Eigenfrequency and Buckling Optimization of Laminated Composite Shell Structures Using Discrete Material Optimization

Abstract

Abstract:The design problem of maximizing the lowest eigenfrequency or the buckling load factor of laminated composite shell structures is investigated using the socalled Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material, stacking sequence and fiber orientation simultaneously is illustrated for two multi-layered multi-material plate examples.

SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies

“…In Figure 6, it is seen that the proposed SFP parameterization with a penalty on the intermediate values of the design variables is very similar to the SIMP law classically used in topology optimization [17]. (4) and (8), the sensitivity analysis proposed in [9][10][11][12][13][14] could be easily adapted to the SF and SFP definitions.…”

“…In most practical applications, the candidate materials are restricted to 0, 45, -45 and 90° plies, which are the conventional orientations used in aeronautics. In their recent work, Lund and coworkers [9][10][11][12][13][14] have proposed the Discrete Material Optimization (DMO) approach to parameterize the topology optimization problem of structures made of fibers reinforced composite materials. This approach is an extension of the multiphase topology optimization proposed in [15].…”

“…Figure 1. Identification of the optimal material for the ply in a DMO scheme Several schemes have been proposed in [9][10][11][12][13][14] for defining the value of the weighting factors wi in (1). According to [12], the schemes of Equations (3) and (4) are the most reliable ones.…”

“…According to those authors [9][10][11][12][13][14], the problem with DMO4 (3) is that the condition (2) is only verified for design variables xi equal to 0 or 1, which could lead to convergence problems; the difficulty with DMO5, which is a scaled version of DMO4, is that the effect of the penalization p is less predominant, and the results can be made of many intermediate densities.…”

“…Nevertheless, both DMO4 and DMO5 perform well, and interesting solutions have been obtained in [9][10][11][12][13][14]. Finally, DMO is a very general method able to manage an arbitrary number of candidate materials.…”