Buckling of Long Sandwich Cylindrical Shells Under External Pressure

2004 ◽  
Vol 72 (4) ◽  
pp. 493-499 ◽  
Author(s):  
G. A. Kardomateas ◽  
G. J. Simitses
Keyword(s):  
Transverse Shear ◽  
Shell Thickness ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Stability Loss ◽  
External Pressure ◽  
Composite Construction ◽  
The Core ◽  
Sandwich Construction

An elasticity solution to the problem of buckling of sandwich long cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. All constituent phases of the sandwich structure, i.e., the facings and the core, are assumed to be orthotropic. The loading is a uniform hydrostatic pressure, which means that the loading remains normal to the deflected surface during the buckling process. Results are produced for laminated facings, namely, boron/epoxy, graphite/epoxy and kevlar/epoxy laminates with 0deg orientation with respect to the hoop direction, and for alloy-foam core. Shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are compared, one based only on the core, and the other based on an effective shear modulus that includes the face sheets. The results show that the shell theory predictions without transverse shear can produce highly non-conservative results on the critical pressure, but the shell theory formulas with transverse shear correction produce reasonable results with the shear correction based on the core only being in general conservative (i.e., critical load below the elasticity value). The results are presented for four mean radius over shell thickness ratios, namely 15, 30, 60, and 120 in order to assess the effect of shell thickness (and hence that of transverse shear). For the same thickness, the differences between elasticity and shell theory predictions become larger as the mean radius over thickness ratio is decreased. A comparison is also provided for the same shell with homogeneous composite construction. It is shown that the sandwich construction shows much larger differences between elasticity and shell theory predictions than the homogeneous composite construction. The solution presented herein provides a means of a benchmark for accurately assessing the limitations of shell theories in predicting stability loss in sandwich shells.

Buckling of Thick Orthotropic Cylindrical Shells Under External Pressure

1993 ◽  
Vol 60 (1) ◽  
pp. 195-202 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Critical Load ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Stability Loss ◽  
External Pressure ◽  
Elasticity Solution ◽  
Composite Shells

An elasticity solution to the problem of buckling of orthotropic cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. The results show that the shell theory predictions can produce nonconservative results on the critical load of composite shells with moderately thick construction. The solution provides a means of accurately assessing the limitations of shell theories in predicting stability loss.

Three-Dimensional Printed Dielectric Substrates for Radio Frequency Applications

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Vana Snigdha Tummala ◽  
Ahsan Mian ◽  
Nowrin H. Chamok ◽  
Dhruva Poduval ◽  
Mohammod Ali ◽  
...  
Keyword(s):  
Radio Frequency ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Volume Fractions ◽  
The Core ◽  
Sandwich Construction ◽  
3D Printed ◽  
Rf Antenna

Engineered porous structures are being used in many applications including aerospace, electronics, biomedical, and others. The objective of this paper is to study the effect of three-dimensional (3D)-printed porous microstructure on the dielectric characteristics for radio frequency (RF) antenna applications. In this study, a sandwich construction made of a porous acrylonitrile butadiene styrene (ABS) thermoplastic core between two solid face sheets has been investigated. The porosity of the core structure has been varied by changing the fill densities or percent solid volume fractions in the 3D printer. Three separate sets of samples with dimensions of 50 mm × 50 mm × 5 mm are created at three different machine preset fill densities each using LulzBot and Stratasys dimension 3D printers. The printed samples are examined using a 3D X-ray microscope to understand pore distribution within the core region and uniformity of solid volumes. The nondestructively acquired 3D microscopy images are then postprocessed to measure actual solid volume fractions within the samples. This measurement is important specifically for dimension-printed samples as the printer cannot be set for any specific fill density. The experimentally measured solid volume fractions are found to be different from the factory preset values for samples prepared using LulzBot printer. It is also observed that the resonant frequency for samples created using both the printers decreases with an increase in solid volume fraction, which is intuitively correct. The results clearly demonstrate the ability to control the dielectric properties of 3D-printed structures based on prescribed fill density.

Approximate Elasticity Solution for Orthotopic Cylinder Under Hydrostatic Pressure and Band Loads

1970 ◽  
Vol 37 (1) ◽  
pp. 101-108 ◽  
Author(s):  
A. P. Misovec ◽  
J. Kempner
Keyword(s):  
Approximate Solution ◽  
Shell Theory ◽  
Good Accuracy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
External Pressure ◽  
Theory Of Elasticity ◽  
Numerical Comparison ◽  
Axial Loads ◽  
Special Case

An approximate solution to the Navier equations of the three-dimensional theory of elasticity for an axisymmetric orthotopic circular cylinder subjected to internal and external pressure, axial loads, and closely spaced periodic radial loads is developed. Numerical comparison with the exact solution for the special case of a transversely isotropic cylinder subjected to periodic band loads shows that very good accuracy is obtainable. When the results of the approximate solution are compared with previously obtained results of a Flu¨gge-type shell solution of a ring-reinforced orthotropic cylinder, it is found that the shell theory gives fairly accurate representations of the deformations and stresses except in the neighborhood of discontinuous loads. The addition of transverse shear deformations does not improve the accuracy of the shell solution.

A Rate-Independent Constitutive Model for Square Honeycomb Core

Aerospace ◽  
2004 ◽  
Author(s):  
Zhenyu Xue
Keyword(s):  
Constitutive Model ◽  
Blast Resistance ◽  
Three Dimensional ◽  
Honeycomb Core ◽  
Plate Structures ◽  
The Core ◽  
Sandwich Construction ◽  
Alternative Means ◽  
Anisotropic Elastic ◽  
Numerical Finite Element

All-metal sandwich construction with square honeycomb core holds promise for significant improvements in stiffness, strength and blast resistance for built-up plate structures. Analysis of the performance of sandwich plates under various loads, static and dynamic, requires modeling of face sheets and core with some fidelity. While it is possible to model full geometric details of the core for a few selected problems, this is unnecessary and unrealistic for larger complex structures under general loadings. A continuum constitutive model is recently developed as alternative means of modeling the cores. The constitutive model falls within the framework of a compressible rate-independent, anisotropic elastic-plastic solid. A multi-scale computing approach based on it has been developed for modeling the sandwich structures. The validity of the approach is established by comparing numerical finite element simulations using the model with those obtained by a full three-dimensional meshing of the core geometry for a clamped sandwich plate with square honeycomb core subject to uniform pressure load. Limitations of the model are also discussed.

Three-Dimensional Elasticity Solution for the Buckling of Sandwich Columns

2001 ◽  
Author(s):  
George A. Kardomateas
Keyword(s):  
Transverse Shear ◽  
Sandwich Structure ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Dimensional Theory ◽  
Column Buckling ◽  
The Core ◽  
Timoshenko Column ◽  
Three Dimensional Elasticity

Abstract A study of the buckling of a sandwich column, based on the three dimensional theory of elasticity, and a comparison with the simple Euler or transverse shear correction Engesser / Haringx / Timoshenko column buckling formulas, is presented. All three phases of the sandwich structure (two face sheets and the core) are assumed to be orthotropic and the column is in the form of a hollow circular cylinder. The Euler or Engesser / Haringx / Timoshenko loads are based on the equivalent axial modulus. Representative results show the significance of the effect of transverse shear in these sandwich structures.

Stability Loss in Thick Transversely Isotropic Cylindrical Shells Under Axial Compression

1993 ◽  
Vol 60 (2) ◽  
pp. 506-513 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Axial Compression ◽  
Critical Loads ◽  
Shell Theory ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Stability Loss ◽  
Theory Of Elasticity ◽  
Dimensional Theory ◽  
Perfect Agreement ◽  
The Stability

The stability of equilibrium of a transversely isotropic thick cylindrical shell under axial compression is investigated. The problem is treated by making appropriate use of the three-dimensional theory of elasticity. The results are compared with the critical loads furnished by classical shell theories. For the isotropic material cases considered, the elasticity approach predicts a lower critical load than the shell theories, the percentage reduction being larger with increasing thickness. However, both the Flu¨gge and Danielson and Simmonds theories predict critical loads much closer to the elasticity value than the Donnell theory. Moreover, the values of n, m (number of circumferential waves and number of axial half-waves, respectively, at the critical point) for both the elasticity, and the Flu¨gge and the Danielson and Simmonds theories, show perfect agreement, unlike the Donnell shell theory.

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