In this paper the solution of some inverse problems for potential ®elds is tackled. The aim is to compute the position and shape of an unknown¯aw within a body, using some experimental measures as additional data. By the linearization of the dierence between the Boundary Integral Equation for the actual con®guration and the same equation for an assumed con®guration, an integral equation for the variations is deduced. This integral equation is carried to the boundary by a limiting process and a solution procedure is devised to compute an approximation to the actual¯aw. The solution method proceeds iteratively, solving a direct and an inverse problem in every step, but no minimization algorithm is involved. The performance of the method is shown in several numerical examples. 7
This paper presents a graphic methodology for the structural analysis of domes and other surfaces of revolution, based on a combined use of funicular and projective geometry. By considering a dome as a network of lines of latitude and longitude, the equilibrium of the network is analyzed in both horizontal and vertical projection. The resulting dual configuration is also a spatial system that can be considered by its projection in a horizontal and a vertical plane. The dome is divided by latitude and longitude into an arbitrary number of sectors, and the equilibrium is enforced at each node. The tangential forces can be considered for their net effect at each node; the net effect of two tangential forces, equal in magnitude, at a node is a radially directed force in the plane of the line of latitude, acting outwards (compression) or inwards (tension). Considering their horizontal projection, and its dual form, it is possible to choose the shape of the radial force diagram (the vertical projection and the force diagram), and identify the radial forces associated with it, and thus the tangential forces. The new methodology is presented through its application to a hemispherical brick dome of small thickness. The hemispherical brick dome has been also analyzed by applying the slicing technique, considering different hypotheses regarding the structural behavior of the haunch filling, according to its morphological characterization. The structural analysis of the brick dome using both methodologies allows us to contrast the results obtained.
INTRODUCTIONThis paper presents a new graphic methodology for the structural analysis of domes and other surfaces of revolution, based on a combined use of funicular and projective geometry.
Decellularized vascular scaffolds are promising materials for vessel replacements. However, despite the natural origin of decellularized vessels, issues such as biomechanical incompatibility, immunogenicity risks, and the hazards of thrombus formation still need to be addressed. In this study, we assess the mechanical properties of two groups of porcine carotid blood vessels: (i) native arteries and (ii) decellularized arteries. The biomechanical properties of both groups (n = 10, sample size of each group) are determined by conducting uniaxial and circumferential tensile tests by using an ad hoc and lab-made device comprising a peristaltic pump that controls the load applied to the sample. This load is regularly incremented (8 grams per cycle with a pause of 20 seconds after each step) while keeping the vessels continuously hydrated. The strain is measured by an image cross-correlation technique applied on a high-resolution video. The mechanical testing analyses of the arteries revealed significant differences in burst pressure between the native (1345.08±96.58 mbar) and decellularized (1067.79±112.13 mbar) groups. Moreover, decellularized samples show a significantly lower maximum load at failure (15.78±0.79 N) in comparison with native vessels (19.42±0.80 N). Finally, the average ultimate circumferential tensile also changes between native (3.71±0.37 MPa) and decellularized (2.93±0.18 MPa) groups. This technique is able to measure the strain in the regime of large displacements and enables high-resolution image of the local strains, thus providing a valuable tool for characterizing several biomechanical parameters of the vessels also applicable to other soft tissue presenting hyperelastic behaviours.
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