Minimum-Weight Design of Thin-Walled Cylinders Subject to Flexural and Torsional Stiffness Constraints

1980 ◽  
Vol 47 (1) ◽  
pp. 106-110 ◽  
Author(s):  
R. D. Parbery ◽  
B. L. Karihaloo
Keyword(s):  
Minimum Weight ◽  
Torsional Stiffness ◽  
Contour Length ◽  
Minimum Weight Design ◽  
Cross Sectional ◽  
Weight Design ◽  
Thin Walled ◽  
Sectional Shape ◽  
Elliptical Cylinders ◽  
Walled Cylinder

We consider the problem of determining the cross-sectional shape of a thin-walled cylinder of constant (unknown) wall thickness and given contour length that uses the least possible material to achieve prescribed minimum stiffness in torsion and bending. The corresponding variational problem is shown to belong to a class with nonadditive functionals whose Euler equation is an integrodifferential equation. Cross-sectional shapes are presented for various stiffness ratios and compared with circular and elliptical cylinders.

Minimum Weight Design of Thin–walled Cells in Torsion

1955 ◽  
Vol 59 (530) ◽  
pp. 120-126 ◽  
Author(s):  
V. Cadambe ◽  
S. Krishnan
Keyword(s):  
Structural Design ◽  
Necessary Conditions ◽  
Minimum Weight ◽  
Local Buckling ◽  
Design Criteria ◽  
Minimum Weight Design ◽  
Weight Design ◽  
Uniform Wall ◽  
Thin Walled ◽  
Twisting Deformation

The minimum weight approach to structural design was introduced by F. R. Shanley with reference to narrow and wide columns and shells subjected to bending, and was later dealt with more comprehensively in a book by the same author. This was further extended to structures like tapered round thin-walled columns and frames. In this paper expressions giving optimum sectional dimensions for long thin walled cells of circular, semi–circular, rectangular and triangular shapes and uniform wall thickness have been derived. The design criteria used to obtain the minimum necessary conditions are (1) failure by local buckling and (2) a limit on the twisting deformation of the cells. Working curves from which the optimum sectional dimensions can be read for given torque and limiting twist have been plotted. And finally, a method of approach to the problem of combined bending and torsion has also been indicated.

Analytic Treatment of Minimum Weight Design of Cantilevers

1974 ◽  
Vol 41 (2) ◽  
pp. 512-515
Author(s):  
J. E. Brock
Keyword(s):  
Analytic Solution ◽  
Minimum Weight ◽  
Practical Importance ◽  
Cantilever Beams ◽  
Minimum Weight Design ◽  
Concentrated Force ◽  
Cross Sectional ◽  
Section Modulus ◽  
End Conditions ◽  
Weight Design

Minimum weight design is considered for cantilever beams which must sustain a concentrated moment and a concentrated force at the tip as well as their own distributed weight. An analytic solution is obtained for the case where the variation of cross section is such that section modulus varies as a power of cross-sectional area. Three cases, having practical importance, are studied in detail; two of these lead to nonlinear differential or integral relationships. Cases having more complicated laws of variation and other end conditions are discussed.

Note on the Minimum-Weight Design of Thin-Walled Cells in Combined Bending and Torsion

1956 ◽  
Vol 60 (541) ◽  
pp. 65-66 ◽  
Author(s):  
V. Cadambe ◽  
S. Krishnan
Keyword(s):  
Minimum Weight ◽  
Bending Moment ◽  
Rational Approach ◽  
Pure Torsion ◽  
Minimum Weight Design ◽  
Weight Design ◽  
Thin Walled

In a recent paper the authors suggested that the minimum weight design of thin-walled cells in combined bending and torsion could be tackled by using the well-known concept of equivalent bending moment and torque. It is now felt that a more rational approach would be to base the analysis on the buckling behaviour of the walls of the cell under combined compression and shear and choose the dimensions such that the cell will just resist buckling. The second criterion for design is taken as a limit on the twist as adapted in the case of pure torsion. Two types of sections, rectangular and circular, are discussed in this note.

Minimum Weight Optimization of Offshore Jackets

1991 ◽  
Vol 113 (4) ◽  
pp. 292-296
Author(s):  
V. S. R. Murty ◽  
C. L. Rao ◽  
K. Rajagopalan
Keyword(s):  
Minimum Weight ◽  
Wave Forces ◽  
Weight Optimization ◽  
Wave Direction ◽  
Minimum Weight Design ◽  
Cross Sectional ◽  
Space Truss ◽  
The World ◽  
Weight Design ◽  
Period Wave

Offshore steel jackets are extensively used all over the world for the extraction of hydrocarbons from the reservoirs lying underneath the seabed. In this paper, the results of research carried out by the authors on the minimum weight optimization of the jacket for wave forces have been described. The gradient projection method has been used in the optimization. The jacket is modeled as a space truss and the cross-sectional areas of the tubular members have been the variables in the optimization process. The optimization histories with different sets of group area variables have been presented. The minimum weight design has been repeated over a range of ocean wave parameters, such as wave period, wave height, and wave direction, and the results are presented to indicate their interplay in the optimal picture.

Torsional Stiffness of a Thin-Walled Beam Braced by Pinned or Rigidly Fixed Transverse Diaphragms

1973 ◽  
Vol 15 (5) ◽  
pp. 351-356
Author(s):  
T. Harrison ◽  
J. M. Siddall
Keyword(s):  
Experimental Evidence ◽  
Theoretical Work ◽  
Torsional Stiffness ◽  
Cross Sectional ◽  
Cross Sectional Profile ◽  
Thin Walled ◽  
Sectional Profile ◽  
Good Agreement

The torsional stiffness of a thin-walled beam of open cross-sectional profile braced by evenly spaced transverse diaphragms is studied. Diaphragms rigidly fixed or attached by frictionless pins are treated and it is seen that, in either case, the only effect is to modify the St Venant torsional constant for the thin-walled beam. The theoretical work is supported by experimental evidence from two braced perspex channels which simulate the two assumed methods of attaching the diaphragms. Good agreement is demonstrated.

scholarly journals Simplified and Accurate Stiffness of a Prismatic Anisotropic Thin-Walled Box

2018 ◽  
Vol 12 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Giacomo Canale ◽  
Felice Rubino ◽  
Paul M. Weaver ◽  
Roberto Citarella ◽  
Angelo Maligno
Keyword(s):  
Cross Sections ◽  
Torsional Stiffness ◽  
Element Analysis ◽  
Cross Sectional ◽  
Analysis And Design ◽  
Proposed Model ◽  
Vertical Walls ◽  
Thin Walled ◽  
High Level ◽  
Realistic Geometries

Background:Beam models have been proven effective in the preliminary analysis and design of aerospace structures. Accurate cross sectional stiffness constants are however needed, especially when dealing with bending, torsion and bend-twist coupling deformations. Several models have been proposed in the literature, even recently, but a lack of precision may be found when dealing with a high level of anisotropy and different lay-ups.Objective:A simplified analytical model is proposed to evaluate bending and torsional stiffness of a prismatic, anisotropic, thin-walled box. The proposed model is an extension of the model proposed by Lemanski and Weaver for the evaluation of the bend-twist coupling constant.Methods:Bending and torsional stiffness are derived analytically by using physical reasoning and by applying bending and torsional stiffness mathematic definition. Unitary deformations have been applied when evaluation forces and moments arising on the cross section.Results:Good accuracy has been obtained for structures with different geometries and lay-ups. The model has been validated with respect to finite element analysis. Numerical results are commented upon and compared with other models presented in literature.Conclusion:For cross sections with a high level of anisotropy, the accuracy of the proposed formulation is within 2% for bending stiffness and 6% for torsional stiffness. The percentage of error is further reduced for more realistic geometries and lay-ups.The proposed formulation gives accurate results for different dimensions and length rations of horizontal and vertical walls.

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