A Bracing Nonlinear Walk in Applied Mechanics: Memoirs and Reflections

This article is an informal auto-biographical memoir by Mike Thompson, reflecting in retirement on his scientific researches in nonlinear phenomena, wandering pictorially from shell buckling, through bifurcations and chaos to climate tipping points. Some ideas and advice to young researchers are offered whenever it seems appropriate. Two research groups at University College London, and their two IUTAM Symposia are given some prominence, as are the ten years editing the Philosophical Transactions of the Royal Society.

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

Seismic design of liquid-containing concrete structures

The seismic design of structures is a requirement for any places [sic] where earthquake [sic] occurs, and the design is based upon the codes that vary according to the jurisdictions in which the code was developed for. This study introduces and assesses the document ACI 350.3-06 which was developed by the ACI Committee to guide the design of liquid containing structures, and compares to other codes such as ACI 350.3-01 and NZS 3106 of New Zealand Standard. The importance of liquid containing structures cannot be stressed further, as it is apparent in nuclear applications. The failure of tanks could be due to many reasons: 1) Shell buckling, caused by axial compression due to overall bending. 2) Roof damage as a result of sloshing of the upper portion of the containing liquid due to insufficient provision of freeboard. 3) Failure of inlets and outlets due to their inability to accommodate the deformations of the flexible tank. 4) Differential settlement or failure of supporting soil. The pressures resulted from earthquake [sic] can cause catastrophic disaster, and they [sic] are the impulsive and convective mode which exerts pressures on the walls of the tank. The hydrodynamic model used to estimate these pressures in the ACI 350.3-06 document has also adopted earlier works from Housner, Veletsos, and Shivakumar. Throughout the years, the code has transformed tremendously, and this study shows that the codes are very similar in many ways, yet their differences can yield significantly different results. Furthermore, the results from the various codes are illustrated using the same example, and the validity of the results are determined as well. The effects on seismic design due to the types of structure, whether the tank is rigid or flexible, and the support system are also introduced; moreover, their absences and the variations in the estimation of seismic parameters in some codes are also shown to have a large effect on the load estimation.

Seismic design of liquid-containing concrete structures

The seismic design of structures is a requirement for any places [sic] where earthquake [sic] occurs, and the design is based upon the codes that vary according to the jurisdictions in which the code was developed for. This study introduces and assesses the document ACI 350.3-06 which was developed by the ACI Committee to guide the design of liquid containing structures, and compares to other codes such as ACI 350.3-01 and NZS 3106 of New Zealand Standard. The importance of liquid containing structures cannot be stressed further, as it is apparent in nuclear applications. The failure of tanks could be due to many reasons: 1) Shell buckling, caused by axial compression due to overall bending. 2) Roof damage as a result of sloshing of the upper portion of the containing liquid due to insufficient provision of freeboard. 3) Failure of inlets and outlets due to their inability to accommodate the deformations of the flexible tank. 4) Differential settlement or failure of supporting soil. The pressures resulted from earthquake [sic] can cause catastrophic disaster, and they [sic] are the impulsive and convective mode which exerts pressures on the walls of the tank. The hydrodynamic model used to estimate these pressures in the ACI 350.3-06 document has also adopted earlier works from Housner, Veletsos, and Shivakumar. Throughout the years, the code has transformed tremendously, and this study shows that the codes are very similar in many ways, yet their differences can yield significantly different results. Furthermore, the results from the various codes are illustrated using the same example, and the validity of the results are determined as well. The effects on seismic design due to the types of structure, whether the tank is rigid or flexible, and the support system are also introduced; moreover, their absences and the variations in the estimation of seismic parameters in some codes are also shown to have a large effect on the load estimation.

Magneto-active elastic shells with tunable buckling strength

Shell buckling is central in many biological structures and advanced functional materials, even if, traditionally, this elastic instability has been regarded as a catastrophic phenomenon to be avoided for engineering structures. Either way, predicting critical buckling conditions remains a long-standing challenge. The subcritical nature of shell buckling imparts extreme sensitivity to material and geometric imperfections. Consequently, measured critical loads are inevitably lower than classic theoretical predictions. Here, we present a robust mechanism to dynamically tune the buckling strength of shells, exploiting the coupling between mechanics and magnetism. Our experiments on pressurized spherical shells made of a hard-magnetic elastomer demonstrate the tunability of their buckling pressure via magnetic actuation. We develop a theoretical model for thin magnetic elastic shells, which rationalizes the underlying mechanism, in excellent agreement with experiments. A dimensionless magneto-elastic buckling number is recognized as the key governing parameter, combining the geometric, mechanical, and magnetic properties of the system.