Abstract

We propose here an efficient approach for treating the interaction between membranes and fluids. Slight compressibility of the fluid is assumed. Classical total Lagrangian formulation including wrinkling is adopted for the membrane representation, whereas fluid is treated in an updated Lagrangian manner, developed in the current work. Assumption of slight compressibility of the fluid enables one to define the monolithic fluid-membrane system in a natural way. The displacements are the primary variables of both the fluid and the membrane domains. The formulation adopts the Particle Finite Element Method (PFEM) philosophy for free-surface identification and mesh regeneration. Three examples illustrate the functionality of the formulation in application to FSI problems involving motion of membranes in water

Abstract

This paper shows applications of a recently developed shell element to the analysis of thin shell and membrane structures. The element is a three node triangle with only translational DOFs (rotation free) that uses the configuration of the three adjacent elements to evaluate the strains. This allows to compute (constant) bending strains and (linear) membrane strains. A total Lagrangian formulation is used. Strains are defined in terms of the principal stretches. This allows to consider rubber materials and other type of materials using the Hencky stress-strain pair. An explicit central difference scheme is used to integrate the momentum equations. Several examples, including inflation and deflation of membranes show the excellent convergence properties and robustness of the element for large strain analysis of thin shells and membranes.

Abstract

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

Abstract

In modeling and numerically implementing a follower pressure in a geometrically nonlinear setting, one needs to compute the volume enclosed by a surface and its variation. For closed surfaces, the volume can be expressed as a surface integral invoking the divergence theorem. For periodic systems, widely used in computational physics and materials science, the enclosed volume calculation and its variation is more delicate and has not been examined before. Here, we develop simple expressions involving integrals on the surface, on its boundary lines, and point contributions. We consider two specific situations, a periodic tubular surface and a doubly periodic surface enclosing a volume with a nearby planar substrate, which are useful to model systems such as pressurized carbon nanotubes, supported lipid bilayers or graphene. We provide a set of numerical examples, which show that the familiar surface integral term alone leads to an incorrect volume evaluation and spurious forces at the periodic boundaries.

Abstract

Buildair S.A. has recently designed, manufactured and built an inflatable hangar (termed H75 hangar) for the aeronautic industry in Jeddah Airport (Kingdom of Saudi Arabia). H75 hangar is the largest aircell inflated structure ever built in the world, finally erected in July 2019. The structural analysis and design of the main body of the hangar has involved complex structural concepts due to the specificity of the structural elements employed, like membranes and straps which lead to a highly non-linear mechanical problem, or the treatment of wind over the structure without a defined standard for inflatable structures. In this paper, the structural conception and specificities of the structure are presented, as well as the design procedure for the H75 hangar based in the numerical analysis, to fulfill the design requirements in terms of stresses, and deformations for the structural elements of the main body.