Heterogeneous upper-bound finite element limit analysis of masonry walls out-of-plane loaded

A heterogeneous approach for FE upper bound limit analyses of out-of-plane loaded masonry panels is presented. Under the assumption of associated plasticity for the constituent materials, mortar joints are reduced to interfaces with a Mohr–Coulomb failure criterion with tension cut-off and cap in compression, whereas for bricks both limited and unlimited strength are taken into account. At each interface, plastic dissipation can occur as a combination of out-of-plane shear, bending and torsion. In order to test the reliability of the model proposed, several examples of dry-joint panels out-of-plane loaded tested at the University of Calabria (Italy) are discussed. Numerical results are compared with experimental data for three different series of walls at different values of the in-plane compressive vertical loads applied. The comparisons show that reliable predictions of both collapse loads and failure mechanisms can be obtained by means of the numerical procedure employed.     

A wave finite element‐based formulation for computing the forced response of structures involving rectangular flat shells

The harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave‐based form. A global wave‐based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave‐based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique. Copyright © 2013 John Wiley & Sons, Ltd.     

压电复合材料层板弱界面的四种力电热物理模型

基于对压电复合材料层合结构弱界面弹性场、电场、温度场的宏观和细观尺度分析, 构建了四种界面力-电-热模型, 分别为非耦合型、耦合型和混合型。依据这些界面模型, 得到了柱面弯曲简支压电复合材料层板的力-电-热多场耦合解。结果表明, 损伤界面的多场耦合物理描述介于宏观和细观尺度之间, 需要多尺度考虑, 且基于不同尺度的描述也可获得相似的规律。在热载和力载下, 不同的界面模型对弹性场影响趋同、差异甚小, 而对电场和温度场, 四种模型的影响各异、但规律相似; 在电载作用下, 不同的界面模型无论对弹性场还是电场, 都有显著的影响。     

NEAR FIELD TRANSIENT AXISYMMETRIC WAVES IN LAYERED STRUCTURES: EFFECTS OF WEAK COUPLING

Axisymmetric stress wave transmission through the leading layers of layered structures of infinite radial but finite axial extent is numerically studied by employing two different computational approaches: a technique based on the numerical inversion of Double Integral Transformations (DIT), and a Finite Element (FE) analysis. Considering the first approach, careful selections of the limits of the numerical inversions and the sampling rates are required in order to overcome inherent numerical instabilities associated with exponential dichotomy. This type of numerical instability is more evident in layered media with weak coupling. In such systems, direct multiplications of layer transfer matrices are avoided by employing a global scheme to assemble well-conditioned global transfer matrices. Moreover, the specific structure of the propagation and attenuation zones of the structure are taken into account for increasing the efficiency and effectiveness of the transfer matrix manipulations. Satisfactory agreement between the DIT and FE numerical results is observed, at least for early times. Close to the region of application of the external pressure, the FE simulations suffer from the discretization of the applied load, node-to-node oscillations and reflections from ‘infinite’ elements (‘silent boundaries’). Using the aforementioned numerical techniques, transient wave transmission in two-layered systems (one with weak and one with strong interlayer coupling) is considered, and the effects of weak coupling on the wave transmission is studied. We show that at early times, weak coupling results in stress localization in the region close to the applied pressure, a result which can have potential application in the use of layered media as shock isolators. © 1997 by John Wiley & Sons, Ltd.     

An embedded statistical method for coupling molecular dynamics and finite element analyses

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with finite element (FE) nodes at their common interface, necessarily requiring that the FE mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modelling to two‐dimensional material domains due to difficulties in simulating full three‐dimensional material processes. In the present work, a new approach to MD–FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and FE nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. Thus, the method lends itself for use with any FEM or MD code. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three‐dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied. Published in 2009 by John Wiley & Sons, Ltd.     

Modeling fatigue crack nucleation at primary inclusions in carburized and shot-peened martensitic steel

The mechanics of high cycle fatigue crack nucleation (formation of a stable crack that can grow away from the influence of the notch root of the inclusion) at subsurface primary inclusions in carburized and shot-peened martensitic steel subjected to cyclic bending is investigated using three-dimensional (3D) finite element (FE) analysis. FE models are constructed using a voxellation technique to address the shape, size, and distribution of primary inclusions within clusters. The critical depth for fatigue crack nucleation is predicted considering the gradient in material properties arising from carburization, prestrain and compressive residual stress distribution due to shot peening, and the gradient of applied bending stress. The influence of inclusion shape and interface condition (intact or debonded) with the matrix on the driving force for fatigue crack nucleation is examined. It is observed that the inclusion shape has minimal influence on the predicted results while the effect of the interface condition is quite significant. For partially debonded interfaces, the predicted critical depth from surface for fatigue crack nucleation agrees qualitatively with experimental observations.     

Nonlinear behavior of shear deficient RC beams strengthened with near surface mounted glass fiber reinforcement under cyclic loading

The aim of this investigation is to evaluate experimentally and numerically the cyclic loading response of reinforced concrete (RC) beams strengthened in shear with Glass Fiber Reinforced Polymer (GFRP) rods using the near surface mounted (NSM) technique. The experimental results indicated that the use of GFRP rods as NSM strengthening systems can significantly enhance the overall capacity and ductility of shear deficient RC members when subjected to cyclic loading. In particular, the increase in the load-carrying capacity of the strengthened specimens over the unstrengthened control specimen was in the range of 49–66%. Furthermore, the increase in the displacement over the control specimen ranged between 112% and 172%. A 3D finite element (FE) model was also developed to simulate the response of the tested specimens. The developed FE model integrates multiple simulation techniques, nonlinear material properties and corresponding constitutive laws. The models incorporate concrete cracking, yielding of steel reinforcement, bond–slip behavior between NSM reinforcement and adhesive material and between steel reinforcement and adjacent concrete material, respectively. The load–deflection response envelopes and the load–deflection hysteresis loops of the experimentally tested beams and those simulated by the FE models were compared. Good matching was observed between the predicted and measured results at all stages of cyclic loading.     

Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Making use of a mixed variational formulation including the Green function of the soil and assuming as independent fields both the structure displacements and the contact pressure, a finite element (FE) model is derived for the static analysis of a foundation beam resting on elastic half-plane. Timoshenko beam model is adopted to describe structural foundations with low slenderness and to impose displacement compatibility between beam and half-plane without requiring the continuity of the first order derivative of the surface displacements enforced by Euler–Bernoulli beam. Numerical results are obtained by using locking-free Hermite polynomials for the Timoshenko beam and constant reaction over the soil. Foundation beams loaded by many load configurations illustrate accuracy and convergence properties of the proposed formulation. Moreover, the different behaviour of the Euler–Bernoulli and Timoshenko beam models is thoroughly discussed. Rectangular pipe loaded by a force in the upper beam exemplifies the straightforward coupling of the foundation FE with a structure described by usual FEs.     

Efficient coupled refined finite element for dynamic analysis of sandwich beams containing embedded shear-mode piezoelectric layers

An efficient and computationally low cost finite element (FE) model is developed for dynamic free and forced response of sandwich beams with embedded shear piezoelectric layers based on a coupled refined high-order global-local theory. Contrary to most of the available models, all of the kinematic and stress boundary conditions are ensured at the interfaces of the shear piezoelectric layers. Moreover, both the electrical-induced strains components and transverse flexibility are taken into account for the first time in the present theory. For validation of the proposed model, various free and forced vibration tests for thin and thick sandwich beams are carried out. For various electrical and mechanical boundary conditions, excellent agreement has been found between the results obtained from the proposed formulation with previously published and the coupled two-dimensional (2D) FE results.     

Damage detection with genetic algorithms taking into account a crack contact model

This paper deals with the crack detection in structural elements by means of a genetic algorithm optimization method. The crack model takes into account the existence of contact between the interfaces of the crack. Many of the methods to detect a crack in beam-like structures are based on linear one dimensional models and are not straightforwardly applicable to structures such as beams or arcs with a breathing crack with or without contact. The present study addresses bi- and three-dimensional models to handle the dynamics of a structural element with a transverse breathing crack. The methodology is not restricted to beam-like structures since it can be applied to any arbitrary shaped 3D element. The crack is simulated as a notch or a wedge with a unilateral Signorini contact model. The contact can be partial or total. All the simulations are carried out using the general purpose partial differential solver FlexPDE, a finite element (FE) code. A genetic algorithm (GA) optimization method is successfully employed for the crack detection. The dynamic response at some points of the damaged structures are compared with the solution of the computational (FE) model using least squares for each proposed crack depth and location. An objective function arises which is then optimized to obtain an estimate of both parameters. Physical experiments were performed with a cantilever damaged beam and the resulting data used as input in the detection algorithm.     

Fastener pull-through in a carbon fibre epoxy composite joint

This paper considers the capability of finite element (FE) modelling to accurately predict fastener pull-through failure of composite laminates. Such failures are dominated by inter-ply delamination and through-thickness shear failure of the laminate and the common modelling approach is to use computationally expensive, detailed three-dimensional models that include delamination for every ply interface, fastener contact and prestress. This paper considers a simplified FE modelling strategy achieved through judicious use of symmetry boundary conditions, hybrid shell/solid modelling and reduced numbers of interfaces for delamination. The LS-DYNA FE software was used for this study using the available composite material and cohesive failure models. The conclusion drawn from this work is that the use of simplified FE models does have merit in modelling fastener pull-through provided the material is quasi-isotropic and the boundary conditions are uniform around a circular perimeter. Additional work is however required to determine suitable cohesive properties and progressive shear failure parameters.     

Thermal Expansion of Hybrid Chiral Mechanical Metamaterial with Patterned Bi-Strips

Hybrid chiral mechanical metamaterials with center squares connecting by bi-layer strips (bi-strips) with patterned interfaces are designed and fabricated via multimaterial 3D printing. Due to the thermal mismatch between the bi-strips and the chirality-induced rotation, the designs will undergo either thermal expansion or shrinkage under constant temperature increase, resulting in widely tuned overall thermal expansion coefficients (CTEs) for the chiral mechanical metamaterials. Analytical models of both the bi-strips with arbitrary dissimilar interface morphology and the chiral designs under temperature change are developed to predict the curvature of the bi-strips and the overall CTEs of the chiral designs. Two design regions with opposite trends are observed and explored. The models are verified via systematic finite element (FE) simulations and experiments on 3D-printed specimens. This investigation enlarges the design space of chiral mechanical metamaterials for achieving desired CTEs in a wide range.     

Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models

We propose a direct method for computing modal coupling coefficients—due to geometrically nonlinear effects—for thin shells vibrating at large amplitude and discretized by a finite element (FE) procedure. These coupling coefficients arise when considering a discrete expansion of the unknown displacement onto the eigenmodes of the linear operator. The evolution problem is thus projected onto the eigenmodes basis and expressed as an assembly of oscillators with quadratic and cubic nonlinearities. The nonlinear coupling coefficients are directly derived from the FE formulation, with specificities pertaining to the shell elements considered, namely, here elements of the “Mixed Interpolation of Tensorial Components” family. Therefore, the computation of coupling coefficients, combined with an adequate selection of the significant eigenmodes, allows the derivation of effective reduced-order models for computing—with a continuation procedure —the stable and unstable vibratory states of any vibrating shell, up to large amplitudes. The procedure is illustrated on a hyperbolic paraboloid panel. Bifurcation diagrams in free and forced vibrations are obtained. Comparisons with direct time simulations of the full FE model are given. Finally, the computed coefficients are used for a maximal reduction based on asymptotic nonlinear normal modes, and we find that the most important part of the dynamics can be predicted with a single oscillator equation.     

高速永磁电机机组轴系临界转速及振动模态

对于高速电机机组而言,在设计阶段准确预测转子动态特性,尽量减小发生故障的可能性是至关重要的。该文用有限元分析及实验方法计算由柔性联轴器耦合的多跨转子轴系临界转速及振动模态,用有限元软件的弹簧单元模拟弹性联轴器的轴向、径向及扭转刚度,分析联轴器刚度、结构参数对轴系临界转速的影响。研究表明:轴系临界转速及振动模态不同于单转子,可以通过改变膜片的刚度、结构参数等来调整系统某些阶次的临界转速,使转子具有良好的动态特性。     

Selective damping method for the weak‐Arlequin coupling of molecular dynamics and finite element method

An artificial damping force is introduced in the weak coupling between the molecular dynamics (MD) and finite element (FE) models, to reduce the reflection of the high‐frequency motion that cannot be transmitted from the MD domain to the FE domain. We take advantage of the orthogonal property of the decomposed velocity in the weak coupling method and apply the damping force only to the high‐frequency part, therefore minimizing its effect on the low‐frequency part, which can be transmitted into the FE domain. The effectiveness of the damping method will be demonstrated by 1D numerical examples with linear force field applied to the atomistic model. In addition, we emphasize the importance of using the Arlequin energy interpolation, which is usually ignored in the weak coupling literature. Non‐uniform rational basis spline functions have been used to interpolate the MD data for the weak coupling method, and the influence of changing the number and order of basis functions on the interpolation accuracy has been investigated numerically. For this work, we restrict our discussion to mechanical problems only, involving only mechanical energy terms (e.g., strain potential and kinetic energy). Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

The present paper shows a comparison between classical two-dimensional (2D) and three-dimensional (3D) finite elements (FEs), classical and refined 2D generalized differential quadrature (GDQ) methods and an exact three-dimensional solution. A free vibration analysis of one-layered and multilayered isotropic, composite and sandwich cylindrical and spherical shell panels is made. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the FE and GDQ methods (numerical solutions) and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 3D and 2D finite element results are obtained by means of a well-known commercial FE code. Classical and refined 2D GDQ models are based on a generalized unified approach which considers both equivalent single layer and layer-wise theories. The differences between 2D and 3D FE solutions, classical and refined 2D GDQ models and 3D exact solutions depend on several parameters. These include the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.     

Accurate calculation of transverse shear stresses for soft-core sandwich laminates

Accurate evaluation of transverse stresses in soft-core sandwich laminates using the existing 2D finite element (FE) models involves cumbersome post-processing techniques. In this paper, a simple and robust method is proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in soft-core sandwich laminates by using a displacement-based C⁰ continuous 2D FE model derived from refined higher-order shear deformation theory (RHSDT) and a least square error (LSE) method. In this refined higher-order shear deformation theory (RHSDT), the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly early varying displacement field. The transverse displacement is assumed to have a quadratic variation within the core, and it remains constant in the faces beyond the core. The proposed C⁰ FE model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C¹ continuity requirement of the transverse displacements associated with the RHSDT. The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. Thus, the proposed method is quite simple and elegant compared to the usual method of integrating the 3D equilibrium equations at the post-processing stage for the calculation of transverse stresses in a sandwich laminates. The accuracy of the proposed method is demonstrated in the numerical examples through the comparison of the present results with those obtained from different models based on HSDT and 3D elasticity solutions.     

Thermal resistance of nanoscopic liquid-liquid interfaces: dependence on chemistry and molecular architecture

Systems with nanoscopic features contain a high density of interfaces. Thermal transport in such systems can be governed by the resistance to heat transfer, the Kapitza resistance (RK), at the interface. Although soft interfaces, such as those between immiscible liquids or between a biomolecule and solvent, are ubiquitous, few studies of thermal transport at such interfaces have been reported. Here we characterize the interfacial conductance, 1/RK, of soft interfaces as a function of molecular architecture, chemistry, and the strength of cross-interfacial intermolecular interactions through detailed molecular dynamics simulations. The conductance of various interfaces studied here, for example, water-organic liquid, water-surfactant, surfactant-organic liquid, is relatively high (in the range of 65-370 MW/m2 K) compared to that for solid-liquid interfaces ( approximately 10 MW/m2 K). Interestingly, the dependence of interfacial conductance on the chemistry and molecular architecture cannot be explained solely in terms of either bulk property mismatch or the strength of intermolecular attraction between the two phases. The observed trends can be attributed to a combination of strong cross-interface intermolecular interactions and good thermal coupling via soft vibration modes present at liquid-liquid interfaces.     

An efficient FE model and Least Square Error method for accurate calculation of transverse shear stresses in composites and sandwich laminates

Accurate evaluation of transverse stresses in laminated composites and sandwich plates using 2D FE models involves cumbersome post-processing techniques. In this paper a simple and efficient method has been proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in composites and sandwich laminates by using a displacement based C⁰ FE model (2D) derived from Refined Higher Order Shear Deformation Theory (RHSDT) and a Least Square Error (LSE) method. The C⁰ FE model satisfies the inter-laminar shear stress continuity conditions at the layer interfaces and zero transverse shear stress conditions at the top and bottom of the plate. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of C¹ continuity associated with the above plate theory (RHSDT). The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. Thus the proposed method is quite simple and elegant compared to the usual method of integrating the 3D equilibrium equations at the post-processing stage for calculation of transverse stresses in a composite laminate. In the proposed method, the first two equations of equilibrium are utilized to compute the transverse shear stress variation through the thickness of a laminated plate whereas the third equation of equilibrium gives the normal stress variation. Accuracy of the proposed method is demonstrated in the numerical examples through comparison of the present results with those obtained from different models based on higher order shear deformation theory (HSDT) and 3D elasticity solutions.