Abstract Thin-walled structures are widely used as lightweight energy absorbers, but conventional corrugated tubes still suffer from limited deformation controllability and high peak crushing force (PCF). Inspired by the periodic joints of natural bamboo, this study proposes a bionic bamboo-joint corrugated tube (BBCT) to improve crashworthiness. Quasi-static compression experiments and finite element simulations are conducted to reveal its deformation mechanism and validate the numerical model. Parametric analyses show that the bamboo-joint design promotes stable progressive folding and improves specific energy absorbed (SEA), mean crushing force (MCF) and crushing force efficiency compared with traditional corrugated and circular tubes under identical geometric and loading conditions. A theoretical model based on the simplified super folding element theory is established to predict the MCF, showing good agreement with numerical results. Furthermore, Kriging-based multi-objective optimization combined with Non-dominated Sorting Genetic Algorithm II is performed to maximize SEA and minimize PCF. Engineering-scale high-speed rail collision simulations demonstrate that the BBCT-based anti-climbing device achieves a 76.3–217.0% higher SEA than representative railway energy-absorbing structures reported in the literature, confirming its potential for lightweight impact energy management.
Abstract In this work, we present a mathematical framework to model mechanical behaviours of a polarized cell monolayer based on a Cosserat elasticity theory of thin structures. We show that cell polarization must remain tangential at free boundaries, resulting in an experimentally observed behaviour called an ‘edge effect’. We show that this behaviour is independent of the cell type. Furthermore, we present Legendre–Hadamard inequalities that must be satisfied at equilibrium for it to be a stable configuration.
Abstract The study of marriage dynamics and of strategies to reduce the likelihood of divorce has been an important research area for many years. Gottman's (Gottman. 1993 J. Consult. Clin. Psychol. 61, 6–15. (doi:10.1037/0022-006X.61.1.6)) research on successful marriages revealed three matched interaction styles: conflict-avoiding, validating and volatile. There has, however, been little progress in explaining how couples develop these styles of interaction and why failure to do so leads to failed marriages. In this paper, we show that these interaction styles arise as solutions to an optimal control problem where spouses jointly maximize a common goal. The validating style arises when the benefit from achieving joint happiness is balanced by the emotional cost of adopting a particular style. The ubiquitous conflict-avoider style arises naturally when spouses do not care about emotional costs. The volatile style is not an optimal solution, but volatile marriages may still be successful for spouses with highly positive natural dispositions. The problem of the spouses having different goals in marriage is relevant to marriage repair, and this problem will be studied in a later paper using differential game theory.
Abstract The attraction or repulsion force between two solid objects at a liquid-gas interface (i.e. the lateral capillary interaction force) is generally considered to be highly dependent on both the shapes of the solid surfaces and the relative positions. To challenge this, we propose an exotic capillary system in which the stationary exotic plate piercing the interface can produce a constant capillary interaction force on a partly immersed cylinder at different horizontal positions. This constancy is owing to the counterbalancing of variations in the horizontal components of the surface tension force and the hydrostatic pressure force on the cylinder. Through analysing the meniscus profiles and the capillary interaction force in the proposed exotic capillary system, five types of exotic plate shapes are identified. More importantly, a further analysis indicates that the lateral capillary interaction force in the proposed exotic capillary system remains constant even for different vertical positions of the cylinder. To verify the practicality of our theory, a three-dimensional numerical investigation is conducted, and the results show that the lateral capillary interaction force can remain nearly constant as expected. The proposed capillary system provides new insight into controlling the capillary interaction force. The constant-force regimes suggest passive routes for interfacial transport and micromanipulation, force regulation and suppression of undesired capillary aggregation.
Abstract This paper examines the modal properties, including modal frequencies and mode shapes, of lumped stiffness-mass systems with one degree-of-freedom (dof) per node. For the first time, it attains recursive solutions for the modal properties of such structures with general configurations. To this end, we introduce a recursive formulation to construct the stiffness and mass matrices of structures, and transform modal analysis into equivalent static problems of ‘modified structures’, where the masses assume a role of negative-stiffness springs. The static analysis of these modified structures hinges on a family of recursive functions, named characteristic rational P-functions, which encode all modal properties of the original structures. This recursive static solution allows modal analysis with an algorithmic complexity linear to the total number of dofs. We further derive exact modal solutions for structures with uniform stiffness and mass. The analysis includes the dispersion of modal frequencies, the linearity of modal periods to structural heights, the spectral distribution and the geometrical interpretation of mode shapes. The cumulative distribution of modal frequencies exhibits a staircase shape that converges to inverse trigonometric functions for a sufficiently large number of dofs. Lastly, we validate the convergence of an infinite-dof discrete model to a continuum model.
