### Abstract

A novel method for the analysis of variable stiffness plate-like structures using a Ritz based approach is presented. Significant improvements in the speed of analysis is achieved by reducing the number of numerical integrations that are be performed. The approach makes use of algebraic recursion relations applicable to Legendre polynomials. The Wigner(3j) coefficient is exploited as it can be used to define the product of two Legendre polynomials. In doing so the analysis is reformulated in ``triple product'' form. The satisfaction of boundary conditions and differentiation of the underlying basis functions are represented as matrix multiplication allowing all integrals to be defined using a common ``triple product'' greatly reducing computational cost. The approach is presented in one dimensional form, together with indicative performance studies showing an order of magnitude speed increase. This method is then generalised to two dimensional problems via the Kronecker matrix product where the increased efficiency of analysis is significant.

Original language | English |
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Title of host publication | 4th Aircraft Structural Design Conference |

Publisher | Royal Aeronautical Society |

Number of pages | 1 |

ISBN (Electronic) | 1 85768 322 6 |

Publication status | Published - 8 Oct 2014 |

## Fingerprint Dive into the research topics of 'Rapid Analysis of Variable Stiffness Plates: Legendre Polynomial Triple Product Formulation'. Together they form a unique fingerprint.

## Profiles

## Dr Matt O'Donnell

- Department of Aerospace Engineering - Honorary Lecturer

Person: Honorary and Visiting Academic

## Cite this

O'Donnell, M. P., & Weaver, P. M. (2014). Rapid Analysis of Variable Stiffness Plates: Legendre Polynomial Triple Product Formulation. In

*4th Aircraft Structural Design Conference*Royal Aeronautical Society.