Resolving the morphological and mechanical properties of palm petioles: shape analysis methods for symmetric sections of natural form

Abstract

Palms support the largest leaves in the world and have evolved on Earth for over 120 million years. They are often reported to be the only structure left standing post-hurricane. Cross-sectional shapes of cantilevered structures are important design factors affecting torsional and bending performance. Understanding the shape contribution of natural sections such as palm petioles (modified leaf stalks) is more difficult than those for simple 2D shapes because conventional methods of calculating section properties are not well suited to these irregular shapes. The role of internal structure, material properties and external shape of palm petioles in cantilever performance has been investigated and three main contributions to knowledge result from this research. Firstly, 3D mapping, i.e., the size, orientation and position, of vascular bundles in the Trachycarpus fortunei palm petiole reveals the distributions of stress and Young’s modulus values, providing a more detailed understanding of petioles than previous work. Secondly, bulk elastic material properties along the longitudinal axis of the same petiole are then input to a bi-layered model of the same petiole establishing the Young’s modulus of the two layers without mechanically testing them individually and for determining that the outer layer is not lignified. Thirdly, the largest contribution is the introduction of modified shape transformers employing the use of circular envelopes, eliminating error caused by approximating second moment of area with the torsional constant. This leads to a novel Shape Edge Mapping (SEM) technique which deconstructs petiole cross section shape elements and enables the structural contribution of these elements to be calculated, improving the understanding of the petiole section and how it relates to its mechanical function. This thesis makes a valuable addition to the knowledge of palm function and presents novel techniques for non-destructive extraction of natural shape data for abstraction and use in preliminary engineering design.