Marco Montemurro

A New Paradigm for the Optimum Design of Variable Angle Tow Laminates

In this work the authors propose a new paradigm for the optimum design of variable angle tow (VAT) composites. They propose a generalisation of a multi-scale two-level (MS2L) optimisation strategy already employed to solve optimisation problems of anisotropic structures characterised by a constant stiffness distribution. In the framework of the MS2L methodology, the design problem is split into two sub-problems. At the first step of the strategy the goal is to determine the optimum distribution of the laminate stiffness properties over the structure, while the second step aims at retrieving the optimum fibres-path in each layer meeting all the requirements provided by the problem at hand. The MS2L strategy relies on: (a) the polar formalism for describing the behaviour of the VAT laminate, (b) the iso-geometric surfaces for describing the spatial variation of the stiffness properties and (c) a hybrid optimisation tool (genetic- and gradient-based algorithms) to perform the solution search. The effectiveness of the MS2L strategy is proven through a numerical example on the maximisation of the first buckling factor of a VAT plate subject to both mechanical and manufacturability constraints.

A General Hybrid Optimization Strategy for Curve Fitting in the Non-uniform Rational Basis Spline Framework

In this paper, a general methodology to approximate sets of data points through Non-uniform Rational Basis Spline (NURBS) curves is provided. The proposed approach aims at integrating and optimizing the full set of design variables (both integer and continuous) defining the shape of the NURBS curve. To this purpose, a new formulation of the curve fitting problem is required: it is stated in the form of a constrained nonlinear programming problem by introducing a suitable constraint on the curvature of the curve. In addition, the resulting optimization problem is defined over a domain having variable dimension, wherein both the number and the value of the design variables are optimized. To deal with this class of constrained nonlinear programming problems, a global optimization hybrid tool has been employed. The optimization procedure is split in two steps: firstly, an improved genetic algorithm optimizes both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the optimum solution provided by the genetic algorithm constitutes the initial guess for the subsequent gradient-based optimization, which aims at improving the accuracy of the fitting curve. The effectiveness of the proposed methodology is proven through some mathematical benchmarks as well as a real-world engineering problem.

On the correlation between stiffness and strength properties of anisotropic laminates

ABSTRACT This paper focuses on the analytical formulation of laminate-level failure criteria which are expressed (under a unified matrix formulation) in the framework of the first-order shear deformation theory (FSDT) in order to take into account the influence of the transverse shear stresses on the failure mechanisms. The proposed unified formulation relies on the utilization of the polar formalism generalized to the FSDT framework: in this background, all the considered criteria are stated in terms of tensor invariants. Furthermore, an important theoretical result is proven: the existence of a set of analytical relationships between the laminate strength and stiffness invariants.