatter in the self-weight buckling of open-topped cylindrical shells to the statical determinacy of the situation, which allows a post-buckling dimple to grow at a well-defined “plateau load”. Conversely, the large experimental scatter in tests on cylinders with closed ends may be attributed to the lack of statical determinacy there. Our paper contains several arguments that are not mathematically water-tight, in contrast to many reports in the field of mechanics of structures. We plead that the problem which we have tackled is so difficult that the only way forward is one of “over-simplification”. We hope that our work will be judged not with respect to its absence of mathematical precision, but by the light which it sheds upon the problem under investigation.

Enhancing the Hydrophilicity and Cell Attachment of 3D Printed PCL/Graphene Scaffolds for Bone Tissue Engineering

Scaffolds are physical substrates for cell attachment, proliferation, and differentiation, ultimately leading to the regeneration of tissues. They must be designed according to specific biomechanical requirements, i.e., certain standards in terms of mechanical properties, surface characteristics, porosity, degradability, and biocompatibility. The optimal design of a scaffold for a specific tissue strongly depends on both materials and manufacturing processes, as well as surface treatment. Polymeric scaffolds reinforced with electro-active particles could play a key role in tissue engineering by modulating cell proliferation and differentiation. This paper investigates the use of an extrusion-based additive manufacturing system to produce poly(ε-caprolactone) (PCL)/pristine graphene scaffolds for bone tissue applications and the influence of chemical surface modification on their biological behaviour. Scaffolds with the same architecture but different concentrations of pristine graphene were evaluated from surface property and biological points of view. Results show that the addition of pristine graphene had a positive impact on cell viability and proliferation, and that surface modification leads to improved cell response.

Up-regulation of tension-related proteins in keloids: knockdown of Hsp27, α2β1-integrin, and PAI-2 shows convincing reduction of extracellular matrix production.

Background: Keloid disease is a fibroproliferative disorder, with an ill-defined treatment that is characterized by excessive extracellular matrix deposition. Mechanical tension promotes deposition of extracellular matrix and overexpression of tension-related proteins, which is associated with keloid disease. The aim of this study was to investigate the effect of tension-related proteins on extracellular matrix steady-state synthesis in primary keloid fibroblasts. Methods: Keloid fibroblasts (n = 10) and normal skin (n = 4) fibroblast cultures were established from passages 0 to 3. A panel of 21 tension-related genes from microarray data were assessed at mRNA (quantitative reverse-transcriptase polymerase chain reaction) and protein (in-cell Western blotting) levels. Three genes were significantly altered in keloid tissue and fibroblasts, and their functional role was assessed using siRNA knockdown. Results: Hsp27, &agr;2&bgr;1-integrin, and PAI-2 were significantly up-regulated (p < 0.05)in keloid tissue and fibroblasts compared with normal skin. Hsp27, &agr;2&bgr;1-integrin, and PAI-2 expression was inhibited by RNA interference. Both the mRNA and protein levels of Hsp27, &agr;2&bgr;1-integrin, and PAI-2 significantly decreased (p < 0.05) in keloid fibroblasts at 48 hours after transfection. After down-regulation of Hsp27, &agr;2&bgr;1-integrin, and PAI-2, the expression of intracellular extracellular matrix was significantly reduced (p < 0.05). Water-soluble tetrazolium salt-1 assay showed that transfection of Hsp27, &agr;2&bgr;1-integrin, and PAI-2 did not influence the viability/metabolic activity of keloid fibroblasts. Conclusions: This study demonstrates overexpression of key tension-related proteins in keloid tissue and keloid fibroblasts. Knockdown of Hsp27, PAI-2, and &agr;2&bgr;1-integrin by RNA interference attenuates the expression of mRNA and protein levels and certain other extracellular matrix molecules.

Skin equivalent tensional force alters keloid fibroblast behavior and phenotype.

Skin tension may influence keloid scar behavior, development, and spreading, e.g., butterfly‐shaped keloid disease in the sternum. Here, we developed a three‐dimensional (3D) in vitro model to mimic in vivo tension and evaluate keloid fibroblast (KF) behavior and extracellular matrix synthesis under tension. In vivo skin tension measured in volunteers (n = 4) using 3D image photogrammetry enabled prediction of actual force (35 mN). A novel cell force monitor applied tension in a fibroblast‐populated 3D collagen lattice replicating the in vivo force. The effect of tension on keloid (n = 10) fibroblast (KF) and normal skin (n = 10) fibroblasts (NF) at set time points (6, 12, and 24 hours) was measured in Hsp27, PAI‐2, and α2β1 integrin, tension‐related genes demonstrating significant (p < 0.05) time‐dependent regulation of these genes in NF vs. KF with and without tension. KF showed higher (p < 0.05) proliferation post‐tension. Knockdown of all three genes in 24 and 48 hours with and without tension showed significant down‐regulation in NF vs. KF. Additionally, we show significant (p < 0.05) modification of the expression of extracellular matrix‐related genes post‐tension following down‐regulation of Hsp27, PAI‐2, or α2β1 integrin. Finally, we demonstrate significant alteration in NF compared with KF morphology following knockdown. In conclusion, this study shows induction of tension‐related genes expression following mechano‐regulation in KFs, with potential relevance to its development and therapy.

Application of a lattice Boltzmann-immersed boundary method for fluid-filament dynamics and flow sensing

Complex fluid-structure interactions between elastic filaments, or cilia, immersed in viscous flows are commonplace in nature and bear important roles. Some biological systems have evolved to interpret flow-induced motion into signals for the purpose of feedback response. Given the challenges associated with extracting meaningful experimental data at this scale, there has been particular focus on the numerical study of these effects. Porous models have proven useful where cilia arrangements are relatively dense, but for more sparse configurations the dynamic interactions of individual structures play a greater role and direct modelling becomes increasingly necessary. The present study reports efforts towards explicit modelling of regularly spaced wall-mounted cilia using a lattice Boltzmann-immersed boundary method. Both steady and forced unsteady 2D channel flows at different Reynolds numbers are investigated, with and without the presence of a periodic array of elastic inextensible filaments. It is demonstrated that the structure response depends significantly on Reynolds number. For low Reynolds flow, the recirculation vortex aft of successive filaments is small relative to the cilia spacing and does not fully bridge the gap, in which case the structure lags the flow. At higher Reynolds number, when this gap is fully bridged the structure and flow move in phase. The trapping of vortices between cilia is associated with relatively lower wall shear stress. At low to intermediate Reynolds, vortex bridging is incomplete and large deflection is still possible, which is reflected in the tip dynamics and wall shear stress profiles.

Evaluation of performance and design of GFRP dowels in jointed plain concrete pavement - part 1: experimental investigation

Dowel bars are provided at the transverse joints of the jointed plain concrete pavement to allow for expansion and contraction of the pavement due to moisture and temperature changes. This paper presents experimental and analytical investigations for the deflection response of glass fibre-reinforced polymer (GFRP) dowels for different joint widths and concrete grades. The results were compared with those obtained from investigations into the conventional epoxy-coated steel dowel bars of similar rigidity. The experimental results showed that the 38 mm (1.5 in.) GFRP dowels perform better in terms of joint face deflection compared with 25 mm (1 in.) epoxy-coated steel dowel bars. In addition, these results showed that the deflection of the GFRP dowel was significantly affected by changing the concrete compressive strength and the joint widths.

Effect of asymmetric meshing on the buckling behavior of composite shells under axial compression

ABSTRACT Asymmetric meshing technique (AMT) is a perturbation method to introduce disturbances (i.e., imperfections) in a finite-element model without changing geometry, boundary conditions, or loading conditions. For cylindrical shells under axial compression, asymmetric meshing in the form of a square patch of three different surface areas and a band in axial and/or circumferential directions with different areas is discussed in the first half of the article. The element size in the patch or band is lowered to a varying degree as compared to the rest of the shell in order to produce the asymmetry. The reduction in the buckling load was observed from 15% to 20%, which depends mainly on the total area of asymmetric meshing, and less on the amplitude of asymmetry, i.e., reduction in element size. While loading the shell, an isolated dimple formed near the bifurcation point that increased in size to reach a stable state in the postbuckling region corresponding to the postbuckling plateau load. The load-displacement behavior using asymmetric meshing is similar to the experimental results and the numerical results obtained by introducing initial geometric imperfections. Asymmetric meshing in the form of varying element size in both axial direction and circumferential direction of the shell is discussed in the second half of the article. Asymmetric meshing showed reduction in the buckling load up to 7% with small amplitude of asymmetry that further increases with increase in amplitude of asymmetry in meshing. Asymmetric meshing has relatively less influence on predicted buckling load but significant effect on load displacement behavior in the postbuckling range; overall buckling behavior depends on the directionality of asymmetric meshing employed in the model.