Constant Bending Stiffness Research Articles

Self-Bending Behavior and Varying Bending Stiffness of Black Phosphorus/Molybdenum Disulfide (BP/MoS2) Heterostructure.

Vertically-stacked black phosphorus/molybdenum disulfide (BP/MoS2) heterostructures have broad prospects in flexible electronics. Bending is a common and highly concerned deformation for these flexible devices. However, the discrepancy in structures and properties among the components of 2D heterostructures often induces complex bending deformations. Here, the bending behaviors of BP, MoS2 and BP/MoS2 are investigated based on a molecular dynamics simulation. Compared with the constant bending stiffness of individual BP and MoS2, that of BP/MoS2 varies with the bending angle. Notably, a self-bending configuration induced by the lattice mismatch and size difference is found in BP/MoS2. The corresponding self-bending amplitude depends on the degree of size difference of each component and the “soft/hard” competition between them. Moreover, the size difference leads to a weakened bending stiffness, which is ascribed to the reduction in interlayer interaction. A prediction formula is proposed to evaluate the bending stiffness of BP/MoS2 with the size difference. This finding reveals novel ways for regulating the bending properties of 2D heterostructures, including the bending angle, characteristic size and stacking order. It offers an effective strategy for designing flexible devices with tunable bending performance.

Cell twisting during desiccation reveals axial asymmetry in wall organization

Plant cell size and shape are tuned to their function and specified primarily by cellulose microfibril (CMF) patterning of the cell wall. Arabidopsis thaliana leaf trichomes are unicellular structures that act as a physical defense to deter insect feeding. This highly polarized cell type employs a strongly anisotropic cellulose wall to extend and taper, generating sharply pointed branches. During elongation, the mechanisms by which shifts in fiber orientation generate cells with predictable sizes and shapes are unknown. Specifically, the axisymmetric growth of trichome branches is often thought to result from axisymmetric CMF patterning. Here, we analyzed the direction and degree of twist of branches after desiccation to reveal the presence of an asymmetric cell wall organization with a left-hand bias. CMF organization, quantified using computational modeling, suggests a limited reorientation of microfibrils during growth and a maximum branch length limited by the wall axial stiffness. The model provides a mechanism for CMF asymmetry, which occurs after the branch bending stiffness becomes low enough that ambient bending affects the principal stresses. After this stage, the CMF synthesis results in a constant bending stiffness for longer branches. The bending vibration natural frequencies of branches with respect to their length are also discussed.

Swinging and tumbling of multicomponent vesicles in flow

Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations and a two-dimensional system, we develop a reduced-order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid-body tumbling behaviour. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.

Simulating the effect of fabric bending stiffness on the wrinkling behaviour of biaxial fabrics during preforming

A macroscopic finite element model has been established to investigate the forming-induced wrinkling behaviour for bi-axial fabrics. Results indicate that using a linear bending model with a constant bending stiffness produces unrealistic wrinkle patterns in the fabric plies. A non-linear bending model produces more accurate forming induced wrinkle patterns compared to experimental data, since the bending stiffness parameter is varied as a function of the applied forming load to account for the onset of fibre buckling. Areas of high in-plane shear are more likely to induce out-of-plane wrinkles, indicating a positive correlation between wrinkling onset and shear deformation. A new methodology has been developed to quantitatively evaluate the severity of fabric wrinkles based on the FE simulation results. The distance between the surface of the preform and the mould tool is used to locate areas with out-of-plane defects, using the principal curvature to isolate wrinkles from areas of fabric bridging (poor conformity).

New Classes of Traveling Waves in a Planar Kirchhoff Beam with Nonlinear Bending Stiffness

New traveling wave solutions are presented for motion of an inextensible, unshearable, planar Kirchhoff beam endowed with rotary inertia and a generalized strain energy function for bending which models nonlinear stiffening and softening. It is shown that although sonic waves (i.e., wave traveling at the bar speed in the beam) do not exist for constant bending stiffness, nonlinear bending stiffness supports new classes of solutions that admit nonlinear waves traveling with axial tension or compression. In addition, it is shown that waves traveling at the bar wave speed may be compactons (i.e., solitary waves of finite span). Surprisingly, for a large class of constant and nonlinear bending stiffness, initially circular rods do not support traveling waves.

Analytical Solution of Optimization Problem of Stability of Frame Systems

The article deals with the problem of optimizing multi-story frame systems from the condition of stability. When solving the problem of optimizing the cross-sections of the elements of frame systems, the bearing capacity of which is determined by their stability, the known parameters are configuration, support fastenings, material and nodal loads. As an optimized parameter, the constant bending stiffness within each rod is assumed. The optimization problem is solved by the criterion of minimum volume of the frame material. The mathematical model compiled by the authors in a general form is a nonlinear mathematical programming task. To solve it, the method of Lagrange multipliers is used. The problem is solved in two stages. At the first stage of the stationary conditions, the authors obtained the relationships between the nodal displacements for free and non-free frames. In the second stage, at the found values of these relations, the determinant condition of the critical state of the frame structure can be represented in the form of a system of equations. In this case, the system of equations obtained by the method of Lagrange multipliers becomes analytically solvable with respect to unknown linear stiffnesses, since the equations entering into it do not contain reciprocal products of transcendental functions from unknowns. In this article, in closed form, equations are obtained that allow determining the optimal linear stiffnesses of columns and crossbars of free and non-free frames. The analytical solution obtained has been checked. To select the optimal stiffnesses from the stability condition, it is necessary to define the critical parameters using the constructive flexibility of the elements, using the functions presented in the paper, and then determine the linear stiffnesses of the posts and crossbars.

Material Selection for CFRP-Aluminium-Foam-Sandwiches Manufactured by a PUR Spraying Process

Sandwich structures are ideal for planar parts which require a high bending stiffness ata low weight. Usually, sandwich structures are manufactured using a joining step, connecting theface sheets with the core. The PUR spraying process allows to include the infiltration of the facesheet fibres, the curing of the matrix and the joining of the face sheets to the core within one processstep. Furthermore, this manufacturing process allows for the use of open cell core structures withoutinfiltrating the core, which enables a comparison of different material configurations, assembled bythe same manufacturing process. The selection of these materials, with the aim of the lowest possiblemass of the sandwich composite at a constant bending stiffness, is displayed systematically within thiswork.It could be shown that the bending modulus calculated from the component properties matched theexperimentally achieved values well, with only few exceptions. The optimum of the bending modulus,the face sheet thickness and the resulting effective density could be calculated and also matched theexperimental values well. The mass-specific bending stiffness of the sandwich composites with corestructures of open cell aluminium foams was higher than with closed cell aluminium foams, but wasexceeded by sandwich composites with Nomex honeycomb cores.

Structure–performance relationships for cantilever-type piezoelectric energy harvesters

This study provides comprehensive analysis of the structure–performance relationships in cantilever-type piezoelectric energy harvesters. It provides full understanding of the effect of all the practical global control variables on the harvester performance. The control variables considered for the analysis were material parameters, areal and volumetric dimensions, and configuration of the inactive and active layers. Experimentally, the output power density of the harvester was maximum when the shape of the beam was close to a square for a constant bending stiffness and a fixed beam area. Through analytical modeling of the effective stiffness for the piezoelectric bimorph, the conditions for enhancing the bending stiffness within the same beam volume as that of a conventional bimorph were identified. The harvester configuration with beam aspect ratio of 0.86 utilizing distributed inactive layers exhibited an giant output power of 52.5 mW and power density of 28.5 mW cm−3 at 30 Hz under 6.9 m s−2 excitation. The analysis further indicates that the trend in the output power with varying damping ratio is dissimilar to that of the efficiency. In order to realize best performance, the harvester should be designed with respect to maximizing the magnitude of output power.

Time History Modeling of Vibrations on Overhead Conductors With Variable Bending Stiffness

Although bending stiffness of cables is small, it has a large influence on the deformed shape near constraints. A practical application where it is important is for the prediction of the deflection curve of transmission-line conductors during aeolian vibrations. These vortex-induced vibrations may cause fretting fatigue failure at or near the location of clamped devices. The objective of this paper is to model with a nonlinear time history finite-element analysis the deformed shape of conductors during aeolian vibrations using available bending stiffness models. The deformed shape obtained numerically is compared to laboratory measurements available in the literature. It was found that theoretical bending stiffness models can be used to predict the deformed shape of cables near the clamps. However, the results obtained with variable bending stiffness are not significantly more accurate than those for a constant bending stiffness equal to half of the maximum theoretical bending stiffness. In general, the variation of bending stiffness found experimentally is less important than the prediction of nonlinear models. The dynamic nonlinear numerical method presented here remains a powerful tool for the prediction of the deformed shape of vibrating conductors.

Optimal Design of Cantilever with Circular Cross Section Made of Gradient Material by Symbolic Manipulation.

In this paper we consider optimal distribution of a gradient material at the circular cross section of a cantilever. The design variables are the parameters which express the distribution of the material density or the elastic constant, and Young's modulus is assumed to be linear in the material density. Two problems are analyzed : (1) maximization of the bending stiffness with constant weight, and (2) minimization of the maximum stress at the cross section with constant bending stiffness. In a general case, the above problems reduce to generalized eigenvalue problems which are formulated and solved by symbolic manipulation and numerical calculation. The optimal distribution indicates that for (1), the density is concentrated at the circular surface such as of a circular cylinder, and for (2), Young's modulus decreases with respect to the radius. The obtained results are also applicable to the optimal design of composite materials where the distribution of the material density is not continuous.

Non-dimensional probabilistic coefficients for laterally loaded piles

Non-dimensional probabilistic curves in terms of displacement and flexural moment coefficients are presented under the hypothesis of linear variation of the secant soil modulus of the soil reaction with depth to enable rapid estimations of probabilistic responses of laterally loaded piles. The soil properties are expressed in terms of p-y curves and the lateral head loads are considered to be random. Values of probabilistic non-dimensional coefficients are given for typical cases of piles having constant bending stiffness and driven in soft saturated clays.

On the optimal structural design for a nonconservative, elastic stability problem

The design of a cantilever column under a follower load is considered with the aim of maximizing the critical value of the load. The optimality condition is derived, and a modified Ritz method is used to determine an approximate solution for the bending stiffness. Results are obtained numerically for the case of a sandwich column with constant bending stiffness in each of two segments. It is found that, for the same structural weight, the optimal design yields a critical load significantly higher than that for a uniform column.