The construction of optimum three-dimensional shapes within the framework of a model of local interaction

Analytical solutions for variational problems on con¦gurations of threedimensional (3D) bodies with the maximal lift-to-drag ratio at a given base area or a planform area are found within the limits of a localised interaction between the supersonic §ow and the body surface. Functionals of considered variational problems depend on derivatives of the desired function with respect to independent variables only, and this simpli¦es the solution and allows studying the structure of the extremal surface. It is shown that the lower surface of optimal bodies is planar. If a base area is given, the upper surface is cylindrical with the generating line parallel to the oncoming §ow velocity vector. If a planform area is given, the optimal body is a §at plate with the highest possible value of the liftto-drag ratio at a prescribed Mach number and friction coe©cient. The optimal body with a planar upper surface is a wedge. These results are valid if the base pressure is taken into account and also for zero base pressure.

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“…At the same time, the span of the optimal delta wing is 1.5 times greater than the span of a body de¦ned by the relations (6).…”

Section: Progress In Flight Physicsmentioning

confidence: 91%

On optimal configurations in supersonic flow

Lapygin

Sazonova

Yakunina

2013

Progress in Flight Physics

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“…However, few studies are conducted to clarify the penetration mechanism of ECSPs. The research work of Ben-Dor et al and Yakunina et al [9][10][11][12] pointed out that when the projectile structure was formed by the surface of a circular cone and its tangential plane combination, the projectile has the smallest penetration resistance and the highest penetration efficiency. In 1978, Dhaliwal and Singh [13] gave the derivation process of the penetration force for the rigid projectile with arbitrary cross-section shape to punch into an elastic object, and proposed a simple closedform expression of the penetration force required for projectiles with six types of cross-section shapes.…”

Section: Introductionmentioning

confidence: 99%

Study on the penetration of elliptical cross-section projectiles into concrete targets: theory and experiment

Liu

Zhang

Wei

et al. 2022

Lat. Am. j. solids struct.

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To better understand the penetration mechanism of the elliptical cross-section projectile (ECSP) into semiinfinite concrete target, penetration experiments using three types of ECSPs with different shape ratios (1, 1.25 and 1.61) and with striking velocities ranged from 550 m/s to 1050 m/s were conducted. Penetration depths, penetration trajectory and mass erosion rates of the projectile were obtained after the experiments. The experiment results show that the penetration performance and ballistic stability of the ECSP are equivalent to those of the circular cross-section projectile (CCSP). Based on the theory of complex variable function and conformal transformation, a semi-analytical model which can calculate the cavity boundary stress distribution of elliptical section cavity controlled by the displacement boundary condition was established and the model was validated by comparing the model degenerate solution with Kirsch problem results. Theoretical calculation results show that the radial stress of elliptical section cavity increases progressively from the minor axis to the major axis. In addition, a formula combining with the semi-analytical theoretical model and the local interaction theory was developed. The predicted penetration depths were compared with 30 groups of experiment data with different projectile parameters and striking velocities and coincide quite well with the corresponding experimental data. Finally, the influence of shape ratio and caliberradius-head (CRH) on the penetration performance of projectile and the application prospect of ECSPs on hypersonic weapon platform were studied.

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Effects of Sliding Friction on the Optimal 3D- Nose Geometry of Rigid Rods Penetrating Media

Yakunna

2005

Optim Eng

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Friction effects on the optimum shape design for a normal impacting, rigid body are investigated and the optimum 3D-nose shapes of rods are proposed for deep penetration into soil, concrete and metal media. The study is conducted by assuming that the normal and tangent stresses, that act on the impactor nose, are of the Poncelet and Coulomb forms, respectively. The geometrical characteristics of the shapes maximizing penetration depth are compared with those of the minimal resistance bodies obtained at the initial stage of the penetration event. When mass, shank radius and nose length of the rods are fixed, a comparative study of the penetration depths of the optimal impactors and impactors with conical and ogival nose shapes is carried out. The conditions, when the benefits of the optimal configurations in providing deep penetration into soil, concrete and metal media become significant in comparison with other shapes, have been obtained. The model parameters are taken from the published reports on penetration data obtained for striking velocities to 1.5 km/s while the impactors remained rigid and visibly undeformed.

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The construction of optimum three-dimensional shapes within the framework of a model of local interaction

Cited by 15 publications

References 1 publication

On optimal configurations in supersonic flow

On optimal configurations in supersonic flow

Study on the penetration of elliptical cross-section projectiles into concrete targets: theory and experiment

Effects of Sliding Friction on the Optimal 3D- Nose Geometry of Rigid Rods Penetrating Media

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