A microstructure-dependent nonlinear Euler–Bernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the ...principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Kármán geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler–Bernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response.
A unified integro-differential nonlocal model Khodabakhshi, Parisa; Reddy, J.N.
International journal of engineering science,
October 2015, 2015-10-00, 20151001, Letnik:
95
Journal Article
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In this paper a unified integro-differential nonlocal elasticity model is presented and its use in the bending analysis of Euler–Bernoulli beams is illustrated. A general (for an elastic continuum) ...finite element formulation for the two-phase integro-differential form of Eringen nonlocal model is provided. The equations are specialized for the case of the Euler–Bernoulli beam theory. Several numerical examples, including the paradoxical cantilever beam problem that eluded other researchers, are provided to show how the present nonlocal model affects the transverse displacement of beams. The examples show that Eringen nonlocal constitutive relation has a softening effect on the beam, except for the case of the simply supported beam. A brief discussion on the applicability of the integro-differential model to other problems is also presented. Finally, the transition from the stiffened nonlocal simply supported beam to the softened nonlocal clamped beam is also investigated.
The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Kármán nonlinear strains. The equations of ...equilibrium of the nonlocal beam theories are derived, and virtual work statements in terms of the generalized displacements are presented for use with the finite element model development. The governing equilibrium equations of the classical and first-order shear deformation theories of plates with the von Kármán nonlinearity are also formulated. The theoretical development presented herein should serve to obtain the finite element results and determine the effect of the geometric nonlinearity and nonlocal constitutive relations on bending response.
The third-order shear deformation plate theory of Reddy A simple higher-order theory for laminated composite plates,
J. Appl. Mech. 51 (1984) 745–752 is reformulated using the nonlocal linear ...elasticity theory of Eringen. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and free vibration of a simply supported rectangular plate are presented using this theory to illustrate the effect of nonlocal theory on deflection and natural frequency of the plates. Finally, the relations between nonlocal third-order, first-order and classical theories are discussed by numerical results.
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches ...and, among them, one set of papers deals with Eringen's differential non-local model and another deals with the strain gradient theories. The present paper has the objective of establishing the fact that the length scales present in non-local elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nano-scale. The numerical results based on the new non-local strain gradient theory reveal some new findings with respect to lattice dynamics and wave propagation experiment that could not be matched by both the classical non-local stress model and the contemporary strain gradient theory. Thus, this higher-order non-local strain gradient model provides an explanation to some observations in the classical and non-local stress theories as well as: the strain gradient theory in these aspects.
In this paper a general nonlinear third-order plate theory that accounts for (a) geometric nonlinearity, (b) microstructure-dependent size effects, and (c) two-constituent material variation through ...the plate thickness (i.e., functionally graded material plates) is presented using the principle of virtual displacements. A detailed derivation of the equations of motion, using Hamilton’s principle, is presented, and it is based on a modified couple stress theory, power-law variation of the material through the thickness, and the von Kármán nonlinear strains. The modified couple stress theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The governing equations of motion derived herein for a general third-order theory with geometric nonlinearity, microstructure dependent size effect, and material gradation through the thickness are specialized to classical and shear deformation plate theories available in the literature. The theory presented herein also can be used to develop finite element models and determine the effect of the geometric nonlinearity, microstructure-dependent size effects, and material grading through the thickness on bending and postbuckling response of elastic plates.
Various available beam theories, including the Euler–Bernoulli, Timoshenko, Reddy, and Levinson beam theories, are reformulated using the nonlocal differential constitutive relations of Eringen. The ...equations of motion of the nonlocal theories are derived, and variational statements in terms of the generalized displacements are presented. Analytical solutions of bending, vibration and buckling are presented using the nonlocal theories to bring out the effect of the nonlocal behavior on deflections, buckling loads, and natural frequencies. The theoretical development as well as numerical solutions presented herein should serve as references for nonlocal theories of beams, plates, and shells.
Control of lipid droplet (LD) nucleation and copy number are critical, yet poorly understood, processes. We use model peptides that shift from the endoplasmic reticulum (ER) to LDs in response to ...fatty acids to characterize the initial steps of LD formation occurring in lipid-starved cells. Initially, arriving lipids are rapidly packed in LDs that are resistant to starvation (pre-LDs). Pre-LDs are restricted ER microdomains with a stable core of neutral lipids. Subsequently, a first round of "emerging" LDs is nucleated, providing additional lipid storage capacity. Finally, in proportion to lipid concentration, new rounds of LDs progressively assemble. Confocal microscopy and electron tomography suggest that emerging LDs are nucleated in a limited number of ER microdomains after a synchronized stepwise process of protein gathering, lipid packaging, and recognition by Plin3 and Plin2. A comparative analysis demonstrates that the acyl-CoA synthetase 3 is recruited early to the assembly sites, where it is required for efficient LD nucleation and lipid storage.
•Built-up steel sections as seismic metamaterial is studied.•Attenuation of surface waves is reported in single and six layered soil medium.•Low frequency wide bandgaps with relative bandwidth ...greater than 1.5 is achieved.•The competency of bandgaps is validated by frequency and time domain analyses.•More than 50% wave signal amplitude reduction is observed.
The purpose of this work is to investigate the propagation of surface waves through periodically arranged built-up steel section (resonator) in single and multiple layered soil medium (substrate) and to study the feasibility of surface waves attenuation by finite element technique. Two types of simple and small geometric size built-up sections are taken into consideration. Due to occurrence of local resonance between resonator and surface waves propagating on the surface of semi-infinite substrate, low frequency wide bandgaps are reported. Generation of local resonance is mainly governed by (i) impedance mismatch between the resonator and substrate (ii) coupling of longitudinal resonance modes of resonator with surface waves propagating on the surface of semi-infinite substrate. To have a more general and realistic study, surface wave propagation in single and six-layered soil medium is considered and the bandgaps are compared. Furthermore, with the variation in geometrical configuration of built-up section and change in material properties (soil profile), bandgap width and location changes. In the case of a layered soil medium, a relative bandwidth greater than 1.5 for both types of resonator is achieved. This implies that the proposed built-up sections are capable of attenuating surface waves in an extremely low frequency range. The position and width of bandgaps are further validated through finite unit cell based frequency response and time transient analyses. The findings substantiate the infinite unit cell model proposed here with the conclusion of more than 50% reduction in surface wave amplitude. The feasibility study manifests that the built-up structural steel sections can be applied as resonant barriers for mitigating seismic waves to protect important civil infrastructures from earthquake hazards.
Lipid droplets (LDs) are intracellular organelles that provide fatty acids (FAs) to cellular processes including synthesis of membranes and production of metabolic energy. While known to move ...bidirectionally along microtubules (MTs), the role of LD motion and whether it facilitates interaction with other organelles are unclear. Here we show that during nutrient starvation, LDs and mitochondria relocate on detyrosinated MT from the cell centre to adopt a dispersed distribution. In the cell periphery, LD-mitochondria interactions increase and LDs efficiently supply FAs for mitochondrial beta-oxidation. This cellular adaptation requires the activation of the energy sensor AMPK, which in response to starvation simultaneously increases LD motion, reorganizes the network of detyrosinated MTs and activates mitochondria. In conclusion, we describe the existence of a specialized cellular network connecting the cellular energetic status and MT dynamics to coordinate the functioning of LDs and mitochondria during nutrient scarcity.
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