Flat Circular Membrane Research Articles

In situ tests by flat dilatometer : Marchetti, S J Geotech Engng Div ASCE, V106, NGT3, March 1980, P299–321

A flat blade shaped tip, with a thin flat circular steel membrane fitted flush with one side, is jacked into the ground. At 20-cm depth intervals the penetration is stopped, the membrane is inflated and the following readings are taken: A = pressure at which the membrane starts to expand against the soil; B = pressure needed to deflect the membrane center 1.00 mm against the soil. Simple expressions derived in the paper are used to determine the parameters I\dD (material index), K\dD (horizontal stress index), E\dD (dilatometer modulus) from the field readings. The profiles of I\dD, K\dD, E\dD are used with the empirical correlations presented in the paper to obtain estimates of a number of soil parameters used in geotechnical engineering design.

In Situ Tests by Flat Dilatometer

A flat blade shaped tip, with a thin flat circular steel membrane fitted flush with one side, is jacked into the ground. At 20-cm depth intervals the penetration is stopped, the membrane is inflated and the following readings are taken: A = pressure at which the membrane starts to expand against the soil; B = pressure needed to deflect the membrane center 1.00 mm against the soil. Simple expressions derived in the paper are used to determine the parameters ID (material index), KD (horizontal stress index), ED (dilatometer modulus) from the field readings. The profiles of ID, KD, ED are used with the empirical correlations presented in the paper to obtain estimates of a number of soil parameters used in geotechnical engineering design.

Deformations of elastic membranes—Effect of different constitutive relations

Results for the nonlinear axisymmetric deformations of flat circular membranes and of spherical cap membranes subjected to a uniform pressure are presented. The emphasis of the study is on the effect of two different constitutive relations on the nature of the deformation when the membrane deforms into an approximate hemispherical shape.

Finite Deflections of Circular Membranes

The behavior of membrane-like structures is of interest in conjunction with problems concerning slack diaphragms, inflatable structures, explosive forming of metals, interpretation of hydrostatic bulge tests, and continuous analysis of cable nets. For rotationally symmetric loadings of initially flat elastic circular membranes (the subject of this note), the Foppl-Von Karman equations are usually used to carry out the stress and deformation analysis. These equations are valid for moderate rotations and deformations and small strains. The membrane form of the equations given by Reissner represents a generalization of the Foppl-Von Karman theory to the case of arbitrarily large rotations and deformations, while retaining the small strain assumption. The purpose of the present work is to obtain some solutions to the Reissner membrane equations and compare these results to those previously found from the Foppl-Von Karman equations.

On the analysis of non-linear membranes

This paper presents a non-linear analysis of hinged flat circular and spherical membranes undergoing arbitrarily large axisymmetric deformations when subjected to internal pressure. No assumptions as to the magnitude of strains and displacement gradients are made and the non-linear constitutive relation for a highly elastic incompressible solid is used. The non-linear membrane equilibrium equations are formulated in terms of the displacement components and the known geometry of the undeformed surface for the general nonorthogonal midsurface coordinate case and are simplified for the axisymmetric shell of revolution problem, a particular case of which is the flat circular membrane. Because of the type of constitutive relation used in the formulation, the inflation pressure is a highly nonlinear function of the displacements. Using finite differences and a Newton Raphson iterative scheme, a technique is developed whereby all three equilibrium configurations, associated with a particular value of the inflation pressure, are established. Results are presented graphically in a nondimensionalized form and where possible are compared with solutions obtained by others.

Interaction of a compressible fluid and an elastic membrane

The paper presents results from a computer method for analyzing the unsteady interaction of a fluid and an initially flat circular elastic membrane. The method consists of an implicit coupling of computer programs for the fluid flowfield and for the membrane. The pressures and velocities in the flowfield are determined from a scheme based on the method of characteristics in three independent variables. The membrane is represented by a discrete number of points which are tracked as a function of time; lines connecting these points separate the fluid field into noninteracting regions. Deflected membrane shapes, pressure profiles, and the flowfield at various times are presented. The maximum deflection from the coupled analysis is shown to be only 60% of that obtained when the pressure on the membrane is maintained at the pressure associated with stagnating the freestream. Cp c E h hr M N P Ps R r s t U

Indentation of a Circular Membrane

The problem of axisymmetric deformations of an elastic membrane has been formulated in terms of three first-order nonlinear ordinary differential equations. In this paper, the application of these equations is made to the problem of a circular flat membrane indented by a smooth sphere. The membrane is then deformed into an axisymmetric surface. The deformed membrane is divided into two regions: a region of contact with the sphere, and a region which is free of external load except at the boundaries. The common boundary of the two regions is not known a priori. The nonlinear membrane equations are applied specifically to each region and continuity of stress and deformation are required at the common boundary. Numerical solutions are obtained for the membrane of Mooney model material. Applications are pointed out in the discussion.