A displacement-based optimization for truss structures subjected to static and dynamic constraints

Missoum, Samy; Hernandez, Pascal; Gürdal, Zafer; Guillot, Jean

doi:10.2514/6.1998-4793

Cited by 8 publications

(4 citation statements)

References 6 publications

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“…[1,2] that the derivatives of the implicit optimal weight, which is being minimized in the outer problem, with respect to the displacements can be computed readily from the Lagrange multipliers of the inner problem. In the case of frames, the objective function is the sum of the structural weight and the slack variables.…”

Section: Derivative Informationmentioning

confidence: 99%

“…The method has proven to be efficient for truss structures [1,2] that exhibit both linear and nonlinear response, reducing drastically the computational time to reach an optimum solution. In the linear case, a description of some properties of the optimization in the displacement space can be found in [1,3].…”

Section: Introductionmentioning

confidence: 98%

“…In the linear case, a description of some properties of the optimization in the displacement space can be found in [1,3].…”

Section: Introductionmentioning

confidence: 99%

“…The method was originally implemented for optimization of truss structures that exhibit linear or geometrically nonlinear behavior [1,2]. The method is applied here to two-dimensional frames in order to address the more realistic problems that involve the bending of structural members.…”

Section: Introductionmentioning

confidence: 99%

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A displacement based optimization for nonlinear frame structures

Missoum

Gürdal

2001

19th AIAA Applied Aerodynamics Conference

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An extension of the displacement based optimization method to frames with geometrically nonlinear response is presented. This method, when applied to trusses with linear and nonlinear response, provides a substantial reduction in computational time for design optimization. The efficiency of the method is due to the elimination of numerous finite element analyses that are required in using the traditional optimization approach. For frame problems, the number of degrees of freedom is typically larger than the number of cross sectional area design variables leading to difficulties in the implementation of the method compared to the truss implementation. A scheme that relaxes the nodal equilibrium equations is introduced, and the method is validated using test examples. The optimal designs obtained by using the displacement based optimization and the classical approaches are compared to demonstrate the computational efficiency of the method for frame structures. Nomenclature K = Stiffness matrix u = Displacement vector f = Force vector a = Cross section properties vector a u = Cross section upper bounds vector ai = Cross section lower bounds vector e = Slack variable vector l o = Original length of a frame member 1 = Updated length of a frame member m = Number of frame elements n = Number of degrees of freedom nc = Number of constraints gi = Constraint W = Structural weight INTRODUCTIONStructural optimization has been a rapidly developing research field for the last three decades. A substantial amount of the research performed so far is based on the evaluation of structural response and its sensitivities using finite element method (FEM). In those problems, cross sectional areas of rods and thicknesses of plate and shell elements are commonly used as the optimization design variables. A typical strategy for the solution of an optimization problem is an iterative process in which the structural analysis equations are solved repeatedly until no progress can be made. Depending on the number of variables, such a technique may require a large number of analyses

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Section: Derivative Informationmentioning

confidence: 99%