Buckling sensitivity analysis and optimal design of thin laminated structures

Mateus, H.C.; Soares, Carlos A. Mota

doi:10.1016/s0045-7949(96)00130-7

Cited by 21 publications

(10 citation statements)

References 18 publications

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“…Later, buckling optimization of composite structures was considered in a finite element framework where the buckling load was determined by the solution to the linearized discretized matrix eigenvalue problem at an initial prebuckling point. Optimization of laminated composite plates has been studied by [27,28,29,30,31,32], while others considered more complex composite structures as curved shell panels and circular cylindrical shells, see [33,34,35,36,37,38,39,40]. However, applications of optimization methods to stability analysis and design of a general type of complex laminated composite shell structures have been very limited.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear buckling optimization of composite structures

Lindgaard

Lund

2010

Computer Methods in Applied Mechanics and Engineering

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The paper presents an approach to nonlinear buckling fiber angle optimization of laminated composite shell structures. The approach accounts for the geometrically nonlinear behaviour of the structure by utilizing response analysis up until the critical point. Sensitivity information is obtained efficiently by an estimated critical load factor at a precritical state. In the optimization formulation, which is formulated as a mathematical programming problem and solved using gradient-based techniques, a number of the lowest buckling factors is included such that the risk of "mode switching" during optimization is avoided. The presented optimization formulation is compared to the traditional linear buckling formulation and two numerical examples, including a large laminated composite wind turbine main spar, clearly illustrate the pitfalls of the traditional formulation and the advantage and potential of the presented approach.

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Section: Introductionmentioning

confidence: 99%

Nonlinear buckling optimization of composite structures

Lindgaard

Lund

2010

Computer Methods in Applied Mechanics and Engineering

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“…As far as the geometric stiffness matrix is concerned, inconsistent forms have been often adopted by assuming ad hoc shape functions for within the element (Bathe and Ho, 1981;Mateus et al, 1997;Doyle, 2001;Khosravi et al, 2007). If the modified approximations obtained for and after enforcing the Kirchhoff constraint at selected points are used to generate the geometric stiffness matrix, such a matrix is said to be consistent because their shape functions are the same used in establishing the bending stiffness matrix.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

Neto

Araripe

Monteiro

et al. 2017

Lat. Am. j. solids struct.

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A large number of references dealing with the geometric stiffness matrix of the DKT finite element exist in the literature, where nearly all of them adopt an inconsistent form. While such a matrix may be part of the element to treat nonlinear problems in general, it is of crucial importance for linearized buckling analysis. The present work seems to be the first to obtain an explicit expression for this matrix in a consistent way. Numerical results on linear buckling of plates assess the element performance either with the proposed explicit consistent matrix, or with the most commonly used inconsistent matrix.

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“…The global displacements or stresses are functions of design variables, however, in the sensitivity analysis of the GSM, their influences are often neglected, e.g., by ignoring the terms containing their derivatives with respect to the design variables, for the purpose of simplification in coding and of reducing computational costs (Neves et al 1995;Mateus et al 1997;Bruyneel et al 2008). In doing so, the sensitivity analysis of buckling optimization is treated in the same way as that of a free vibration problem, which has been considered one of the error sources in a gradient-based optimization method for buckling analysis (Neves et al 1995;Mateus et al 1997;Bruyneel et al 2008). As explicit sensitivity analysis is not conducted in MIST (Tong and Lin 2011;Vasista and Tong 2012), issue (a) is not involved in the iterative processes.…”

Section: Introductionmentioning

confidence: 99%

Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method

Luo

Tong

2015

Struct Multidisc Optim

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This paper investigates topology design optimization for maximizing critical buckling loads of thin-walled structures using a moving iso-surface threshold (MIST) method. Formulation for maximizing linear buckling loads with additional constraints on load-path continuity and lower bound of eigenvalue is firstly presented. New physical response functions are proposed and expressed in terms of the strain energy densities determined in the two-steps of finite element buckling analysis. A novel approach by introducing a connectivity coefficient is developed to ensure continuity of effective load-path in optimum topology. The lower bound of eigenvalue is defined to eliminate spurious localized buckling modes. The MIST algorithm and its interfaces with commercial finite element (FE) software are given in detail. Numerical results are presented for topology optimization of plate-like structures to maximize critical buckling forces or displacements considering in-plane and out-of-plane buckling respectively. The FE analyses of the re-meshed final solid topologies with and without void material reveal that the presence of the void material has a significant effect on the out-of-plane buckling loads and a minor influence on the in-plane buckling loads.

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Buckling sensitivity analysis and optimal design of thin laminated structures

Cited by 21 publications

References 18 publications

Nonlinear buckling optimization of composite structures

Nonlinear buckling optimization of composite structures

An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method

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