A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method

The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Kármán geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced computational cost. Currently the literature describes a small number of high-order numerical forced vibration problems, the majority of which are limited to DQM. To obtain forced vibration solutions using WQEM, the authors propose two different methods to obtain frequency response curves. The obtained results indicate that the frequency response curves generated by either method closely match their DQM counterparts obtained from the literature, and this is despite the low mesh density used for the WQEM systems

A novel formulation for the weak quadrature element method for solving vibration of strain gradient graded nonlinear nanobeams

A novel formulation of the weak form quadrature element method, referred to as the locally adaptive weak quadrature element method, is proposed to develop elements for nonlinear graded strain gradient Timoshenko and Euler–Bernoulli nanobeams. The equations of motion are obtained based on Hamilton principle while accounting for the position of the physical neutral axis. The proposed elements use Gauss quadrature points to ensure full integration of the variational statement. The proposed formulation develops matrices based on the differential quadrature method which employs Lagrange-based polynomials. These matrices can be modified to accommodate any number of extra derivative degrees of freedom including third-order beams and higher-order strain gradient beams without requiring an entirely new formulation. The performance of the proposed method is evaluated based on the free vibration response of the linear and nonlinear strain gradient Timoshenko and Euler–Bernoulli nanobeams. Both linear and nonlinear frequencies are evaluated for a large number of configurations and boundary conditions. It is shown that the proposed formulation results in good accuracy and an improved convergence speed as compared to the locally adaptive quadrature element method and other weak quadrature element methods available in the literature.Other Information Published in: Acta Mechanica License: https://creativecommons.org/licenses/by/4.0See article on publisher's website: http://dx.doi.org/10.1007/s00707-022-03321-4</p

A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method

The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Kármán geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced computational cost. Currently the literature describes a small number of high-order numerical forced vibration problems, the majority of which are limited to DQM. To obtain forced vibration solutions using WQEM, the authors propose two different methods to obtain frequency response curves. The obtained results indicate that the frequency response curves generated by either method closely match their DQM counterparts obtained from the literature, and this is despite the low mesh density used for the WQEM systems.Other Information Published in: Archive of Applied Mechanics License: https://creativecommons.org/licenses/by/4.0See article on publisher's website: http://dx.doi.org/10.1007/s00419-020-01713-3</p

Nonlocal and surface effects on nonlinear vibration response of a graded Timoshenko nanobeam

The free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported by on a nonlinear foundation is considered in this paper. The main contribution of this study is to propose a new formulation for the dynamic response of this beam by combining nonlocal and surface elasticity in addition to employing the physical neutral axis method which eliminates the quadratic nonlinearity from the equation of motion. Using the principle of virtual work, a fourth-order nonlinear partial differential equation is formulated and Galerkin technique is employed to yield a fourth-order ordinary differential equation with cubic nonlinearity in the temporal domain. The method of multiple scales is employed to obtain the analytical expression of the nonlinear frequency of the beam and its frequency response curve from a primary resonance analysis. To assess the accuracy of this analytical solution, it is compared with a numerical solution obtained using the differential quadrature method. The obtained analytical results are successfully validated for particular cases of the considered problem with results published by other authors. The effects of surface elasticity, nonlocality, the physical neutral axis, the beam aspect ratio, the power-law index and the elastic foundation coefficients on the free and forced vibration response of the graded Timoshenko nanobeam are thoroughly investigated for different types of boundary conditions .Other Information Published in: Archive of Applied Mechanics License: https://creativecommons.org/licenses/by/4.0See article on publisher's website: http://dx.doi.org/10.1007/s00419-022-02120-6</p

Computational modeling of die swell of extruded glass preforms at high viscosity

Computational simulations of glass extrusion are performed to quantify the effects of material behavior and slip at the die/glass interface on the die swell. Experimental data for three glass types are used to guide the computational study, which considers glass material to be viscous with and without shear thinning and viscoelastic using the Maxwell upper-convected model. The study starts with assuming no-slip at the glass/die interface to see if material behavior alone can explain the die swell results, and then considers slip using the Navier model where interface shear is directly proportional to the relative slip speed at the interface. Consistent with the possibility of slip and intended high viscosity applications, viscosity ranging from 107.4–108.8 Pa·s was used. Based on optimization of the various input parameters required to achieve the measured die swell and ram force values, the study concludes that interface slip occurred as only extreme values of the shear thinning parameters provided an alternative.Mohamed Trabelssi, Heike Ebendorff-Heidepriem, Kathleen C. Richardson, Tanya M. Monro and Paul F. Josep

[Postoperative C-reactive protein is a reliable marker to detect complications after radical cystectomy]

International audiencePURPOSE: Postoperative serum C-reactive protein (CRP) can be measured after major abdominal surgery to predict of complications at postoperative day (POD) 4. However, in urology, no studies have been conduced to analyze the role of CRP after radical cystectomy. The present study aims to analyze the relationship between a high postoperative level of CRP and the presence of complications after radical cystectomy for cancer. MATERIALS AND METHODS: This multicenter retrospective study included 313 patients treated with radical cystectomy for cancer between January 2013 and July 2016. Among the patients, 57.5% of patients received urinary diversion using a Bricker ileal conduit, 30.5% an orthotropic ileal neobladder, and 11.5% had an ureterocutaneostomy. RESULTS: Three hundred and thirteen patients were included (mean age 68.1\textpm9.2 years). Among the patients, 26.5% had grade>=2 complications, according to the Clavien-Dindo classification. In multivariate analysis, only CRP level at POD 4 predicted the risk of a complication (P\textless0.001). CRP\textgreater150mg/L at POD 4 was strongly associated with a risk of a postoperative complication after a cystectomy (OR=81.42, 95% CI [25.6-258.3], P\textless0.001). CRP assessed on POD4 was reliable at ruling out the existence of an infectious complications with a negative predictive value of 0.94. The main limitation of our study was it observational design. CONCLUSIONS: CRP at POD4 with a threshold of 150mg/L would reliably predict the risk of postoperative complications after cystectomy. Monitoring postoperative CRP could help adapt rehabilitation protocols after radical cystectomy and also the early management of complications

Computational Modeling Of Hole Distortion In Extruded Microstructured Optical Fiber Glass Preforms

Extrusion of glass preforms that are used to draw microstructured optical fibers was simulated using computational mechanics. The study focused on a preform with a cross-section geometry that contains 36 holes arranged in three hexagonal rings. Symmetry allowed for the modeling of a 30° portion of the cross section, which included five holes within this reduced computational domain. The simulations took into account flow through an array of 13 feed holes, flow along five circular pins to create the holes, exit from the die, and the development of a constant profile for the cross section of the preform. The primary concern in the study was exploring the capacity of the model to reproduce the observed distortion of the extruded holes, i.e., the difference between the holes that develop and the negative of the pin arrangement, by taking into account the complexity of the flow. The key features that describe the model are viscous flow, uniform temperature, interface slip using the Navier friction model, and the assumption of a steady-state solution. Validation of the procedure was based on a comparison between the predicted cross section and an actual preform. The results show that distortion of the holes is rather sensitive to the level of friction, which provides insight into reducing the magnitude of distortion in future experimental work

Nanotechnological formation of nanomers

The article presents such components of nanoindustry as nanomaterials, nanotools, nanointermediaty products with nano-components, as well as a variety of nano-objects and nanocomposites. The authors analyzed the main methods of obtaining nanomaterials