Showing papers in "European Journal of Mechanics A-solids in 2018"

Stress-driven nonlocal integral model for Timoshenko elastic nano-beams

Abstract: Size-dependent structural behavior of inflected Timoshenko elastic nano-beams is investigated by nonlocal continuum mechanics . An innovative stress-driven integral model of elasticity is conceived by swapping source and output fields of Eringen's strain-driven theory. Unlike Eringen's model, the stress-driven nonlocal integral formulation leads to well-posed structural problems. Solution uniqueness and continuous dependence on data are thus ensured. Selected case-studies of technical interest are examined and exact nonlocal solutions of Timoshenko nano-beams are provided, detecting thus also new benchmarks for numerical analyses. The contributed results are compared with those obtained by the gradient theory of elasticity and by the differential constitutive model consequent (not equivalent) to Eringen's strain-driven theory equipped with Helmholtz's kernel.

On the validity range of strain-gradient elasticity: A mixed static-dynamic identification procedure

Abstract: Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the wavelength approaches this characteristic size) important quantities, such as phase and group velocity, deviate considerably from their low frequency/long wavelength values. This well-known phenomenon is called dispersion of waves. Objective of this work is to show that strain-gradient elasticity can be used to quantitatively describe the behaviour of a microstructured solid, and that the validity domain (in terms of frequency and wavelength) of this model is sufficiently large to be useful in practical applications. To this end, the parameters of the overall continuum are identified for a periodic architectured material, and the results of a transient problem are compared to those obtained from a finite element full field computation on the real geometry. The quality of the overall description using a strain-gradient elastic continuum is compared to the classical homogenization procedure that uses Cauchy continuum. The extended model of elasticity is shown to provide a good approximation of the real solution over a wider frequency range.

Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories

Abstract: The present paper is focused on the size-dependent shear buckling of nanoplates embedded in Winkler-Pasternak foundation and hygrothermal environment. Hence, the refined higher-order plate theories (Polynomial, Exponential, and Hyperbolic) needless of any shear correction factor are used in the formulations. The equations of motion are derived based on the mentioned theories in conjunction with the nonlocal strain gradient theory employing Hamilton's principle. The four unknown functions denoting the buckling load of plates are defined in a modal manner, and Navier solution method is used to find the shear buckling response. Results for the shear buckling and thermal buckling analysis of nanoplates are approved by existing literature to demonstrate the accuracy of present formulation and solution method. From our knowledge, it is the first time that the hygrothermal environment and also the nonlocal strain gradient theory are applied to study on shear buckling of nanoplates. Hence, the influence of nanoplate geometry, various hygrothermal conditions, elastic medium, nonlocal parameter and gradient parameter on the shear buckling load are obtained and discussed using different plate theories. The numerical results indicate that the shear buckling of nanoplate in the absence of strain gradient parameter is significantly affected by the temperature and moisture variations.

Comparison of constraint analyses with global and local approaches under uniaxial and biaxial loadings

Abstract: Fracture toughness is an important material property used to perform the integrity assessment of engineering components containing cracks. Due to the difference in crack tip constraint, specimens may show different fracture toughness. The constraint difference for cruciform specimen with shallow crack, compact tension (CT) specimen and three point bending specimen with shallow and deep cracks are investigated. Both linear elastic and elastic-plastic fracture mechanics are applied to study the constraint effect based on two-parameter fracture criterion . Crack tip constraint depends on the applied loading. J-A 2 method is used to precisely capture the crack tip constraint and crack tip stress distributions. Local approach to fracture can be applied to transfer the fracture toughness among different specimens under uniaxial and biaxial loadings . In case of positive T -stress, T-stress increases with KI. In the case of negative T-stress, T-stress decreases with KI. Q-stress generally decreases with applied loading for both deep crack and shallow crack cases. Loss of constraint occurs for the single-edged bending (SEB) specimen with deep crack and thus raises the question whether the SEB specimen is proper to be used to obtain material toughness. For the cruciform bending (CRB) specimen, the constraint at the crack tip surface shows a least constraint while the deepest point has a relatively higher constraint. At a fracture probability of 10%, the fracture toughness difference between CT specimen and CRB specimen is about 50 MPa m0.5, i.e 200% of the fracture toughness. This big difference demonstrates the importance of considering the constraint effects in the integrity analysis.

Size-dependent analysis of FG-CNTRC microplates based on modified strain gradient elasticity theory

Abstract: We present in this study a size-dependent computational approach based on the modified strain gradient theory (MSGT) and higher-order shear deformation theory for static bending and free vibration analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microplates. Three material length scale parameters (MLSPs) are taken into account in MSGT to capture size effects of microplate behavior. The effective material properties of FG-CNTRC microplates are obtained by an extended rule of mixture. Four types of carbon nanotube distributions, which are either uniform or functionally graded (FG) through the plate thickness, are considered. The governing equations are derived from the principle of virtual work and are then solved by isogeometric analysis (IGA). The IGA is suitable for a numerical implementation of the size-dependent models since it requires higher-order gradients in the weak form. The inclusion of geometrical parameters, boundary conditions, distributed types of carbon nanotube and material length scale parameters are studied to evaluate the displacement and natural frequency of FG-CNTRC microplates. In addition, the present size-dependent model can be retrieved into the modified couple stress model or classical model when a few MLSPs are ignored.

Form II of Mindlin's second strain gradient theory of elasticity with a simplification: for materials and structures from nano- to macro-scales

Abstract: The fundamental equations for Form II of Mindlin's second strain gradient elasticity theory for isotropic materials are first derived. A corresponding simplified formulation is then proposed, with six and two higher-order material parameters for the strain and kinetic energy, respectively. This simplified model is still capable of accounting for free surface effects and surface tension arising in second strain gradient continua. Within the simplified model, at first, surface tension effects appearing in nano-scale solids near free boundaries are analyzed. Next, a thin strip under tension and shear is considered and closed-form solutions are provided for analyzing the free surface effects. Expressions for effective Poisson's ratio and effective shear modulus are proposed and found to be size-dependent. Most importantly, for each model problem a stability analysis is accomplished disallowing non-physical solutions (befallen but not exclusively disputed in a recent Form I article). Finally, a triangular macro-scale lattice structure of trusses is shown, as a mechanical metamaterial, to behave as a second strain gradient continuum. In particular, it is shown that initial stresses prescribed on boundaries can be associated to one of the higher-order material parameters, modulus of cohesion, giving rise to surface tension. For completeness, a numerical free vibration eigenvalue analysis is accomplished for both a fine-scale lattice model and the corresponding second-order continuum via standard and isogeometric finite element simulations , respectively, completing the calibration procedure for the higher-order material parameters. The eigenvalue analysis confirms the necessity of the second velocity gradient terms in the kinetic energy density .

Two-stage data-driven homogenization for nonlinear solids using a reduced order model

Abstract: The nonlinear behavior of materials with three-dimensional microstructure is investigated using a data-driven approach. The key innovation is the combination of two hierarchies of precomputations with sensibly chosen sampling sites and adapted interpolation functions : First, finite element (FE) simulations are performed on the microstructural level. A sophisticated sampling strategy is developed in order to keep the number of costly FE computations low. Second, the generated simulation data serves as input for a reduced order model (ROM). The ROM allows for considerable speed-ups on the order of 10–100. Still, its performance is below the demands for actual twoscale simulations. In order to attain the needed speed-ups, in a third step, the use of radial numerically explicit potentials (RNEXP) is proposed. The latter combine uni-directional cubic interpolation functions with radial basis functions operating on geodesic distances. The evaluation of the RNEXP approximation is realized almost in real-time. It benefits from the computational efficiency of the ROM since a higher number of sampling points can be realized than if direct FE simulations were used. By virtue of the dedicated sampling strategy less samples and, thus, precomputations (both FE and ROM) are needed than in competing techniques from literature. These measures render the offline cost of the RNEXP manageable on workstation computers. Additionally, the chosen sampling directions show favorable for the employed kernel interpolation. Numerical examples for highly nonlinear hyperelastic (pseudo-plastic) composite materials with isotropic and anisotropic microstructure are investigated. Twoscale simulations involving more than 10 6 DOF on the structural level are solved using the RNEXP and the influence of the microstructure on the structural behavior is quantified.

A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates

Abstract: Dynamic modeling of nanoplates constructed from porous functionally graded (FG) and metal foam materials is presented based on nonlocal strain gradient theory (NSGT). In this model, both stiffness-softening and stiffness-hardening effects are considered for more reliable forced vibration analysis of nanoplates. The present nano-resonator is based on a vibrating higher order nanoscale plate subjected to transverse uniform dynamic load. Porosities inside FG material are incorporated to the model based on a modified rule of mixture. Also, porosities inside metal foam nanoplate are non-uniformly distributed thorough the thickness. Applying Galerkin's method, the resonance frequencies and dynamic deflections are obtained. It is indicated that the forced vibration characteristics of the nanoplate are significantly influenced by the excitation frequency, porosities, nonlocal parameter, strain gradient parameter, elastic foundation and dynamic load characteristics.

Stability analysis of thin-walled spinning reinforced pipes conveying fluid in thermal environment

Abstract: The divergence and flutter instabilities of the thin-walled spinning pipes reinforced by single-walled carbon nanotubes in thermal environment are investigated. The material properties of carbon nanotube-reinforced composites are assumed to be uniform distribution as well as two types of functionally graded distribution patterns. The thermal effects are also considered and the material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent. The cantilever pipe conveying fluid is spinning along its longitudinal axis and subjected to an axial force at the free end. Based on the thin-walled Timoshenko beam theory, the governing equations of motion are derived using the extended Hamilton's principle and discretized via the Galerkin method. The resulting thermal-structural-fluid eigenvalue problem is solved and the frequency and the critical fluid velocities are calculated. The effects of carbon nanotubes distributions, volume fraction of carbon nanotubes, compressive axial force, spinning speed, gravity and fluid mass ratio on the critical divergence and flutter velocities of the thin-walled spinning pipe conveying fluid are studied.

A quantitative assessment of the scale separation limits of classical and higher-order asymptotic homogenization

Abstract: Classical homogenization techniques are known to be effective for materials with large scale separation between the size and spacing of their underlying heterogeneities on the one hand and the structural problem dimensions on the other. For low scale separation, however, they generally become inaccurate. This paper assesses the scale separation limit of classical asymptotic homogenization applied to periodic linear elastic composite materials and demonstrates the effectiveness of higher-order homogenization in stretching this limit. A quantitative assessment is performed on a two-dimensional elastic two-phase composite consisting of stiff circular particles in a softer matrix material and subjected to anti-plane shear, as introduced by Smyshlyaev and Cherednichecko (J. Mech. Phys. Solids 48:1325–1358, 2000). Reference solutions are created rigorously using full-scale numerical simulations in which a family of translated microstructures is considered and the ensemble average of their solutions is defined as the homogenized solution. This solution is used as a reference, which is compared with the periodic homogenization solution for a range of scale ratios. It is shown that the zeroth-order classical homogenization solution significantly deviates from the exact solution below a certain scale ratio for a given microstructure. Below this limit, the higher-order solutions provide a clear improvement of the match. Further, the performance of classical and higher-order asymptotic homogenization solution are evaluated for varying stiffness contrast ratio between the two phases of the microstructure and error contours are presented by comparison with full-scale numerical simulations.

Classical, higher-order, zig-zag and variable kinematic shell elements for the analysis of composite multilayered structures

Abstract: In the present work, a shell finite element with a variable kinematic field based on a new zig-zag power function is proposed for the analysis of laminated shell structures . The kinematic field is written by using an arbitrary number of continuous piecewise polynomial functions. The polynomial expansion order of a generic subdomain is a combination of zig-zag power functions depending on the shell thickness coordinate. As in the classical layer-wise approach, the shell thickness can be divided into a variable number of mathematical subdomains. The expansion order of each subdomain is an input parameter of the analysis. This feature enables the solution to be locally refined over generic regions of the shell thickness by enriching the kinematic field. The advanced finite shell elements with variable kinematics are formulated in the framework of the Carrera Unified Formulation. The finite element arrays are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modelling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on linear static stress analyses of composite laminated shell structures. The governing equations are obtained by applying the Principle of Virtual Displacements, and they are solved using the Finite Element method . Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to contrast the shear locking phenomenon . Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present shell element.

Vibration response of multi-span fluid-conveying pipe with multiple accessories under complex boundary conditions

Abstract: Realistic multi-span fluid-conveying pipe may contain various accessories such as valves, clamps, flanges , elastic supports and vibration absorbers under complex boundary conditions in engineering applications. The dynamic response of the multi-span pipe may be affected by the presence of accessories, giving rise to complex mode shapes. Simplified and reliable methods for multi-span mode shapes calculation from eigenvector of the characteristic equation are widely applied in the pipeline engineering community. However, current methods are not valid when it comes to the amplitude of the eigenvector with a resonance frequency . Consequently, corresponding stresses cannot be further evaluated exactly. To address the above mentioned issues, a novel Frequency Response Function (FRF)-based method is proposed in this paper for the calculation of the mode shapes exactly. Furthermore, a method combining the Spectral Analysis Method (SAM) and Transfer Matrix Method (TMM) is first proposed in this paper to obtain the natural frequencies and transient response for the cascaded pipeline. The results calculated by the present method are validated by comparing them with those obtained from existing literature and conventional Finite Element Method (FEM). The effects of the accessories on the vibration characteristics of the multi-span pipes are further analyzed.

Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading

Abstract: The stochastic dynamic stability analysis of laminated composite curved panels under non-uniform partial edge loading is studied using finite element analysis. The system input parameters are randomized to ascertain the stochastic first buckling load and zone of resonance. Considering the effects of transverse shear deformation and rotary inertia, first order shear deformation theory is used to model the composite doubly curved shells. The stochasticity is introduced in Love's and Donnell's theory considering dynamic and shear deformable theory according to the Sander's first approximation by tracers for doubly curved laminated shells. The moving least square method is employed as a surrogate of the actual finite element model to reduce the computational cost. The results are compared with those available in the literature. Statistical results are presented to show the effects of radius of curvatures, material properties, fibre parameters, and non-uniform load parameters on the stability boundaries.

Analysis of a doubly curved piezoelectric nano shell: Nonlocal electro-elastic bending solution

Abstract: Nonlocal electro-elastic bending analysis of a doubly curved nano shell is studied in this paper based on nonlocal elasticity theory and first order shear deformation theory . Nonlocal piezo-elasticity relations are used for analysis of the problem. The doubly curved piezoelectric nano shell is subjected to transverse loads and applied voltage . In addition, the structure is resting on Winkler-Pasternak foundation. The governing equations of nonlocal electro-elastic bending are derived based on principle of virtual work. The nonlocal electro-elastic bending results of doubly curved nano shell are investigated using Navier's method. Influence of nonlocal parameter, applied electric potential, Winkler and Pasternak's parameters of foundation is studied on the mechanical and electrical components of the piezoelectric doubly curved nano shell.

Dynamic flexoelectric effect on piezoelectric nanostructures

Abstract: Flexoelectricity , which represents the spontaneous electric polarization induced by the strain gradient , is a universal electromechanical coupling effect regardless of symmetry in all dielectric material. In solid dielectric material, the contribution from flexoelectricity can be due to four related phenomena: static and dynamic bulk flexoelectricity, surface flexoelectricity and surface piezoelectricity. While the surface flexoelectric effect can be negligible, the magnitude of the remaining three phenomena are comparable. Presently, the role of the static bulk flexoelectric and surface piezoelectric effects in the energy harvesters has been intensively studied, the contribution from dynamic flexoelectric effect remains unclear. In this work, based on the conventional beam theory, equations of motion considering dynamic flexoelectric effect are investigated. Consequently, the free vibration of the simply supported beam is studied in order to examine the influence of the dynamic flexoelectricity on natural frequency. From the numerical studies, it is found that dynamic flexoelectric effect is more influential on thick beam model and higher vibration modes . In addition, the results show that the relation between the static and dynamic flexoelectric coefficients can also alter the free vibration response.

Reissner stationary variational principle for nonlocal strain gradient theory of elasticity

Abstract: The general form of Reissner stationary variational principle is established in the framework of the nonlocal strain gradient theory of elasticity. Including two size-dependent characteristic parameters, the nonlocal strain gradient elasticity theory can demonstrate the significance of the strain gradient as well as the nonlocal elastic stress field. Based on the Reissner functional, the governing differential and boundary conditions of dynamic equilibrium and differential constitutive equations of the classical and first-order nonlocal stress tensor are derived in the most general form. Additionally, the boundary congruence conditions are formulated and discussed for the nonlocal strain gradient theory. To exhibit the application value of Reissner variational principle, it is employed to examine the nonlinear vibrations of size-dependent Bernoulli-Euler and Timoshenko beams. In the case of immovable boundary conditions, employing the weighted residual Galerkin method, the homotopy analysis method is also utilized to determine the closed form analytical solutions of the geometrically nonlinear vibration equations. Consequently, the analytical expressions for the nonlinear natural frequencies of Bernoulli-Euler and Timoshenko nonlocal strain gradient beams are derived.

Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory

Abstract: An original and consistent first-order shear deformation theory that retains all the nonlinear terms in the in-plane displacements and rotations is presented here. The theory is developed for dynamics and is applied to study large-amplitude, geometrically nonlinear vibrations. The numerical application to a simply supported, composite laminated circular cylindrical shell is implemented for illustration and validation purposes. Initially the theory is compared to an accurate third-order nonlinear shear deformation theory for the case of pressurized shell. This comparison validates the theory for buckling, which arises in case of external pressure, and post-buckling. The pressure is accurately modelled as displacement-dependent. Then, the nonlinear vibrations due to harmonic forcing around a resonance are studied in detail. The coupling between driven and companion mode gives a chaotic oscillation region near the linear resonance associated to a travelling-wave vibration. Results are presented in the frequency and time domains, in addition to sections of Poincare maps.

Assessment of porosity influence on vibration and static behaviour of functionally graded magneto-electro-elastic plate: A finite element study

Abstract: In this paper, the free vibration characteristics and the static behaviour of porous functionally graded magneto-electro-elastic (FGMEE) plate is investigated using finite element method . The porosities arise due to the maladies in the fabrication processes and such porosities or micro-voids are accounted using modified power law. Influence of different porosity distributions on the behaviour of PFGMEE plate are considered in this study. The through thickness variation of material properties is achieved to obtain a functionally graded MEE plate. The coupled constitutive equations along with the principle of virtual work are used to develop a FE model for FGMEE plates. Influence of various porosity distributions on the structural behaviour of the plate is thoroughly investigated. The effect of porosity volume and material gradient index on the free vibration and static behaviour is explicitly studied. This study also includes the evaluation of the effect of geometrical parameters such as thickness ratio , aspect ratio, and boundary condition on the structural characteristics of porous FGMEE plate.

Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams

Abstract: A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.

On the effects of roughness on the nonlinear dynamics of a bolted joint: A multiscale analysis

Abstract: Accurate prediction of the vibration response of friction joints is of great importance when estimating both the performance and the life of build-up structures. The contact conditions at the joint interface, including local normal load distribution and contact stiffness, play a critical role in the nonlinear dynamic response. These parameters strongly depend on the mating surfaces, where the surface roughness is well known to have a significant impact on the contact conditions in the static case. In contrast, its effects on the global and local nonlinear dynamic response of a build-up structure is not as well understood due to the complexity of the involved mechanisms. To obtain a better understanding of the dependence of the nonlinear dynamic response on surface roughness, a newly proposed multiscale approach has been developed. It links the surface roughness to the contact pressure and contact stiffness, and in combination with a multiharmonic balance solver, allows to compute the nonlinear dynamic response for different interface roughness. An application of the technique to a single bolted lap joint highlighted a strong impact of larger roughness values on the pressure distribution and local contact stiffness and in turn on the nonlinear dynamic response.

Effects of electric field and strain gradients on cracks in piezoelectric solids

Abstract: The paper presents a general approach to analyze 2-D crack problems where the electric field and displacement gradients exhibit a size effect. The finite element method (FEM) is developed to analyze the general 2D boundary value problems in size-dependent piezoelectric solids with cracks if the electric field gradients are considered in the constitutive equations for the electric displacements. The size-effect phenomenon in micro/nano electronic structures is described by the strain- and electric field-gradient effects. The electric field-strain gradient coupling is considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions using the variational principle. The FEM formulation is subsequently developed and implemented for strain- and electric field-gradient piezoelectricity. In the framework of this theory the path-independent J-integral is derived.

On the constitutive modelling of recruitment and damage of collagen fibres in soft biological tissues

Abstract: The aim of this work is to propose a recruitment and damage constitutive model for collagen fibres in soft biological tissues. Similarly to other published models, our model employs probability distribution functions in order to capture the progressive recruitment and damage of fibrils in a collagen fibre. We rigorously investigate the continuum mechanical treatment of recruitment and damage using a multiplicative decomposition of the deformation gradient. Our proposed model stems from the correction, generalisation and extension to damage of the recruitment model proposed by Martufi and Gasser (2011, J. Biomech. , 44, 2544–2550). We demonstrate that the generalised model is equivalent to the recruitment and damage model proposed by Hurschler et al. (1997, J. Biomech. Eng. , 119, 392–399). Finally, we explore the sensitivity of the proposed model to the parameters describing recruitment and damage, implement the model into Finite Elements and show an example of application, which gives good agreement with published experimental data.

Rayleigh-type wave in a nonlocal elastic solid with voids

Abstract: The present work is concerned with propagation of surface waves in an isotropic homogeneous nonlocal elastic solid half-space with voids. Dispersion relation for Rayleigh-type surface wave has been derived, which is found to be complex in nature. The variation of phase speed and corresponding attenuation of Rayleigh-type wave against frequency, nonlocality and void parameters is computed for a specific model and presented graphically. It is shown that only one mode of Rayleigh-type wave exists, which faces a critical frequency same as the critical frequency of shear wave. The dispersion arises due to the presence of voids and nonlocality in the medium. The particle motion is elliptical and a tilt in the plane of particle motion occurs due to the presence of void parameter ‘τ’ in the medium. In the low frequency range, the variation in ellipticity is due to the presence of voids in the medium. Some particular cases have been deduced from the present formulation.

Finite element dynamic analysis of beams on nonlinear elastic foundations under a moving oscillator

Abstract: This paper presents a study on the dynamic response of beams on elastic foundations, subjected to a uniformly moving oscillator. Using a finite element model programmed within a MATLAB environment the response of the system is studied for three different types of mechanical behaviour of the foundation: (a) linear elastic (classical Winkler model), (b) nonlinear elastic (in which the foundation reaction displays a cubic dependence on the beam displacement) and (c) bilinear elastic (with different compressive and tensile stiffnesses). The effects of the oscillator's natural frequency and velocity and of the foundation's stiffness and damping are investigated. In particular, critical velocities of the oscillator and ranges of velocities for which the system is dynamically unstable are numerically determined for the first time in the above mentioned nonlinear cases.

Statics and dynamics of nanorods embedded in an elastic medium: Nonlocal elasticity and lattice formulations

Abstract: This paper is focused on the static and the dynamic behaviour of an axial lattice (with direct neighbouring interaction) loaded by some distributed forces and in interaction with an elastic medium. Some exact analytical solutions are provided both in static and in dynamic settings, for the finite lattice system under general boundary conditions including fixed- and free-end boundary conditions. A nonlocal rod model based on the introduction of one additional length scale, is then constructed by continualization scheme of the lattice difference equations, to capture the scale effects associated with the lattice spacing. The continualized nonlocal model coincides with a phenomenological Eringen's nonlocal model, except eventually for the boundary conditions. These new continualized nonlocal boundary conditions are derived from the end lattice boundary conditions. The enriched nonlocal wave equation augmented by the elastic medium interaction has a spatial derivative which coincides with the local wave equation, thus avoiding the need of higher-order boundary conditions. The static and the dynamic responses of the equivalent nonlocal bar are also analytically studied and compared to the lattice problem. It is shown that the nonlocal solution efficiently fits the lattice one, both in static and in dynamic settings. The nonlocal model can be also introduced from variational arguments, thus leading to a nonlocal optimal Rayleigh quotient. For very high frequencies, the nonlocal model is corrected by a two-length scale model, which is shown to capture efficiently the frequency spectra of the lattice model for all frequency range.

Nonlinear thermo-mechanical buckling and post-buckling of multilayer FGM cylindrical shell reinforced by spiral stiffeners surrounded by elastic foundation subjected to torsional loads

Abstract: The nonlinear buckling and postbuckling behavior of Multilayer functionally graded (FGM) cylindrical shells reinforced by ring, stringer and/or spiral stiffeners made of isotropic material under torsional loads and thermal load is proposed by an analytical approach. The thin shell is composed of three layers: isotropic layer – FGM layer – isotropic layer and surrounded by Pasternark type elastic foundation. The governing equations are based on the Donnell shell theory with von Karman-Donnell-type geometrical nonlinearity, combining the improvability of Lekhnitskii's smeared stiffeners technique for spiral stiffeners. The effects of mechanical and thermal loads are considered in this paper. The number of spiral stiffeners, angle stiffeners, temperature change, and volume fraction index of shells, foundation and stiffeners are numerically investigated. A very large effect of spiral stiffeners on buckling behavior of shell in comparison with orthogonal stiffeners is approved in numerical results.

Corner failure in masonry buildings: An updated macro-modeling approach with frictional resistances

Abstract: The failure mode of a free corner in masonry buildings , still poorly investigated, is one of the most common failure mechanisms occurring and clearly recognizable in the aftermath of a seismic event. It is characterized by the formation of a masonry wedge, mainly due to the thrust of roof elements in addition to inertial forces , and it generally involves rocking-sliding motions along the cracks on the interlocked orthogonal walls. The onset of this failure mode is herein analyzed by means of an upgraded macro-block model, based on the kinematic approach of limit analysis and accounting for the influence of frictional resistances on the collapse load multiplier and the related crack pattern. An original criterion weighting the role of rocking vs. sliding motion on the collapse load factor is developed and a formulation with general applicability is obtained. Several parametric analyses are performed in order to highlight the influence of geometrical, mechanical and loading parameters on the seismic capacity of the corner. The reliability of the proposed model and solution procedure is confirmed through the comparison with the results provided by other macro-block models existing in the literature. The final perspective is the next implementation of the proposed model in FaMIVE (Failure Mechanism Identification and Vulnerability Evaluation) applicative.

Efficient attenuation of beam vibrations by inertial amplification

Abstract: We demonstrate efficient attenuation of flexural vibrations by attaching a simple inertial amplification (IA) mechanism to a slender elastic beam. The mechanism generates enhanced inertial forces between two attachment points, which effectively counteracts the elastic forces in the beam for certain anti-resonance frequencies. These anti-resonances may be generated in the low-frequency range, even for a small added mass. Furthermore, the hybrid structures are shown to exhibit two neighbouring anti-resonance dips providing wide and deep attenuation regions in the frequency domain. The obtained numerical results are validated with the experimental data.

Point-wise evaluation of the growth driving direction for arbitrarily shaped delamination fronts using cohesive elements

Abstract: The identification of the delamination propagation direction in three-dimensional structures with arbitrarily shaped fronts is needed in many applications. In the cohesive element framework, the propagation direction may be computed as the normal direction to a numerical damage isoline. The damage isoline tracking requires to exchange information between neighboring elements, thus post-processing global data, which is computationally expensive. This work presents a novel approach for the evaluation of the growth driving direction, only using local element information. The method can be directly implemented in a user-defined element subroutine and be evaluated at the execution time of the analysis. The presented formulation and its implementation in the commercial Finite Element code Abaqus is validated by comparison to the damage isoline shape rendering using global information.

Multiphysical modeling of the photopolymerization process for additive manufacturing of ceramics

Abstract: Additive manufacturing (AM) of ceramics through vat photopolymerization is a promising technique in which a ceramic filled photopolymer is selectively solidified in a layer-wise manner towards the final part geometry. Large scale adoption and optimization of AM for ceramics requires an in depth understanding of the process, which is pursued through a theoretical-numerical approach in this work. A modeling framework is proposed that integrates the coupled effect of four relevant physical mechanisms: (i) light propagation through the heterogeneous matter; (ii) conversion of the photopolymer; (iii) thermal effects and (iv) evolution of mechanical properties upon solidification. Interestingly, the inclusion of ceramic particles (compared to the regular vat photopolymerization process) has a marked influence for each individual physical mechanism. Even though the individual key ingredients are established, the coupled and integrated framework provides innovative insights, demonstrating how difficult it is to achieve homogeneous polymerization for ceramic-filled resins.