THERMAL STRESS IN LONG CYLINDRICAL SHELLS DUE TO TEMPERATURE VARIATION ROUND THE CIRCUMFERENCE, AND THROUGH THE WALL

1937 ◽  
Vol 15a (4) ◽  
pp. 49-58 ◽  
Author(s):  
J. N. Goodier
Keyword(s):  
Thermal Stress ◽  
Circular Cylinder ◽  
Temperature Variation ◽  
Cross Section ◽  
Maximum Stress ◽  
Cylindrical Shells ◽  
Axial Direction ◽  
Temperature Distributions ◽  
Thin Walled ◽  
The Cross

The thermal stress in thin-walled cylinders of any cross section has been investigated for internal and external temperatures each varying in any manner round the circumference but not in the axial direction. The thickness also may vary round the circumference.A method is given for calculating the stress from given temperature distributions, whatever the shape of the cross section. The stress is evaluated for uniform, but different, inside and outside temperatures.The circular cylinder is treated in detail and the stress found for the general case of circumferential variation. It is shown that the maximum stress will depend only on the temperature distributions and the material, and not on the thickness or diameter of the cylinder.

Structural bionic design for thin-walled cylindrical shell against buckling under axial compression

2011 ◽  
Vol 225 (11) ◽  
pp. 2619-2627 ◽  
Author(s):  
D Xing ◽  
W Chen ◽  
J Ma ◽  
L Zhao
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Cross Section ◽  
Cylindrical Shells ◽  
High Load ◽  
Vascular Bundles ◽  
Bionic Design ◽  
Load Bearing ◽  
Thin Walled ◽  
The Cross

In nature, bamboo develops an excellent structure to bear nature forces, and it is very helpful for designing thin-walled cylindrical shells with high load-bearing efficiency. In this article, the cross-section of bamboo is investigated, and the feature of the gradual distribution of vascular bundles in bamboo cross-section is outlined. Based on that, a structural bionic design for thin-walled cylindrical shells is presented, of which the manufacturability is also taken into consideration. The comparison between the bionic thin-walled cylindrical shell and a simple hollow one with the same weight showed that the load-bearing efficiency was improved by 44.7 per cent.

Design variation of thin-walled composite beam cross-section properties

2016 ◽  
Vol 12 (3) ◽  
pp. 558-576 ◽  
Author(s):  
Aníbal J.J. Valido ◽  
João Barradas Cardoso
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Laminated Composite ◽  
Adjoint System ◽  
Design Sensitivity ◽  
Content Type ◽  
Design Elements ◽  
Thin Walled ◽  
The Cross ◽  
Cross Section Geometry

Purpose The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section. Design/methodology/approach In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section. Findings The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables. Originality/value The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

scholarly journals Computation of Thin-Walled Cross-Section Resistance to Local Buckling with the Use of the Critical Plate Method

2016 ◽  
Vol 62 (2) ◽  
pp. 229-264 ◽  
Author(s):  
A. Szychowski
Keyword(s):  
Cross Section ◽  
Critical Stress ◽  
Analytical Calculation ◽  
Local Buckling ◽  
Stability Loss ◽  
Longitudinal Stress ◽  
Plate Method ◽  
Thin Walled ◽  
The Cross ◽  
Elastically Restrained

Abstract Thin-walled bars currently applied in metal construction engineering belong to a group of members, the cross-section res i stance of which is affected by the phenomena of local or distortional stability loss. This results from the fact that the cross-section of such a bar consists of slender-plate elements. The study presents the method of calculating the resistance of the cross-section susceptible to local buckling which is based on the loss of stability of the weakest plate (wall). The “Critical Plate” (CP) was identified by comparing critical stress in cross-section component plates under a given stress condition. Then, the CP showing the lowest critical stress was modelled, depending on boundary conditions, as an internal or cantilever element elastically restrained in the restraining plate (RP). Longitudinal stress distribution was accounted for by means of a constant, linear or non-linear (acc. the second degree parabola) function. For the critical buckling stress, as calculated above, the local critical resistance of the cross-section was determined, which sets a limit on the validity of the Vlasov theory. In order to determine the design ultimate resistance of the cross-section, the effective width theory was applied, while taking into consideration the assumptions specified in the study. The application of the Critical Plate Method (CPM) was presented in the examples. Analytical calculation results were compared with selected experimental findings. It was demonstrated that taking into consideration the CP elastic restraint and longitudinal stress variation results in a more accurate representation of thin-walled element behaviour in the engineering computational model.

A Variational Method for Fully Developed Laminar Heat Transfer in Ducts

1959 ◽  
Vol 81 (2) ◽  
pp. 157-164 ◽  
Author(s):  
E. M. Sparrow ◽  
R. Siegel
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Variational Method ◽  
Cross Section ◽  
Cross Sections ◽  
Axial Direction ◽  
Circular Sector ◽  
Thermal Boundary Conditions ◽  
Temperature Distributions ◽  
Good Agreement

A variational method is presented for determining fully developed velocity and temperature distributions for laminar flow in noncircular ducts. The heat addition to the fluid is taken to be uniform in the axial direction, but a variety of thermal boundary conditions are considered around the periphery of the duct cross section. Several illustrative examples are given, and comparisons are made which show good agreement with available exact solutions. These examples include ducts of rectangular and circular-sector cross sections.

Collapse of Thin-Walled Elliptical Tubes for High Values of Major-to-Minor Axis Ratio

1993 ◽  
Vol 115 (4A) ◽  
pp. 432-440 ◽  
Author(s):  
C. Ribreau ◽  
S. Naili ◽  
M. Bonis ◽  
A. Langlet
Keyword(s):  
Contact Pressure ◽  
Cross Section ◽  
External Pressure ◽  
Straight Line Segment ◽  
Minor Axis ◽  
Cross Sectional ◽  
Axis Ratio ◽  
Straight Line ◽  
Thin Walled ◽  
The Cross

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse’s ellipticity ko, defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p1. For p<p1, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).

Effects of Cross-Section Ovalization of Subsea Thin-Walled Bends Under In-Plane Bending

2010 ◽  
Author(s):  
Ranil Banneyake ◽  
Ayman Eltaher ◽  
Paul Jukes
Keyword(s):  
Cross Section ◽  
Computational Cost ◽  
Straight Pipe ◽  
Limit States ◽  
Element Analysis ◽  
High Tendency ◽  
Thin Walled ◽  
Plane Bending ◽  
The Cross ◽  
The Impact

Ovalization of the cross-section of bends under in-plane bending (a.k.a. Brazier effect) is a known phenomenon caused by the longitudinal stress acting on the cross-section as the pipe bends. Besides its tendency to induce stresses in the bend above what is predicted using simple beam theory, excessive cross-section ovalization is particularly critical to subsea pipes, as it can lead to collapse of the pipe under external pressure. Also, being in a plastic regime may cause the bend material to ratchet and undergo excessive strains under cyclic operational loads, especially under high-pressure high-temperature (HPHT) conditions. Ovalization normally results in local increase of stresses and could lead to failure of the bend before the bend globally reaches its limiting capacity. The offshore industry standards and design codes address the impact of initial ovality in straight pipes, but their applicability to bends is not clear. Therefore, this paper presents an investigation into the increased tendency of thin-walled bends to ovalize, and the effect of bend cross-section ovalization on their stiffness and yielding and collapse limit states, with emphasis on offshore applications. Due to the lack of analytical solutions for the bend response taking into account cross-section ovalization, finite element analysis (FEA) is used in this study. Predictions of the bend models are compared with those of straight pipe models and predictions of models of the bend made of beam elements (with pipe section) are compared with those of models made of brick /shell elements. The increased tendency of thin-walled bends to ovalize compared to straight pipes is investigated (e.g. 100 times in the linear range), and the impact and significance of ovalization in bends are assessed (e.g., stress increase of the order of 35% has been observed in some example situations). Also discussed in the paper is the selection of proper element specifications in order to accurately capture the ovalization response while keeping the computational cost manageable. Recommendations as to how to account for ovalization effects are presented. This paper helps to gain a better understanding of the response of subsea thin-walled bends under in-plane bending and their comparatively high tendency to ovalize compared to straight pipe, and emphasizes the significance of local effects such as cross-section ovalization, the overlooking of which may result in a significant underestimation of involved stresses and strains.

scholarly journals Primary Response Assessment Method for Concept Design of Monotonous Thin-Walled Structures

10.14311/750 ◽  
2005 ◽  
Vol 45 (4) ◽  
Author(s):  
V. Zanic ◽  
P. Prebeg
Keyword(s):  
Cross Section ◽  
Response Assessment ◽  
Assessment Method ◽  
Primary Response ◽  
Concept Design ◽  
Fem Model ◽  
Feasibility Assessment ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
The Cross

A concept design methodology for monotonous, tapered thin-walled structures (wing/fuselage/ship/bridge) is presented including modules for: model generation; loads; primary (longitudinal) and secondary (transverse) strength calculations; structural feasibility (buckling/fatigue/ultimate strength criteria); design optimization modules based on ES/GA/FFE; graphics. A method for primary strength calculation is presented in detail. It provides the dominant response field for design feasibility assessment. Bending and torsion of the structure are modelled with the accuracy required for concept design. A ‘2.5D-FEM’ model is developed by coupling a 1D-FEM model along the ‘monotonity’ axis and a 2D-FEM model(s) transverse to it. The shear flow and stiffness characteristics of the cross-section for bending and pure/restrained torsion are given, based upon the warping field of the cross-section. Examples: aircraft wing and ship hull. 

Part II. The Flattening of Monocoque Cylinders

1938 ◽  
Vol 42 (328) ◽  
pp. 302-319
Keyword(s):  
Variational Method ◽  
Potential Energy ◽  
Cross Section ◽  
Radial Displacement ◽  
Bending Moment ◽  
Experimental Investigations ◽  
Pure Bending ◽  
Centre Line ◽  
Thin Walled ◽  
The Cross

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

Boundary-Value Problems of the Thin-Walled Circular Cylinder

1954 ◽  
Vol 21 (4) ◽  
pp. 343-350
Author(s):  
N. J. Hoff
Keyword(s):  
Circular Cylinder ◽  
Differential Equations ◽  
Closed Form ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Cylindrical Shells ◽  
Shear Forces ◽  
Thin Walled

Abstract The homogeneous differential equations of Donnell’s theory of thin cylindrical shells are integrated. Expressions are obtained in closed form for the displacements, membrane stresses, moments, and shear forces.

Pretwisted Beams and Columns

1956 ◽  
Vol 23 (2) ◽  
pp. 165-175
Author(s):  
John Zickel
Keyword(s):  
Cross Section ◽  
Buckling Load ◽  
Structural Members ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
Constant Rate ◽  
Thin Walled ◽  
The Cross ◽  
Stiffening Factor

Abstract A theory is developed for the behavior of pretwisted structural members of thin-walled section with slight initial bending. The stresses are at first determined along and perpendicular to the fibers and are then transformed to stresses in the cross section and along the axis. Although the development is perfectly general the integrations are only indicated for doubly symmetric sections. The buckling of doubly symmetric columns which are initially straight but are pretwisted at a constant rate is treated in detail. The results show that columns of decidedly unequal principal moments of inertia can be strengthened up to 90 per cent, but columns of equal moments of inertia are weakened by initial twist. In analogy to the Euler load of the buckling theory for straight, untwisted columns, a reduced Euler load is defined. The buckling load is the product of this reduced Euler load and a stiffening factor.

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