Discrete material optimization of general composite shell structures

Abstract

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.

A practical multiscale approach for optimization of structural damping

“…An alternative way to achieve a design with discrete microstructures, would be to use an approach similar to what is done in optimization of fiber reinforced composites with a discrete set of fiber angles (see description of discrete material optimization (DMO) by Stegmann and Lund 2005). The implementation would require multiple design fields, and this is not necessary with the formulation presented here.…”

DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures

“…In this paper, we present a gradient based topology optimization method for mass minimization of laminated composite structures by the simultaneous determination of material distribution and thickness variation. The method is labelled Discrete Material and Thickness Optimization (DMTO), being an immediate extension of the original DMO method by Stegmann and Lund (2005). Mass minimization reduces material expenses and issues related to the net weight of the structure.…”

Multi-material topology optimization of laminated composite beams with eigenfrequency constraints

“…Luo and Gea [5] and Gea and Luo [6] presented a strategy for optimizing the location and orientation of stiffeners for eigenfrequency placement design of shell structures. Furthermore, Stegmann and Lund [7] and Pedersen [8] have presented solutions for the maximization of the minimum eigenfrequency design of laminated composite plates. The optimal design of beams with eigenfrequency constraints, however, has mostly concerned two dimensional problems addressing only the optimization of the cross section dimensions along the beam length (see, e.g., Olhoff [9] and Bendsøe and Olhoff [10]).…”

“…The framework is based on the principles of topology optimization (see, e.g., Bendsøe and Sigmund [20]) and relies on extensions to include multiple anisotropic materials of the Solid Isotropic Material with Penalization (SIMP) material interpolation technique (Bendsøe and Kikuchi [21] and Rozvany et al [22]), and the density filtering scheme by Bruns and Tortorelli [23]. This approach is a variation of the so-called discrete material optimization technique originally presented by Lund and Stegmann [24] and Stegmann and Lund [7] and applied to the optimal design of laminated composite shell structures.…”