A stress function for 3D frames

This paper generalises Rankine diagrams for 3D trusses to be applicable to 3D frames. Rankine diagrams are a graphical representation of a state of self-stress in a 3D truss, with the area of reciprocal polygons representing the axial force in their corresponding original bars. Rankine diagrams are a polyhedral version of the continuous Maxwell-Rankine stress function. In this paper we present a new stress function. It is piecewise linear and discontinuous and it allows the analysis of 3D frames, giving all six stress resultants of axial and shear forces and bending and torsional moments in any member. A succinct statement of the stress function is given in terms of Clifford Algebra

A stress function for 3D frames

This paper generalises Rankine diagrams for 3D trusses to be applicable to 3D frames. Rankine diagrams are a graphical representation of a state of self-stress in a 3D truss, with the area of reciprocal polygons representing the axial force in their corresponding original bars. Rankine diagrams are a polyhedral version of the continuous Maxwell-Rankine stress function. In this paper we present a new stress function. It is piecewise linear and discontinuous and it allows the analysis of 3D frames, giving all six stress resultants of axial and shear forces and bending and torsional moments in any member. A succinct statement of the stress function is given in terms of Clifford Algebra

Numerical simulation of wave energy converters using Eulerian and Lagrangian CFD methods

During the last years many concepts of wave energy converters (WEC) have been proposed. All are designed to generate energy at competitive economic rates in average sea states and also to survive extreme wave conditions. Due to the complexity of most offshore wave energy devices and their motion response in different sea states, physical tank tests are common practice for WEC design. Full scale tests are also necessary, but are expensive and only considered once the design has been optimised. Computational Fluid Dynamics (CFD) is now recognised as an important complement to traditional physical testing techniques in offshore engineering. Once properly calibrated and validated to the problem, CFD offers a high density of test data and results in a reasonable timescale to assist with design changes and improvements to the device. Within the EPSRC funded research project "Extreme Wave Loading on Offshore Wave Energy Devices: a Hierarchical Team Approach" the two WECs Pelamis and the Manchester Bobber are investigated using different Eulerian and Lagrangian CFD techniques. Both devices float on the water surface and generate the electricity from the motion of the waves. Pelamis' overall movement is limited due to the mooring system, but the individual segments are allowed to move in 6 degrees of freedom and interact with the waves and the adjacent segments. The dynamics of the Manchester Bobber comprise the nominally vertical motion of the floats, which are arranged in an array, and the highly complex interactions between the floats and the waves. Two test cases leading towards simulation of the full dynamics of Pelamis and the Manchester Bobber have been modelled using different CFD techniques. The problems involve the interaction between regular waves and fixed horizontal cylinders of different levels of submergence. Results are compared with experimental data to calibrate the CFD codes. Furthermore, results for the fluid-structure interaction of an oscillating cone on the water surface are presented. The complexity of this problem is rather high, as it involves rigid body motion of an axisymmetric body. The motion is not linear, but is generated as a Gaussian focused wave packet. Complex jet-effects occur at the intersection of water and body surface. These and the forces on the structure are discussed. Four different CFD codes are applied to simulate the test cases: Smoothed Particle Hydrodynamics, a Cartesian Cut Cell method based on an artificial compressibility method with shock capturing for the interface, and two pressure-based Navier-Stokes codes, one using a Finite Volume and the other a control volume based Finite Element approach. © 2010 by The International Society of Offshore and Polar Engineers (ISOPE)

A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization

International audienceIsogeometric shape optimization has been now studied for over a decade. This contribution aims at compiling the key ingredients within this promising framework, with a particular attention to sensitivity analysis. Based on all the researches related to isogeometric shape optimization, we present a global overview of the process which has emerged. The principal feature is the use of two refinement levels of the same geometry: a coarse level where the shape updates are imposed and a fine level where the analysis is performed. We explain how these two models interact during the optimization, and especially during the sensitivity analysis. We present new theoretical developments, algorithms, and quantitative results regarding the analytical calculation of discrete adjoint-based sensitivities. In order to highlight the versatility of this sensitivity analysis method, we perform eight benchmark optimization examples with different types of objective functions (compliance, displacement field, stress field, and natural frequencies), different types of isogeometric element (2D and 3D standard solids, and a Kirchhoff-Love shell), and different types of structural analysis (static and vibration). The numerical performances of the analytical sensitivities are compared with approximate sensitivities. The results in terms of accuracy and numerical cost make us believe that the presented method is a viable strategy to build a robust framework for shape optimization