Vibration analysis of rotating fully-bonded and delaminated sandwich beam with CNTRC face sheets and AL-foam flexible core in thermal and moisture environments

Abstract

In the present study, the high-order free vibration analysis of rotating fully-bonded and delaminated sandwich beams; with and without vertical contact; containing AL-foam flexible core and carbon nanotubes reinforced composite (CNTRC) face sheets subjected to thermal and moisture field are investigated by using generalized differential quadrature method (GDQM). The compressible core and face sheets of sandwich beam, respectively, are composed of Aluminum alloy foam with variable mechanical properties in the thickness direction and CNTRC with temperature dependent material properties. In this study, the high-order sandwich panel theory (HSAPT) for AL-foam flexible core and Euler-Bernoulli beam theory for CNTRC face sheets are considered. By employing Hamilton’s principle, the governing partial differential equations of motion and associated boundary and continuity conditions for various types of regions (fully-bonded, delaminated with contact, delaminated without contact) are derived and then discretized by using GDQM. The final formulations lead to 14 partial differential equations for the entire structure including five equations for fully-bonded two-headed parts of AL-foam cored sandwich beam (AL-FCSB) and four equations for delaminated middle part of AL-FCSB beam which are combined in axial and transverse deformations. A parametric study is performed to investigate the influence of some important parameters such as existence of delaminated region, type of delaminated region (with or without contact), longitudinal position of delaminated region, slenderness ratio, face sheet thickness ratio, CNT volume fraction, temperature rise, moisture concentration, rotating speed, and hub radius. The obtained results reveal that the 1st frequency of delaminated AL-FCSB beam, whether with or without vertical contact, is less remarkably than ones of fully-bonded AL-FCSB beam which its value for the case of delaminated ‘with contact’ is larger than that of ‘without contact’. Moreover, the 1st frequency variation of the delaminated AL-FCSB beam is symmetrical with regard to the longitudinal position of the debonded region such that the 1st natural frequency declines with moving the debonded region toward the center of the beam. The study of vibration behavior of rotating sandwich beams is very important in design of rotating structural systems, specially damaged ones, such as airplanes, helicopter rotor blades, and robot arms. One of the most important types of damage encountered in mentioned cases is the decomposition of two layers or delamination. Working these rotating structures in the media, are always along with variations of temperature and humidity and hence their mechanical properties may be changed due to the environment conditions.

Communicated by S. Velinsky     

Magnetically driven foldable shell type swimmers at Stokes flow

This paper focuses on the interaction of low Reynolds number (Re) flows and thin shell type deformable structures in the context of flexible body locomotion and addresses the coupled field problem through a numerical solution framework. The thin structure is discretized by enhanced three-node finite elements and coupled with boundary element based treatment of Stokes flow in a monolithic manner. The locomotion is triggered and driven by an external magnetic field that generates displacement dependent body couples over the magnetically sensitive parts of the flexible structure. A particular novelty of the paper is the use of internal hinges through which very large rotations and structural deformations can be combined in an efficient way. Using this concept; new, on the fly locomotion direction reversal mechanisms can be generated as demonstrated by the foldable bi-directional swimmer.

     

Stretching Graphene to 3.3% Strain Using Formvar-Reinforced Flexible Substrate

Background

As a one-atom-thick material, the mechanical loading of graphene in large scale remains a challenge, and the maximum tensile strain that can be realized is through a flexible substrate, but only with a value of 1.8% due to the weak interfacial stress transfer.

Objective

Aims to illustrate the interface reinforcement brought by formvar resins as a buffering layer between graphene and substrates.

Methods

Single crystal graphene transferred to different substrates, applied with uniaxial stretching to compare the interface strength, and finite element analysis was performed to simulate tensile process for studying the influence of Poisson’s ratio of the buffering layer for interface reinforcement.

Results

In this work we use formvar resins as a buffering layer to achieve a maximum uniaxial tensile strain of 3.3% in graphene, close to the theoretical limit (3.7%) that graphene can achieve by flexible substrate stretching. The interface reinforcement by formvar is significantly higher than that by other polymers, which is attributed to the liquid–solid phase transition of formvar for more conformal interfacial contact and its suitable Poisson’s ratio with graphene to avoid its buckling along the transverse direction.

Conclusions

We believe that these results can provide guidance for the design of substrates and interfaces for graphene loading, as well as the support for mechanics analysis of graphene-based flexible electronic devices.

     

Optimal Control of Turbulent Flow as Measure Solutions

Abstract

We use the concept of relaxed or measure-valued solutions for control problems of turbulent flow related to Navicr-Stokes equation. Sufficient conditions guaranteeing the existence of measure solutions arc presented. Results on existence of optimal controls for Blow up time and Bolza problems for such systems are also presented. New results on relaxed necessary conditions of optimality are proved. Further it is shown that the relaxed necessary conditions reduce to classical Pontryagin type necessary conditions if measure solutions degenerate into Dirac structure. The paper is concluded with an algorithm based on the new necessary conditions for computing optimal controls.     

An Experimental-Numerical Hybrid Method for Elastic Contact Problems*

ABSTRACT

An experimental-numerical hybrid technique for determining the contact stress distribution between two elastic bodies having both frictionless as well as bonded contact is discussed in this paper. The hybrid method makes use of experimental data collected at a section far from the contact surface and the numerically generated influence coefficients, in terms of the applied unit normal and shear stresses. The experimental data, i.e., the differences in normal stresses and the shear stress, are obtained using photoelastic analysis for the examples illustrated in this paper. When substituted into equations corresponding to the unit normal and shear stress applied in the contact region, this results in a set of algebraic equations which, when solved, allow the contact stress distribution to be obtained. This method is illustrated with examples involving simple and complex geometries of the contacting bodies.     

HYDROELASTICITY OF THE KIRCHHOFF ROD: BUCKLING PHENOMENA

We consider the nonlinear coupled hydroelastic problem of a general curved and twisted flexible slender structure (i.e. flexible riser, cable system, fish–farm net system, towed arrays, etc.) embedded in a nonuniform flow field such as the ocean environment; the flow direction is arbitrary, relative to the axis of the slender structure. The motion of the elastic structure is coupled with the hydrodynamic loads acting on the slender structure by the ambient flow field. An important input for such hydroelastic problems is the computation of the hydrodynamic loading per unit length experienced by the slender body. A rigorously derived improvement for the inertial loading per unit length over the commonly used Morison-type semi-empirical force (originally obtained for straight long structures in a uniform stream) is used. The structure is also allowed to undergo small (yet finite) deflections from its original reference central-line, due to a particular model of intrinsic elasticity governed by a corresponding nonlinear PDE, which corresponds to the well-known Kirchhoff rod elastic model. The system of coupled hydroelastic equations is investigated in order to derive analytically the influence of the hydrodynamic loading in a uniform stationary stream on the nonlinear stability of the straight rod. It is found that the presence of an ambient stationary stream decreases the critical parameters (critical twist) of the buckling phenomenon which is known to exist for the same rod when placed in a vacuum. Also revealed is a new type of stability loss, which is affected by viscous effects.     

Dynamic Tensile Response of a Microwave Damaged Granitic Rock

Background

Understanding the dynamic tensile response of microwave damaged rock is of great significance to promote the development of microwave-assisted hard rock breakage technology. However, most of the current research on this issue is limited to static loading conditions, which is inconsistent with the dynamic stress circumstances encountered in real rock-breaking operations.

Objective

The objective of this work is to investigate the effects of microwave irradiation on the dynamic tensile strength, full-field displacement distribution and average fracture energy of a granitic rock.

Methods

The split Hopkinson pressure bar (SHPB) system combined with digital image correlation (DIC) technique is adopted to conduct the experiments. The overload phenomenon, which refers to the strength over-estimation phenomenon in the Brazilian test, is validated using the conventional strain gauge method. Based on the DIC analysis, a new approach for calculating the average fracture energy is proposed.

Results

Experimental results show that both the apparent and true tensile strengths increase with the loading rate while decreasing with the increase of the irradiation duration; and the true tensile strength after overload correction is lower than the apparent strength. Besides, the overload ratio and fracture energy also show the loading rate and irradiation duration dependency.

Conclusions

Our findings prove clearly that microwave irradiation significantly weakens the dynamic tensile properties of granitic rock.

     

Videometrics Measurement for Dynamic Topography of Large Flexible Cable Net Based on Tiny Light Spot Markers

Background:

Traditional videometric method can not be used in the measurement of large flexible cable-net structure for its large overall size and small partial size.

Objective

A videometrics technique was proposed in this work to measure the topography and deformation of a large cable net structure.

Methods

Tiny spots with high brightness (and large gray gradient) are used to mark the cable net nodes. By arranging the imaging light path properly, the light spot markers can be enlarged and accurately identified in the captured images.

Results

The relationship between the imaging parameters and the gray distribution of the light spot markers were derived and verified. And a topographical measurement experiment of a cable net structure was carried out with the proposed videometrics technique.

Conclusions

The topography/deformation of the cable net can be measured with tiny-light spot markers, and the effectiveness and robustness of the technique on topography and deformation measurement of large cable-net structures are demonstrated.

     

A Global,Direct Algorithm for Path-Following and Active Static Control of Elastic Bar Structures*

ABSTRACT

A method is presented by means of which the equilibrium path of any elastic bar structure may be traced globally, without applying iteration techniques. The basic idea is that the bar structure is reduced to a set of Initial Value Problems (IVPs) with parameters, and the equilibrium path is piecewise linearly interpolated in the parameter space. The way in which this method is capable of handling problems of active static control is demonstrated. The mathematical basis of this type of method is described by Allgower and Georg [1] as the Piecewise Linear (PL) algorithm. Here it is shown how this algorithm can be applied to problems in structural mechanics.     

Formulating Three-Dimensional Contact Dynamics Problems

ABSTRACT

Complementarity formulations are a promising approach for solving dynamic multi-rigid-body contact problems. Two aspects of simulating contact in a complementarity setting are addressed here. First, an explicit formulation of the differential equations governing contact points for bodies of general surface geometry is developed. These equations may be used to integrate the contact position and to set up the basic dynamics equations. Second, an efficient method for handling frictionless planar contacts of arbitrary boundary shape is presented. Throughout, the problem is set up as explicitly as possible, with special attention being given to the way that the contact geometry is related to the dynamics.     

Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth

Background:

Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip.

Objective:

We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading.

Methods:

Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force.

Results:

The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data.

Conclusions:

The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.

     

A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data

Background

Digital Image and Volume Correlation (DIC and DVC) are non-contact measurement techniques that are used during mechanical testing for quantitative mapping of full-field displacements. The relatively high noise floor of DIC and DVC, which is exasperated when differentiated to obtain strain fields, often requires some form of filtering. Techniques such as median filters or least-squares fitting perform poorly over high displacement gradients, such as the strain localisation near a crack tip, discontinuities across crack flanks or large pores. As such, filtering does not always effectively remove outliers in the displacement field.

Objective

This work proposes a robust finite element-based filter that detects and replaces outliers in the displacement data using a finite element method-based approximation.

Methods

A method is formulated for surface (2D and Stereo DIC) and volumetric (DVC) measurements. Its validity is demonstrated using analytical and experimental displacement data around cracks, obtained from surface and full volume measurements.

Results

It is shown that the displacement data can be filtered in such a way that outliers are identified and replaced. Moreover, data can be smoothed whilst maintaining the nature of the underlying displacement field such as steep displacement gradients or discontinuities.

Conclusions

The method can be used as a post-processing tool for DIC and DVC data and will support the use of the finite element method as an experimental–numerical technique.

     

The Interaction between a Uniformly Loaded Circular Plate and an Isotropic Elastic Halfspace: A Variational Approach

ABSTRACT

The axially symmetric flexural interaction of a uniformly loaded circular plate resting in smooth contact with an isotropic elastic halfspace is examined by using an energy method. In this development the deflected shape of the plate is represented in the form of a power series expansion which satisfies the kinematic constraints of the plate deformation. The flexural behavior of the plate is described by the classical Poisson-Kirchhoff thin plate theory. Using the energy formulation, analytical solutions are obtained for the maximum deflection, the relative deflection, and the maximum flexural moment in the circular plate. The results derived from the energy method are compared with equivalent results derived from numerical techniques. The solution based on the energy method yields accurate results for a wide range of relative rigidities of practical interest.     

Phase interface conditions in a massless electron-positron gas

The steady motion of a massless electron-positron gas in a self-consistent electromagnetic field is considered. In such a gas, two phases are formed for each of the components: a dynamic phase, in which the particles move with the speed of light, and a static phase, in which the particles move with a subluminal speed. The static phase can exist only within the capture region, in which the conditions (E,H)=0 andE ²<H ² are satisfied. Strong and weak discontinuities of the electromagnetic field on the boundary of the capture region (at the phase interface) are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–172, January–February, 1990.     

Dynamic Analysis of a Flexible Vehicle Structure with Nonlinear Force Elements Using Substructure Technique∗

ABSTRACT

The substnicturing technique is used to analyze the motion of a flexible vehicle structure with nonlinear force elements. The number of effective degrees of freedom of the combined system model is greatly reduced by synthesizing the individually modeled substructures, using constraints of geometric compatibility at the interfaces. When combining the substructures, recursive-type nonlinear integral equations (NIE) are introduced instead of the conventional nonlinear differential equations (NDE). It is shown that the NIE formulation is computationally more efficient than the NDE formulation in simulating steady-state and transient responses of a flexible vehicle with nonlinear dampers. The NIE formulation is further applied to the nonlinear damping optimization problem, and it is found that this method is efficient for optimization.     

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Background

Image-based global correlation involves a class of ill-posed inverse problems associated with speckle quality and deformation gradients on specimen surfaces. However, the method used to simultaneously integrate the prior information related to images and deformations and effectively regularize these inverse problems still faces severe challenges, especially when complex heterogeneous deformation gradients exist over sample surfaces with locally degraded speckle patterns.

Objective

We propose a novel self-adaptive meshing-based regularization for global image correlation to determine spatially complex heterogeneous deformations.

Methods

A virtual truss system with a linearly elastic constitutive relationship is employed to self-adaptively implement surface meshing by numerically balancing the exerted virtual forces under the constraints of the local speckle image quality and deformation gradients. The 2-norm-based condition number of the local stiffness matrix is introduced to ensure numerical stability during meshing.

Results

The algorithms can behave as a smart regularization procedure integrating all the prior information during numerical calculations, consequently achieving an accurate, precise and robust characterization of heterogeneous deformations, as demonstrated by virtual simulations and actual experiments.

Conclusions

The regularization strategy coupled to image-based correlation is also promising for automatic quantification of complex heterogeneous deformations, particularly from images with locally degraded speckle patterns.

     

A hemivariational inequality approach to the unilateral contact problem and substationarity principles

Summary The present paper deals with contact problems of structures for which the contact region is not a priori known. For the boundary conditions describing the contact both convex and nonconvex potential functions are considered. The first lead to variational inequalities and minimum energy principles and the second to a new type of variational forms, called hemivariational inequalities, and substationary-energy principles. Static and dynamic contact problems with friction and/or brittle fracture effects are considered. Applications illustrate the theory.

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Behandlung einseitiger Kontaktprobleme mit Hilfe hemivariationeller Ungleichungen und Substationaritätsprinzipe

Übersicht In diesem Aufsatz werden Kontaktprobleme behandelt, bei denen der Bereich des Kontaktes nicht a priori bekannt ist. Für die Randbedingungen, die den Kontakt beschreiben, werden sowohl konvexe als auch nicht-konvexe Potentialfunktionen betrachtet. Aus den konvexen erhält man variationelle Ungleichungen und Minimum Energieprinzipe; die nicht-konvexen führen zu einem neuen Typ variationeller Formen, die als hemivariationelle Ungleichungen und substationäre Energieprinzipe bezeichnet werden. Statische und dynamische Kontaktprobleme mit Reibung und/oder Sprödbruch werden betrachtet. Die Theorie wird anhand von Beispielen erläutert.

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Dedicated to Prof. Dr.-Ing. G. Nitsiotas on the occasion of his 60th birthday     

基于T样条的变网格等几何薄板动力学分析

具有大位移、大变形的薄板在接触碰撞等工况下, 其局部应变会产生剧烈变化. 为了保证对其进行动力学分析的精度和计算效率, 本文整合计算机辅助设计(CAD)与计算机辅助工程(CAE)系统, 提出了一种基于T样条曲面的变网格柔性系统等几何分析方法. 首先, 建立基于T样条曲面单元的基尔霍夫薄板运动学模型, 并根据非线性格林?拉格朗日应变建立由T样条曲面单元离散的薄板弹性模型. 其次, 通过在T网格中的局部区域插入节点的方式, 达到T样条曲面网格局部更新的目的. 利用T样条混合函数细化算法得到计算新广义变量的转换矩阵, 并结合广义α法创建了变自由度系统动力学方程的求解算法, 形成了系统的T样条单元局部细化算法. 最后, 静力学算例与柔性单摆模型分别验证了T样条薄板弹性模型的正确性, 以及T样条薄板单元在动力学分析上的精度和收敛性. 通过对受冲击柔性薄板的动力学分析表明, 本文所提出T样条单元及局部细化算法可以只在接触碰撞等应变剧烈变化的区域实现局部网格细化, 从而控制系统自由度数, 提高计算效率.      

A Comment on the Low Speed Impact of a Clamped Beam by a Heavy Striker∗

ABSTRACT

An approximate theoretical analysis is presented for a rigid, perfectly plastic clamped beam struck transversely at the mid-span by a mass which produces Finite transverse displacements. An alternative quasi-static procedure is proposed for estimating the dynamic plastic response of a beam when struck by a heavy mass that travels at a low speed. The theoretical basis of this method is explained and the accuracy is examined by an error analysis. Finally, it is suggested that this quasi-static procedure could be used for estimating the dynamic plastic response of other structures that are struck by a heavy mass traveling at a low speed,     

New Methodologies for Fracture Detection of Automotive Steels in Tight Radius Bending: Application to the VDA 238–100 V-Bend Test

Background

The VDA 238–100 tight radius V-bend test can be used to efficiently characterize the bendability and fracture limits of sheet metals in severe plane strain bending. Material performance in plane strain bending is critical for the selection of advanced high strength steels for energy absorbing structural components.

Objective

The detection of failure based upon a reduction in the punch force can lead to erroneous predictions of failure for ductile or thin gage alloys in the VDA 238–100 test. New failure criteria were proposed and evaluated across a range of automotive steels.

Methods

Four detection methods in the V-bend test were evaluated based upon the load drop, bending moment, novel stress metric and the strain rate for seven steels with strength levels from 270 to 1500 MPa. The appropriate failure threshold was identified from visual inspection of the surface during bending.

Results

The vertical punch force will decrease as a consequence of the mechanics in the V-bend test at intermediate bend angles even without fracture. The novel stress-based metric accounts for sheet thinning and could successfully identify “false positives” and punch lift-off when considering the strain-rate evolution.

Conclusions

Failure detection using the VDA load threshold method may significantly under-report the bend performance of alloys with intermediate-to-high bendability or thin gauges. The proposed stress-based metric can reliably detect fracture for bend angles in excess of 160° and be readily calculated using the existing data. The VDA load threshold for failure can work well for materials that exhibit significant cracking.