This paper derives expressions for the arc length and the bending energy of quadratic Bézier curves. The formulae are in terms of the control point coordinates. For fixed start and end points of the Bézier curve, the locus of the middle control point is analyzed for curves of fixed arc length or bending energy. In the case of arc length this locus is convex. For bending energy it is not. Given ...

Objectives. The objective was to determine the fracture and cyclic fatigue properties of composite–dentin beams bonded with a self-etching adhesive in four-point bend. Methods. Beams of rectangular cross-section were shaped to a size of ∼0.87mm×0.87mm×10mm and placed in a four-point bending apparatus, with the loading points 1.8 and 7.2mm apart, with the interface centered between the inner rol...

The mechanical properties of thick-walled SiO2 nanotubes (NTs) prepared by a sol-gel method while using Ag nanowires (NWs) as templates were measured by using different methods. In situ scanning electron microscopy (SEM) cantilever beam bending tests were carried out by using a nanomanipulator equipped with a force sensor in order to investigate plasticity and flexural response of NTs. Nanoinde...

This paper derives expressions for the arc length and the bending energy of quadratic Bézier curves. The formulae are in terms of the control point coordinates. For fixed start and end points of the Bézier curve, the locus of the middle control point is analyzed for curves of fixed arc length or bending energy. In the case of arc length this locus is convex. For bending energy it is not. Given ...

This study measured the bending stiffness of the spine when it is subjected to posteroanterior mobilization force. The lumbar spine was modeled as an initially curved beam column supported over the rib cage and the pelvis. Posteroanterior mobilization was assumed to be three-point bending of the beam. The mobilization force was measured by the mounting of a force plate onto the manipulation cou...

This study addresses the effects of varying configurations in board-level 4-point bend testing of BGA packages. The IPC/JEDEC 9702 test method employs 4-point monotonic PCB bending at high strain rates to characterize the PCB strains required to cause board level interconnection failures [1]. While this test is widely used, at present there is little published documentation of the resultant str...

Bending process is one of the most significant fields of application of sheet metal die. In bending process, it is quite vital that the product should have the desired angle. Furthermore, in order to obtain the desired angle in the bent parts, spring-go and spring-back amounts must be known. In this study, 30o, 60o and 90o bending processes were applied to S235JR (1.0038) sheet metal having 3, ...

In this report, the raypath equation is deduced by using plane wave theory and making high frequency approximation. Two kinds of two-point seismic ray tracing iterative nonlinear methods(the Shooting method and the Bending method) are discussed. The Shooting method fixes one end and apply the raypath equation to find the ray path. The Bending method fixes both ends and use Fermat’s principle to...

Methods: Medial meniscectomy was used to induce OA in male Lewis rats. Therapy with zoledronate and human PTH was initiated immediately after surgery. A dynamic weight-bearing system was deployed to evaluate the weight-bearing capacity. At the end of the 10-week study cartilage pathology was evaluated by contrast μCT imaging and histology. Cortical bone geometry at femoral mid-diaphysis was eva...

in this paper, the properties and microstructure of foam glasses obtained from the wasted cathode ray tube (crt) display panels were investigated. the foam glasses were prepared at the temperatures of 850, 950 and 1050c using 2, 4, 6 and 8 wt.% silicon carbide (sic) as the foaming agent. the physical and mechanical properties of the samples including the density, porosity, four-point bending s...