Mathematical Programming Procedures for Mixed Discrete-Continuous Design Problems

1974 ◽  
Vol 96 (1) ◽  
pp. 201-209 ◽  
Author(s):  
M. Pappas ◽  
A. Allentuch
Keyword(s):  
Mathematical Programming ◽  
Minimum Weight ◽  
Nonlinear Problems ◽  
Continuous Variables ◽  
Minimum Weight Design ◽  
Design Problems ◽  
Mixed Variables ◽  
Discrete Search ◽  
Weight Design ◽  
Stiffened Cylindrical Shells

Two mathematical programming procedures for treating nonlinear problems involving mixed variables are presented. One involves a relatively simple concept. First an optimum is located treating all variables as continuous. Adjacent discrete points are then evaluated in order of increasing distance from the all-continuous optimum, each evaluation requiring an optimization of the continuous variables, if any, until a satisfactory design is found. The other method utilizes an optimal discrete search to locate the optimum. These procedures are applied to the minimum weight design of stiffened, cylindrical shells where they prove to be effective.

Minimum Weight Design Problems of Fiber-Reinforced Beam Subjected to Uniform Bending

1985 ◽  
Vol 107 (1) ◽  
pp. 88-93 ◽  
Author(s):  
Juhachi Oda
Keyword(s):  
Minimum Weight ◽  
Bending Moment ◽  
Material Strength ◽  
Sequential Linear Programming ◽  
Volume Percent ◽  
Fiber Volume ◽  
Minimum Weight Design ◽  
Design Problems ◽  
Design Variables ◽  
Weight Design

Problems considered here are that of minimizing the weight of beams, which are subjected to a uniform bending moment and reinforced by the fibers distributed in the direction of beam axis. The beam is simplified as a multilaminate structure, of which the fiber volume percent Vfi of each lamina is considered as the design variables. To formulate this design problem the bending theory of multilaminate beam and the law of mixture for the composite material strength are applied. Furthermore, the sequential linear programming and the sequential unconstrianed minimization techniques are used to obtain the design solutions numerically.

Minimum Weight Design of Stiffened Cylinders

1970 ◽  
Vol 21 (1) ◽  
pp. 49-68 ◽  
Author(s):  
C. Lakshmikantham ◽  
G. Gerard
Keyword(s):  
Stability Theory ◽  
Comparative Evaluation ◽  
Minimum Weight ◽  
Cylindrical Shells ◽  
Minimum Weight Design ◽  
Physical Picture ◽  
Weight Design ◽  
Similarities And Differences ◽  
Stiffened Cylindrical Shells

SummaryIn this paper a generalised presentation for symmetrically stiffened orthotropic cylinders under compression is developed, based on a linear orthotropic stability theory of cylinders. Similarities and differences in the minimum weight behaviour of stiffened cylindrical shells and flat transversely-stiffened wide columns are investigated in some detail to provide a satisfactory physical picture. The concluding results provide a comparative evaluation of various forms of stiffening systems for cylindrical shells under compression.

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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