Optimum Design of Structures: With Special Reference to Alternative Loads Using Geometric ProgrammingThis volume constitutes an important addition in our Lecture Notes in Engineering Series. The search for optimal structural shapes is at the fourtdation of all engineering analysis. Furthermore el)gineering as a whole can be seen as a process of looking for optimum solutions. The importance of Dr Chibani's work is that it deals with the integrated process of analysing and designing the optimum structure in a single operation. The design shape as well as the usual structural constraints are incQr.porated into the mathematical problem. This approach which is more suitable to computer applications has the difficulty of introducing a large number of variables and constraints equations. To overcome this problcm Dr Chibani proposes to apply a multilevel optimization technique which rcduces the dimensionaiity of a large scalc structural problem. The hook exp.I.111ns how a large optimization problem can be divided into Hcvcral partH of .1 smaller dimension which can then be solved eithcr scquentially or in parallel to obtain the solution of the original problem. Applicationsto these type structures provide a demonstration of the effectiveness of the procedure. |
Contents
INTRODUCTION | 1 |
GEOMETRIC PROGRAMMING WITH EQUALITY CONSTRAINTS | 36 |
PARALLEL DECOMPOSITION FOR ALTERNATIVE LOADS | 61 |
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12 CYCLE 20 CYCLE 25-Member Truss algorithm b opt alternative loads analysis equations Area of bar Area of Members area w/o decomposition BAR 1 in² bar element basis reduction coordinate system coordinating constraints coordinating variables coordination algorithm cross-sectional areas CYCLE NO 16 CYCLE NO CYCLE CYCLE NO Fig Cyclic Iteration History design areas design shape variables developed equality constraints Example 1 Algorithm feasible final design finite element first-level problem fully stressed Function for Subproblem geometric program global solution goal coordination method in³ inequality constraints initial design initial relaxation integrated optimum structural linear program load condition Minimize move coordination method multilevel nodal displacements node nonlinear programming objective function obtained optimal design optimization problem optimum structural design posynomial reduced response variables Schmit second level solve the following stiffness equation straints structural design variables subproblem 2 opt subsystem technique Three Bar Truss tion variable linking w/o decomposition AREA