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Lipid nanotubes with well-designed cylindrical structures, tunable dimensions and biocompatible membrane surfaces have found potential applications such as templates to create diverse one-dimensional nanostructures and nanocarriers for drug or gene delivery. In this regard, knowing the encapsulation process is of crucial importance for such developments. The aim of this paper is to study the suction and acceptance phenomena of metallic nanoparticles, and in particular silver and gold, inside lipid nanotubes using the continuum approximation and the 6–12 Lennard-Jones potential function. The nanoparticle is modelled as a perfect sphere and the lipid nanotube is assumed to comprise six layers, namely two head groups, two intermediate layers and two tail groups. Analytical expressions are derived through undertaking surface and volume integrals to evaluate van der Waals potential energy and interaction force of a nanoparticle entering a semi-infinite lipid nanotube. These expressions are then employed to determine the suction and acceptance energies of system. To ascertain the accuracy of the proposed analytical expressions, the multiple integrals of van der Waals interactions are evaluated numerically based on the differential quadrature method. A comprehensive study is conducted to get an insight into the effects of different geometrical parameters including radius of nanoparticles, innermost radius of lipid nanotube, head group and tail group thicknesses on the nature of suction and acceptance energies and van der Waals interactions. Numerical results show that maximum suction energy increases by enlarging the nanoparticle size, while it decreases by increasing the head group thickness or the tail group thickness. It is further found that gold nanoparticle experiences higher maximum suction energies inside lipid nanotubes compared to silver nanoparticle.

In this paper, the elasto-plastic pre- and post-buckling behavior of beams made of functionally graded materials subjected to mechanical loading is investigated. A continuum-based finite element formulation is developed to determine the major characteristics of buckling. The arc-length algorithm is employed to analyze the stability problem. A plane stress von Mises model with isotropic hardening is utilized for the elasto-plastic nonlinear analysis of the beam. Basic idea in geometric and material nonlinear analysis of functionally graded material beams is to use the plasticity capacity of metal phase as a ductile material during loading. The influences of number of axial modes, material index, geometrical parameters and boundary conditions on the critical buckling point, pre- and post-buckling paths, plastic bifurcation point and stress distribution are fully studied. A good agreement between generated results and existing data in the literature is observed.

Side-door impact b eams are widely used in car doors to improve the passenger’s safety during the side impact. Fiber-reinforced polymer composite materials have a high specific strength and stiffness and are considered suitable candidate for this application. The aim of this study was to investigate energy-absorbing capacity of hat-shaped structures made from fiber-reinforced polymer composite materials at different boundary conditions. A finite element analysis model was developed using ABAQUS/Explicit code to achieve optimized fiber orientation and stacking sequence. Unidirectional E-glass fiber/polyester resin was used to construct hat-shaped beam energy absorber. Finite element analysis has revealed the optimized fiber orientations of [75/0/0/−75], [−75/0/0/75], [60/−30/30/-60], [−75/−30/75/30], [30/60/−30/−60] for quasi-static loadings, and [60/45/−45/−60], [45/−45/−60/60], [75/60/−60/−75], [−30/30/45/−45], [−75/−60/75/60] for impact loadings. Quasi-static bending as well as pendulum type impact test was carried out on specimens made with fiber orientation adopted from numerical analysis. Quasi-static bending test demonstrated that in fully clamped boundary conditions, composite layup orientation of [−75/0/0/75] showed maximum energy-absorbing capacity, but in other boundary conditions, composite layup orientation of [60/−30/30/−60] had the maximum energy-absorbing capacity. Contrarily, pendulum impact test for similar boundary conditions showed the highest energy absorption happened in fiber orientations of [−30/30/45/−45] and [−75/−60/75/60]. It was postulated that different modes of loading were the reason for this discrepancy.

This article introduces a new semi-analytical nonlinear finite element formulation for thin cylinders according to a continuum-based approach. A comparison between the continuum-based approach and the classical approach for the buckling behavior of isotropic and orthotropic perfect cylinders validates the results. The classical approach is defined according to thin shell theories based on the von Karman approximation. A mathematical modeling for geometry imperfection of cylinders is derived according to a continuum-based approach whose results are compared with the results of the classical approach for imperfect cylinders. The influence of neglecting some nonlinear terms in the classical approach for perfect and imperfect cylinders on the buckling path is investigated. In the buckling analysis, two methods, i.e. the perturbation and load disturbance methods, which undertake to switch to the post-buckling path, are compared to each other.