Fine Wrinkling on Coarsely Meshed Thin Shells

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.

Eric Harold Mansfield. 24 May 1923—20 October 2016

Eric Mansfield was a structural engineer who worked at the Royal Aircraft Establishment Farnborough from 1943 to 1983 on a wide range of problems in the field of aircraft structures. His main working tool was the mathematical theory of elasticity, which he deployed with skill, ingenuity, perseverance and imagination to investigate many problems related to the design of aircraft structures during a period of development of higher flight performance and new materials. His studies included aircraft wings and fuselages, particularly in the presence of cut-outs and openings—for which he invented the ‘neutral hole’ concept—and problems involving large-deflection structural behaviour of plates, including thermal effects such as flexural and torsional buckling of fins and wings heated in supersonic flight. He also developed the novel and powerful tension field theory for understanding the post-buckling behaviour of thin webs in shear, and the analogous inextensional bending theory of thin wings. His mathematical models were confirmed by elegant experiments. Mansfield's book The bending and stretching of plates contains clear descriptions of many of his research investigations; it has become a classic text. All of Mansfield's writing is incisive and clear. He was widely regarded as a seminal figure in the field of applied structural mechanics in the second half of the twentieth century.

Experiment and Theoretical Analysis Study of ETFE Inflatable Tubes

The load bearing capacity of an ETFE (ethylene-tetra-fluoro-ethylene) inflatable tube is tested in this paper, and a comparative study of two wrinkling theories, the bifurcation theory and the tension field theory, is carried out for wrinkling analysis of the ETFE inflatable tube. Results obtained from the bifurcation theory and experiment reveal the limitations of tension field theory on the wrinkling analysis. The load-displacement curves of inflatable beams under bending load are obtained and compared with the experimental results; curves obtained using the bifurcation theory show coincidence with experimental curves, but the curves obtained using the tension field theory have noticeable deviations between calculated and experimental results.

Wrinkling Analysis of Stiffness Equivalence in Membrane Structures

Based on the tension field theory, a wrinkling analysis method of equivalent stiffness was proposed. The new method was derived and the feasibility was theoretically proved. And a membrane structure was analyzed by the method. The results show that the correct load responses could be quickly attained right after appearance of wrinkled elements, which indicate that the method can be applied to wrinkling analysis of membrane structures.