Minimum Weight Design of Beams With Inequality Constraints on Stress and Deflection

1967 ◽  
Vol 34 (4) ◽  
pp. 999-1004 ◽  
Author(s):  
E. J. Haug ◽  
P. G. Kirmser
Keyword(s):  
Computational Algorithm ◽  
Necessary Conditions ◽  
Minimum Weight ◽  
Inequality Constraints ◽  
Algebraic Equations ◽  
Minimum Weight Design ◽  
State Variable ◽  
Lagrange Problem ◽  
Nonlinear Algebraic Equations ◽  
Weight Design

A nonlinear optimal design problem, with state variable inequality constraints, is solved. The problem is reduced to a Lagrange problem in the Calculus of Variations and necessary conditions are presented. For a certain class of problems, the necessary conditions are reduced to a system of nonlinear algebraic equations which are solved by an iterative procedure. The computational algorithm is efficient and is easily programmed for use on a digital computer.

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.

Optimum Design of Bridge Girders for Electric Overhead Traveling Cranes

1978 ◽  
Vol 100 (3) ◽  
pp. 375-382
Author(s):  
S. S. Rao
Keyword(s):  
Design Problem ◽  
Function Method ◽  
Minimum Weight ◽  
Inequality Constraints ◽  
Bridge Girders ◽  
Penalty Function Method ◽  
Minimum Weight Design ◽  
Overall Stability ◽  
Weight Design ◽  
Load Conditions

The problem of the design of box-type bridge girders for electric overhead traveling cranes is formulated as a minimum weight design problem with inequality constraints. The restrictions placed on the design problem include limitations on the maximum allowable deflections and stresses as well as on the shock absorbing capacity during accidental collision. The overall stability and rigidity considerations are also taken into account. Several load conditions, as per the code specifications, are considered in the design problem. The resulting nonlinear programming problem is solved by using an interior penalty function method. Numerical examples are given to illustrate the effectiveness of the approach. The resulting computer program is used to make a sensitivity analysis of the problem.

Application of Pontryagin’s Principle to a Minimum Weight Design Problem

1970 ◽  
Vol 92 (2) ◽  
pp. 245-250 ◽  
Author(s):  
B. M. E. de Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Theory ◽  
Design Problem ◽  
Minimum Weight ◽  
Inequality Constraints ◽  
Minimum Weight Design ◽  
The Maximum Principle ◽  
Weight Design ◽  
And Control

A minimum weight design problem has been formulated as a general problem in optimal-control theory with the addition of state and control inequality constraints. Complete analytical solutions have been derived using the maximum principle of Pontryagin.

Minimum Weight Design of Ring Stiffened Cylinders Under External Pressure

1961 ◽  
Vol 5 (03) ◽  
pp. 44-49 ◽  
Author(s):  
George Gerard
Keyword(s):  
Yield Strength ◽  
Minimum Weight ◽  
External Pressure ◽  
Compressive Yield Strength ◽  
Minimum Weight Design ◽  
Weight Design

Minimum weight analyses for unstiffened and ring-stiffened cylinders under external pressure are presented for designs based on stability and compressive yield-strength considerations. The results for both types of cylinders are compared in terms of a common set of parameters to establish the efficiency of the stiffening system. The results are then compared on a somewhat different basis to establish the relative efficiencies of various classes of materials. Finally, certain conclusions are drawn of particular pertinence to deep submersibles.

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