A 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. Copyright © 2005 John Wiley & Sons, Ltd.

Discrete material optimization of general composite shell structures

A technique for the multiobjective optimisation of laminated composite structures using genetic algorithms and finite element analysis

Rapid increases in computer processing power, memory and storage space have not eliminated computational cost and time constraints on the use of structural optimization for design. This is due to the constant increase in the required fidelity (and hence complexity) of analysis models. Anecdotal evidence seems to indicate that analysis models of acceptable accuracy have required at least six to eight hours of computer time (an overnight run) throughout the last thirty years. This poses a severe challenge for global optimization or reliability-based design. In this paper, we review how increases in computer power were utilized in structural optimization. We resolve problem complexity into components relating to complexity of analysis model, analysis procedure and optimization methodology. We explore the structural optimization problems that we can solve at present and conclude that we can solve problems with the highest possible complexity in only two of the three components of model, analysis procedure or optimization. We use examples of optimum design of composite structures to guide the discussion due to our familiarity with such problems. However, these are supplemented with other structural optimization examples to illustrate the universality of the message.

Structural optimization complexity: what has Moore’s law done for us?

Multi-objective optimization of fiber reinforced composite laminates for strength, stiffness and minimal mass

Optimum design of composite laminates for maximum buckling load capacity using simulated annealing

Optimal design of hybrid laminates with discrete ply angles for maximum buckling load and minimum cost

An angle-ply laminated plate is optimized with the objective of minimizing the weight of the plate taking into account uncertainties in the multiple transverse loads. The weight is proportional to the laminate thickness which is minimized subject to deflection and buckling constraints under the least favourable loading with the ply angles taken as design variables. The convex modelling approach is employed to analyse the uncertain loading with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirements that these variations are bounded inL2 norm and represented by a finite number of eigenmodes. The effect of uncertainty on the optimal design is investigated quantitatively. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.

Minimum weight design of symmetric angle-ply laminates under multiple uncertain loads

Non-probabilistic modelling and design of sandwich plates subject to uncertain loads and initial deflections

Optimization of shear-deformable laminated plates under buckling and strength criteria

An angle-ply laminated plate is optimized with the objective of minimizing its weight subject to maximum deflection and buckling constraints. The plate has an initial deflection the shape of which is not known a priori, i.e., the initial deflection is not specified in a deterministic manner and as such it is uncertain. The weight is proportional to the laminate thickness which is minimized taking the ply angles as design variables and under the least favorable conditions of initial imperfections. The convex modeling approach is employed to analyze the uncertain initial deflection with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirement that these variations are bounded in L 2 norm. The results are given for both single load and multiple load cases and the effect of uncertainty on the optimal design is investigated. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.

A. Richter

Papers

Optimal design of hybrid laminates with discrete ply angles for maximum buckling load and minimum cost

Minimum weight design of symmetric angle-ply laminates under multiple uncertain loads

Non-probabilistic modelling and design of sandwich plates subject to uncertain loads and initial deflections

Optimization of shear-deformable laminated plates under buckling and strength criteria

Minimum Weight Design of Symmetric Angle-Ply Laminates With Incomplete Information on Initial Imperfections