• Henrik Fredslund Hansen
  • Christian Gram Hvejsel
4. semester, Design af Mekaniske Systemer, Kandidat (Kandidatuddannelse)
Design of modern multi-layered composite shell structures such as wind turbine blades is a highly complex task due to the conflicting requirements of high strength and stiffness at low weight and cost. In the development of such products, design optimization methods have become an increasingly important tool in aiding the designer at obtaining rational designs. Such optimization procedures rely on computationally efficient and robust analysis tools. The objective of the present project is to develop and implement efficient isoparametric degenerated shell finite element formulations for analysis and optimization of laminated composite shell structures. On basis of preliminaries pertaining to the finite element analysis of laminated composite shell structures, the governing equations for linear static stress analysis and linearized buckling analysis are developed. Formulation of degenerated isoparametric shell elements is shown and furthermore the thickness dependency of the strain-displacement relation is expressed explicitly. In combination with a linear approximation through the thickness of the inverse Jacobian matrix, explicit thickness integration is enabled. Consequently, the evaluation of element matrices may be performed efficiently for multi-layered shell elements with more than four layers. For higher number of layers, the formulation is an order of magnitude more efficient compared to layer-wise numerical integration schemes. The explicit thickness integration scheme's similarity with the integrations performed to obtain ABD-matrices in Classical Laminated Plate Theory reveals a link to lamination parameters. Thus, the stiffness matrix may be expressed in terms of an extended set of lamination parameters which turns out to be convenient in stiffness optimization. Structural design optimization is introduced and the maximum stiffness and the maximum stability design problem is formulated. For these problems design sensitivity analysis is shown for generalized design variables. From here, the focus is turned towards design optimization of composite laminates. Problems of non-convexity of a fibre angle parametrization is addressed by two simple examples. To provide convexity in stiffness optimization an alternative laminate parametrization is presented in terms of lamination parameters and the use with an existing laminate optimization procedure is outlined. A number of numerical examples are shown to validate the implementations of a 9- and a 16-node version of the element formulation. Convergence and accuracy of the `new' formulation is very similar to that of the existing isoparametric degenerated shell elements. In the thick shell range, the approximations made to enable explicit thickness integration cause some inaccuracy. For radius of curvature-to-thickness ratios above 25, the deviation of displacements compared to the existing isoparametric formulation is less than 4%. Eventually, two optimization examples confirm the performance gain in multi-layered settings.
Antal sider110
Udgivende institutionInstitut for maskinteknik
ID: 9853028