Studies on tailoring of thermomechanical properties of composites

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>Layered composite materials consisting of thin orthotropic layers offer for a designer many possibilities to tailor the structure: the behaviour and properties of the structure can be influenced not only by varying the geometry and thicknesses of the structure but also by varying the lay-up of the laminate. As new orthotropic materials having high specific strength and stiffness are used in structures, the tailoring is essential to utilize all the benefits of these materials. In this thesis tailoring and optimization of thermomechanical properties of layered composite structures are considered.</p><p>The tailoring problemis formulated and solved as a constrained nonlinear optimization problem. Different types of global thermomechanical properties, such as stiffnesses, coefficients of thermal expansion and natural frequencies and buckling loads of composite plates, as well as layer-wise properties, such as stresses and strains in a certain lamina, are considered. Also, coupled thermalstructural problems are studied.</p><p>When lay-up parameters, i.e. number of layers, and their orientations and thicknesses, are employed as design variables, global as well as layer-wise properties of the laminate can be considered. As relations between thermomechanical properties and lay-up parameters are highly nonlinear, optimization may suffer from various local optima. However, in tailoring the global minima or maxima are not the points of interest but rather the points of design space, where appropriate values for considered properties are achieved.</p><p>In the thesis optimization of global thermomechanical properties is presented also by applying so-called lamination parameters as design variables. The lamination parameters are defined as integrals of the functions, which consist of sines and cosines of the lay-up angles of different layers multiplied by the powers of the thickness co-ordinate z, through the thickness of the laminate. Thus, information of the lay-up of the laminate can be compressed into these parameters and only twelve lamination parameters are needed to describe the behaviour of a common laminate. The use of these parameters as design variables is advantageous, because the number of parameters needed is small and often formulating a convex optimization problem is possible. After finding optimal lamination parameters, a procedure is needed to generate a lay-up corresponding to these parameters. Explicit equations are derived for generating lay-ups having optimal bending lamination parameters. For creating a laminate having both optimal in-plane and bending lamination parameters, a new optimization problem searching laminates having lamination parameters as close as possible to the optimal ones is formulated. In that problem, also layer-wise properties and restrictions of manufacturing are taken into account. Agenetic algorithmsearch is employed for solving that later problem as the value of the objective function can be computed efficiently. Also, often the thicknesses and orientations of different layers can have only discrete values, which can be handled easily in the GA search, where all design variables are discrete in character.</p></div>