Menahem Baruch

On the stability of eccentrically stiffened cylindrical shells under axial compression

Abstract The effect of stiffener eccentricity on the critical load is studied for cylindrical shells under axial compression. Classical simple support and classical clamped end conditions are considered. A detailed physical explanation of the causes of the eccentricity effect is proposed and verified by computations for 350 typical shells. As in the case of buckling under hydrostatic pressure and torsion, the behavior of the eccentricity effect in the case of axial compression also depends very strongly on the geometry of the shell, represented by the Batdorf parameter. On the other hand the geometry of the stiffeners influences only its magnitude. At very low Z, inversion of the eccentricity effect occurs, but for practical dimensions outside stringers always stiffen the shell more than inside ones. The eccentricity effect has a pronounced maximum at practical values of Z. The behavior of the eccentricity effect is very similar for clamped and for simply supported shells. The effects of eccentricity of ring stiffeners are also considered.

A nondestructive dynamic method for the determination of the critical load of elastic columns

A dynamic method for predicting the buckling load of an elastic column is formulated. The method is based on the integral-equation representation of a column with varying cross section and elastic springs at the boundaries. The experimental inputs are the dynamic properties of the unloaded column (trequencies, mode shapes and masses). The buckling loads predicted for three tested configurations agreed well with loads defined by other static and dynamic methods.

Inversion of the Eccentricity Effect in Stiffened Cylindrical Shells Buckling under External Pressure

The analysis of the general instability of stiffened cylindrical shells under hydrostatic pressure carried out earlier is continued in order to study the inversion of the eccentricity effect: 500 typical shells of varying geometries are considered. The results show that for lateral pressure loading the inversion of the eccentricity effect is practically independent of the geometry of the rings but depends very strongly on the shell geometry parameter Z, whereas for hydrostatic pressure the inversion is also influenced by the bending stiffness of the rings. A range of inversion is found for both loadings. A detailed physical explanation of the cause of the eccentricity effect and its inversion is proposed.

Behaviour of an incrementally elastic thick walled sphere under internal and external pressure

Abstract The behaviour of a thick walled sphere underinternal and external pressure is considered. The material of the sphere is assumed to obey an incrementally elastic constitutive law. There is no restriction on the size of the deformation and a solution is given in terms of special functions associated with the non-linear differential equations of the problem. As a numerical example the behaviour of a spherical shell, subjected to internal pressure, is described. It is shown that at a certain critical pressure instability of the second kind (inflation) is obtained.

Analysis of an elasto-plastic thick walled sphere loaded by internal and external pressure

Abstract The non-linear behaviour of a thick walled sphere under internal and external pressure is considered. The material is assumed to be incrementally elasto-plastic in the classical sense. No restriction on the magnitude of the deformation is imposed. For internal pressure a solution is obtained in terms of closed integrals. It is shown that the three dimensional solution reduces exactly to the membrane solution when the thickness of the shell becomes very small. Numerical examples are given for some practical materials used in the aerospace industry. It is shown that at a certain critical pressure instability of the second kind (inflation) is obtained.

Buckling of cylindrical shells under combined axial preload, nonuniform heating and torque

Thin aluminum-alloy cylinders were tested under different combinations of torque and circumferentially varying axial thermal stress. The methods of application of the required loads and the measuring techniques employed are discussed. The buckling process is described and interaction curves are presented.

Buckling of Cylindrical Shells Heated along Two opposite Generators Combined with Axial Compression

A series of tests was carried out on clamped cylindrical shells under a combination of thermal and mechanical loads. The shells were linearly heated along two opposite generators in addition to a uniform axial pressure applied before the heating. The paper describes the test setup, equipment and techniques used. Systems for rapid measurement, data analysis and storage designed for the experimental work are presented.As an outcome of this study, a linear-interaction line is proposed in order to express the interaction between thermal-and mechanical-buckling loads.

Turning Around a Method of Successive Iterations to Yield Closed-Form Solutions for Vibrating Inhomogeneous Bars

In this study, the method of successive approximations is turned around so as to obtain closed form solutions for vibrating inhomogeneous bars. In particular, the method recently developed by the first author for the homogeneous beams is extended for bars.

Mass change detection based on reduced measurements

SummaryChanges in the mass matrix of a dynamic structure can be detected by using reduced measurements [1]. In the here proposed method the stiffness matrix is assumed to be correct. The missing measurements can be calculated by utilizing the connection between the measured and unmeasured quantities through the iterative process of identification of the tested structure. The missing measurements and to some extent the partial measurements obtained during the tests are treated as hidden functions of the mass parameters of the structure. This makes the Euclidean norm of the appropriate matrix to be minimized a nonlinear function of the parameters. This norm may have more than one minimum. The changes in the mass matrix must be identified by looking for the global mininum of the Euclidean norm. The global minimum can be found by changing the initial values of the mass parameters or by changing some special coefficients, or both.In order to identify the mass parameters of the structure the measured and the supplied missing quantities are forced to comply with the general laws for a linear structure. This compliance is achieved during any step of the iterative process.

A criterion for shape control robustness of space structures

In the shape control method of space structures a certain matrix plays a major role. It is proposed here that the reciprocal value of the characteristic number of this matrix be taken as criterion for the robustness of the method.