A particle system approach for modelling flexible wings with inflatable support structures

Abstract

Models of kites with inflatable support structures that are both fast and accurate can accelerate the development of airborne wind energy systems. The fast particle system approach has not yet been used to model inflatable beam structures. The goal of this research is to investigate if the bending behaviour of inflatable beams can be modelled accurately by a particle system approach and how such a model affects the computational costs. The inflatable tubular beam is segmented into a number of discrete elements which are connected by rotational joints which include rotary springs. A cluster of 6 particles interconnected with 13 spring forces in the shape of a pyramid was introduced to approximate each discrete beam segment. The reaction moments in the rotary springs were translated to reaction forces on the particles of two connecting pyramids. The simulation was programmed in a Java based particle system environment which uses the implicit Euler integration method for its stability properties. The required Jacobians of the proposed rotary spring reaction forces were derived analytically. The bending behaviour was defined accurate when the tip-deflection deviated less than 1mm with respect to a reference value. A clamped beam with linear stiffness was modelled and compared to Bernoulli bending theory. An inflatable beam with non-linear bending stiffness was then built and compared to a function that was fitted through experimental data of inflatable beams subjected to a tip-force. Accurate bending behaviour was achieved for both test-cases. The computation costs were measured by counting floating point operations in one iteration of a simulation. A sensitivity analysis was performed on the floating point operations induced by adding normal springs, rotary springs, particles, pyramid elements and iterations in the solver. It was found that the rotary springs are roughly 30 times more expensive to compute than normal spring forces. The real-time computation limit was tested by adding multiple beams to the simulation environment. The model proved computationally heavy as the computation time was bounded by the floating point performance of the hardware. A simulation of 17 beams comprised of approximately 350 particles, 50 rotary springs and 900 normal springs can run real-time on 2.4 Ghz computer using Java.