Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells

Moita, J.S; Barbosa, J. Infante; Soares, Carlos A. Mota

doi:10.1016/s0045-7949(99)00164-9

Cited by 46 publications

(31 citation statements)

References 19 publications

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“…As the neutral surface geometry changes, the direction of the local co-ordinate also changes from the relation described in Equation (11). Thus, this explicit dependency of the constitutive relation can be calculated as…”

Section: Direct DI Erentiation Methodsmentioning

confidence: 99%

“…Consequently, the design optimization of the shell structure has been an active research area for decades [1]. Even though signiÿcant research has been reported for shell structural optimization [2][3][4][5][6][7][8][9][10][11], however, the importance of design sensitivity analysis (DSA) has not been fully uncovered. The ÿnite di erence method (FDM) [2][3][4], the semi-analytical method [5; 6], the discrete method [7; 8], and the continuum method [9][10][11] have been used to calculate sensitivity information for the shell structure.…”

Section: Introductionmentioning

confidence: 99%

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Meshfree analysis and design sensitivity analysis for shell structures

Kim

Choi

Chen

et al. 2002

Numerical Meth Engineering

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SUMMARYA uniÿed design sensitivity analysis method for a meshfree shell structure with respect to size, shape, and conÿguration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. Because of a strong connection to the CAD tool, the design variable is selected from the CAD parameters, and a consistent design velocity ÿeld is then computed by perturbing the surface geometric matrix. The material derivative concept is utilized in order to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and e ciency of the proposed design sensitivity analysis method compared to the analytical solution and the ÿnite di erence solution.

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Section: Direct DI Erentiation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Meshfree analysis and design sensitivity analysis for shell structures

Kim

Choi

Chen

et al. 2002

Numerical Meth Engineering

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show abstract

“…Mathematical programming techniques are purely numerical and are concerned with tuning the optimizer itself rather than reformulating the problem or change the parametrization. Among others Bruyneel and Fleury [8] and Moita and co-workers [9] have applied such methodology with success. Still, these methods do not ensure convergence to the globally optimum solution.…”

Section: Orientation Optimization With Orthotropic Materialsmentioning

confidence: 99%

“…The difference between (10) and (11) becomes clearer when writing out the expression for e.g. three materials (phases) and comparing to (9): …”

Section: Element Level Parametrization-single Layered Structuresmentioning

confidence: 99%

Discrete material optimization of general composite shell structures

Stegmann

Lund

2005

Numerical Meth Engineering

538

223

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SUMMARYA novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested configurations. The applicability of the DMO method is demonstrated for fibre angle optimization of a cantilever beam and combined fibre angle and material selection optimization of a four-point beam bending problem and a doubly curved laminated shell.

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“…Analytical approaches to the optimization of ply angles (like e.g., Prager 1970;Pedersen 1989Pedersen , 1991Duvaut et al 2000;Khosravi and Sedaghati 2008;Vannucci et al 2009) are only available for geometrically simple cases. The application of mathematical programming either risks to get stuck in a local optimal solution (which may be accepted in some situations, like e.g., Topal and Uzman 2008;Johansen et al 2009) or requires extensive tuning of the optimizer itself in order to converge to the global optimal solution (e.g., Moita et al 2000;Bruyneel and Fleury 2002). So far, a transformation of the original to a convex optimization problem e.g., by lamination parameters is not available for general shell structures but only for simple geometries (Grenestedt 1990(Grenestedt , 1991Hammer et al 1997;Miki 1982;Foldager et al 1998;Abdalla et al 2007).…”

mentioning

confidence: 99%

Global laminate optimization on geometrically partitioned shell structures

Keller

2010

Struct Multidisc Optim

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A method aimed at the optimization of locally varying laminates is investigated. The structure is partitioned into geometrical sections. These sections are covered by global plies. A variable-length representation scheme for an evolutionary algorithm is developed. This scheme encodes the number of global plies, their thickness, material, and orientation. A set of genetic variation operators tailored to this particular representation is introduced. Sensitivity information assists the genetic search in the placement of reinforcements and optimization of ply angles. The method is investigated on two benchmark applications. There it is able to find significant improvements. A case study of an airplane's side rudder illustrates the applicability of the method to typical engineering problems.

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Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells

Cited by 46 publications

References 19 publications

Meshfree analysis and design sensitivity analysis for shell structures

Meshfree analysis and design sensitivity analysis for shell structures

Discrete material optimization of general composite shell structures

Global laminate optimization on geometrically partitioned shell structures

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