•An analytical model with moderately large deflection theory is established by using energy minimization.•Theoretical model is proposed to predict the state of epidermal electronics laminated on a ...wavy bio-tissue: fully non-conformal, partially conformal and fully conformal states.•Theoretical model demonstrates that an external pressure can help the system to transform into a meta-stable fully conformal state.•The experimental data is proposed to verify the theoretical models and demonstrates three scenarios, which are consistent to theoretical results.
The conformability of epidermal electronics bonded onto bio-tissue is the key element to realize long-term and real-time monitoring physiological characteristics of human body. Currently, mechanics models of the epidermal electronics conforming to the bio-tissue are only applicable for the epidermal electronics whose thickness is larger than or close to the amplitude parameter of the bio-tissue (i.e., infinitesimal deflection theory). But an analytical model with moderately large deflection theory is proposed in this paper to predict the fully conformal, partially conformal and fully non-conformal states between the epidermal electronics and the bio-tissue through energy minimization, which combines the effects of epidermal electronics and bio-tissue geometries, work of adhesion and modulus of epidermal electronics. The model is verified by the experimental observations, and thereby can provide some guidance to a general design strategy for epidermal electronics bonded onto bio-tissue.
A theoretical formula for calculating the global shear buckling strength of curved corrugated steel webs (CSWs) under simply support conditions was derived. Their geometric parameters, namely the ...corrugation depth-to-web thickness ratio, web slenderness, and radius of curvature, which influence the elastic shear buckling strength, were also assessed. The computational error of the formula for the shear buckling of a curved CSW was verified to be within 2% using finite element analysis. Increasing the corrugation depth-to-web thickness ratio and decreasing web slenderness significantly reduced the elastic shear buckling strength. On the contrary, reducing the height of the web or increasing the web thickness had the opposite effect. Although the radius of curvature has little influence on the shear strength of a curved CSW, it significantly impacts the buckling mode. The results provide a theoretical reference for the design and application of curved CSW bridges.
The effect of membrane stress on axial strength of screw composite thin plate is addressed in this paper. In order to study the post-buckling behavior of the screw composite thin plate, the ...instability mechanism was analyzed theoretically based on the large deflection theory, experimental and numerical investigation were described in this paper. Considering the shear deformation and screw restraint, the calculation model of ultimate stress for the screw composite thin plate was established, and the analytical formula of the ultimate stress of the screw composite thin plate with four simply supported edges and two opposite sides under uniform compression was derived. The composite thin plate obtained from cold-formed steel back-to-back built-up short columns assembled by self-drilling screws, commonly used in practical projects, was used as the test models. Then, the experimental and numerical results were compared with theoretical results mentioned above to modify the proposed formula. According to the comparison, the modified coefficient φ was derived by nonlinear regression, and the modified ultimate stresses were in good agreement with the experimental and numerical results, the results were reasonable and reliable.
The present investigation aims to shed light on an important aspect of graphene reinforced multiscale composites that may appear in the form of reduced dimensional stability of the structure when ...exposed to thermal gradients. The study consists of two main parts: an extensive review of the related literature and a thermo-mechanical analysis of a laminated composite beam made of three-phases: arbitrary oriented Graphene Nanoplatelets (GNPs) embedded in an epoxy resin (ER) polymer matrix, reinforced with E-Glass fibers. The review of related literature reveals that the problem of finding the equivalent coefficient of thermal expansion (CTE) for multiscale composites is not as easy as the conventional composites, the trend is different, and more complicating parameters are involved. The analysis includes the predictions of the effective thermo-elastic properties of the multiscale composite laminate, based on Halpin-Tsai theory and hierarchy modeling, and the formulation of the beam deflection governing equation, based on Timoshenko nonlinear (large deflection) beam theory. Different GNPs weight fractions, different E-glass fiber volume fractions, and three lamination layups are investigated. It is found that the addition of GNPs increases the beam deflections when exposed to temperature gradients and that the laminate longitudinal CTE is the main factor responsible for this effect.
In nature, slender tibiae of stick insects have an excellent performance in resisting buckling, which raises the questions why the natural evolution chooses the pentagonal shape as the tibiae's cross ...section to resist buckling? Why is the proximal base round but the distal end pentagonal in adult tibiae? In this study, 3D geometrical models of the tibiae in stick insects are reconstructed aimed at investigating the buckling resistance strategy of the biological composite with different polygonal cross sections. The numerical result is consistent with the experimental observation. Based on large deflection theory, corresponding mechanical models proposed herein can accurately predict the structural response and mechanical behavior at buckling (including both Euler buckling and local buckling). Eventually, with the help of numerical and theoretical analysis, this article might have found the reason for the tibiae of stick insects naturally evolving to form the cross section with a pentagonal shape. In conclusion, the nature's choice of pentagon (S5) cross section could be a best compromise strategy to balance both Euler buckling and local buckling resistance capability. The knowledge gained from this work will inspire the designs of new advanced materials and structures.
This study demonstrates the reason for the tibiae of stick insects naturally evolving to form a cross section with a pentagonal shape. The results show that nature's choice of pentagonal cross section could be a best compromise strategy to balance both Euler and local buckling resistance capability. The knowledge gained from this work will inspire the designs of new advanced structures.
•A non-linear solution for static deflection of a diaphragm-type piezoactuator was proposed.•The analytical solution was validated with experimental data.•Center displacement and stroke volume of the ...piezoactuator were investigated with the dimensions.•Effects of the imposed loads on the performance of the piezoactuator (stroke volume) were discussed.
Analytical non-linear equations are formulated to predict the deflection of a circular diaphragm-type piezoactuator, which consists of a passive layer, a bonding layer and a PZT layer. Previous similar analytical solutions presented in the literature are based on thin plates with small deflections (linear problem), however the linear solutions fail to predict the deflection of the piezoactuator when the driven loads, such as voltage and pressure loads, are large. In this research, a non-linear analytical solution for the piezoactuator deflection under loads of voltage and pressure is derived using the principal of minimum energy and the Rayleigh-Ritz method. Each of the three layers in the piezoactuator is considered as an individual layer. The energy associated with the solution includes elastic potential energy of the deformed piezoactuator, electric potential energy in the piezodisc, and the work done by the uniform pressure force. The proposed non-liner solution is validated via static deflection measurements, and it approves that the non-linear analytical results are found to be in a good agreement with the measurements while the linear solution is invalid when the loads are large. Based on the non-linear equations, the effects of the piezoactuator dimensions and the imposed loads on the actuator performance (stroke volume) are also investigated.
This work studied the deformation behavior and deformation parameters of dry rice vermicelli in the process of bending fracture based on the large‐deflection theory of compressive rod postbuckling. ...Dry rice vermicelli samples in five different lengths were investigated. Middle‐point deflection and bending angle in different axial displacements were measured using TA‐XT2i Texture Analyzer equipped with an in‐house‐built attachment. It was found that the end bending angle, the middle‐point deflection and the end axial displacement were in one‐to‐one correspondence with each other. The experimental results of middle‐point deflection and end bending angle were in good agreement with those from theoretical calculations and the errors of middle‐point deflection were below 2%. It was proposed that axial displacement instead of the middle‐point deflection or the bending angle should be used to predict bending fracture rate of straight dry rice vermicelli in different lengths as a new standard method.
Practical Applications
Bending fracture is an important indication to the ingredient components and processing quality of dry rice vermicelli. However, the actual determination by hand operation leaks scientificity on measuring the parameters, and the evaluation system should be more integrated and theoretical. Therefore, it is needed to theoretically demonstrate the deformation behavior of dry rice vermicelli in the process of bending fracture and to establish an instrumental method and the evaluation system to predict the bending fracture rate. The work demonstrates the deformation behavior by the large‐deflection theory of compressive rod postbuckling, clarifies the relationships between the three deformation parameters and develops a new method by measuring the axial displacement to predict the bending fracture rate. This method can be used in the quality control and quality detection stages. This study also contributes to develop a foundation of theory and method for predicting the bending resistance of slender straight food.
This paper introduces two semi-analytical models developed for the nonlinear analysis of stability of isotropic and orthotropic plates under uniaxial compression. The possibility of considering fully ...free in-plane displacements at longitudinal edges (or unloaded edges) is the innovation of these models over existing models, where these displacements are always assumed constrained to remain straight. Contributions for the large deflection theory of plates related to the derivation of analytical solutions for the Airy stress function which satisfy Marguerre׳s equations for isotropic and orthotropic plates are presented. Namely, the extension of the Coan and Urbana solution for isotropic plates in order to consider all the terms of the unknown amplitudes of the out-of-plane displacements and the derivation of a solution for orthotropic plates. Comparisons between the semi-analytical model and nonlinear finite element model results are presented in order to discuss the effect of in-plane displacement boundary conditions on behaviour and strength of plates similar to bottom flanges used in steel box girder bridges. This study shows that the semi-analytical models have a clear potential to provide accurate solutions, requiring only a short computer time. It is also shown that the in-plane displacement boundary conditions for the unloaded edges significantly influence the behaviour and strength of plates and this problem cannot be neglected in the definition of the design rules.
•We derived analytical solutions for the Airy stress function which satisfy Marguerre׳s equations.•We developed two semi-analytical models for the nonlinear stability analysis of plates.•Fully free in-plane displacements at unloaded edges is the innovation of these models.•The in-plane displacement conditions at unloaded edges cannot be neglected in the definition of the design rules.
A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges ...laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.
Semi-analytical elastic methods for stiffened plate analysis are computationally very efficient. In addition to eigenvalue analysis, such methods may also offer a viable approach for the prediction ...of ultimate strength limits (USLs) of the plates when combined with appropriate strength criteria. In this paper, existing strength criteria are discussed, and extended criteria proposed for plates with various stiffener arrangements and boundary conditions such as full out-of-plane supports along all edges or plates with a free or partially stiffened edge. The extended criteria reflect in a simplified manner the effect of redistribution of stresses due to the formation of local plastic regions at stiffeners, supporting edges and in the plate interior. The equilibrium path is traced using large deflection theory and the Rayleigh–Ritz approach on an incremental form. The approach is able to account for the reserve strength of slender plates in the postbuckling region. With the considered criteria included, good agreement is obtained with results from fully nonlinear finite element analyses for different support conditions and for a variety of plate and stiffener dimensions.
► Computationally efficient methods for quick ultimate strength prediction of stiffened plates. ► Plates with various geometry, boundary condition and applied loads are considered. ► Extended strength criteria are used in combination with semi-analytical methods. ► Rayleigh–Ritz method is used with large deflection theory to account for reserve strength.
