Showing papers on "Displacement field published in 2016"
TL;DR: In this article, the authors presented a semi-analytical model to analyze an Euler-Bernoulli beam with embedded ABH feature and its full coupling with the damping layers coated over its surface.
150 citations
TL;DR: In this article, the authors presented a new simple four-unknown shear and normal deformations theory (sSNDT) for static, dynamic and buckling analyses of functionally graded material (FGM) isotropic and sandwich plates.
145 citations
TL;DR: In this article, a variational approach to fracture is used to describe all the process of degradation of a body including the nucleation of cracks and their propagation, and the formulation of the damage evolution problem is then based on the concepts of irreversibility, stability and energy balance.
Abstract: The paper is devoted to gradient damage models which allow us to describe all the process of degradation of a body including the nucleation of cracks and their propagation. The construction of such model follows the variational approach to fracture and proceeds into two stages: (1) definition of the energy; (2) formulation of the damage evolution problem. The total energy of the body is defined in terms of the state variables which are the displacement field and the damage field in the case of quasi-brittle materials. That energy contains in particular gradient damage terms in order to avoid too strong damage localizations. The formulation of the damage evolution problem is then based on the concepts of irreversibility, stability and energy balance. That allows us to construct homogeneous as well as localized damage solutions in a closed form and to illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Moreover, the variational formulation leads to a natural numerical method based on an alternate minimization algorithm. Several numerical examples illustrate the ability of this approach to account for all the process of fracture including a 3D thermal shock problem where the crack evolution is very complex.
133 citations
TL;DR: In this article, the second-order displacement second-gradient model is extended to the case of a scalar damage field and two internal variables, i.e., accumulated plastic tension and the accumulated plastic compression, and the softening matrix is introduced as the coefficient matrix in front of the quadratic terms of the two plastic internal variables.
Abstract: A one-dimensional displacement second-gradient damage continuum theory has been already presented within the framework of a variational approach. Damage is associated with strain concentration. Therefore, not only non-local effects of displacement second-gradient modelling should be considered in a comprehensive model, but also any plastic effects. The aim of this paper is therefore to extend such a model to plasticity. The action is intended to depend not only with respect to first and second gradient of displacement field and to a scalar damage field, but also to further two internal variables, i.e. the accumulated plastic tension and the accumulated plastic compression. A constitutive prescription on the stiffness is given in terms of the scalar damage parameter in a usual way, i.e. as in many other works, it is prescribed to decrease as far as the damage increases. On the other hand, the microstructural material length (i.e. the square of the constitutive function in front of the squared displacement second-gradient term in the action functional) is prescribed to increase as far as the damage increases, being this last assumption connected to the interpretation that a damage state induces a microstructure in the continuum and that such a microstructure is more important as far as the damage increases. Initial damage threshold and yield stresses are naturally introduced in the action in front of linear terms, respectively, of damage and plastic internal variables. The hardening matrix is also introduced in a natural way as the coefficient matrix in front of the quadratic terms of the two plastic internal variables. At a given value of damage and plastic parameters, the behaviour is referred to second-gradient linear elastic material. However, the damage and plastic evolutions make the model not only nonlinear, but also inelastic. The second principle of thermodynamics is considered by assuming that the scalar damage and plastic parameters do not decrease their values in the process of deformation, and this implies a dissipation for the elastic strain energy. A novel result of this investigation, where displacement second-gradient and plastic effects are combined, is that the distributed and concentrated external double forces do not make work on the displacement gradient but only to its elastic part and this means that the displacement gradient cannot be prescribed, at the border, independently of the plastic internal variables.
106 citations
TL;DR: Burst overlap interferometry as mentioned in this paper takes advantage of the large squint angle diversity of Sentinel-1 (∼1°) to achieve subdecimetric accuracy on the along-track component of ground motion.
Abstract: Wide-swath imaging has become a standard acquisition mode for radar missions aiming at applying synthetic aperture radar interferometry (InSAR) at global scale with enhanced revisit frequency. Increased swath width, compared to classical Stripmap imaging mode, is achieved at the expense of azimuthal resolution. This makes along-track displacements, and subsequently north-south displacements, difficult to measure using conventional split-beam (multiple-aperture) InSAR or cross-correlation techniques. Alternatively, we show here that the along-track component of ground motion can be deduced from the double difference between backward and forward looking interferograms within regions of burst overlap. “Burst overlap interferometry” takes advantage of the large squint angle diversity of Sentinel-1 (∼1°) to achieve subdecimetric accuracy on the along-track component of ground motion. We demonstrate the efficiency of this method using Sentinel-1 data covering the 2015 Mw8.3 Illapel earthquake (Chile) for which we retrieve the full 3-D displacement field and validate it against observations from a dense network of GPS sensors.
101 citations
TL;DR: In this paper, a general formulation for a higher-order layer-wise theory related to the analysis of the free vibrations of thick doubly-curved laminated composite shells and panels is presented.
Abstract: The present article illustrates a general formulation for a higher-order layer-wise theory related to the analysis of the free vibrations of thick doubly-curved laminated composite shells and panels. The theoretical framework relates to the dynamic analysis of shell structures by using a general displacement field based on the Carrera Unified Formulation (CUF), including the stretching effect for each layer. The order of the expansion along the thickness direction is taken as a free parameter. The starting point of the present general higher-order layer-wise formulation is to propose a kinematic assumption, with an arbitrary number of degrees of freedom. The main aim of this work is to determine the explicit fundamental operators that can be used for the layer-wise (LW) approach. These fundamental operators are obtained for the first time by the author and are related to motion equations of doubly-curved shells described in an orthogonal curvilinear co-ordinate system. The free vibration shell and...
87 citations
TL;DR: In this article, the authors investigated the viscoelastically coupled size-dependent dynamics of a microbeam in the framework of the modified couple stress theory and derived the elastic and viscous components of the stress and deviatoric part of the symmetric couple stress tensors.
87 citations
TL;DR: In this paper, high-tough polyurethane foam specimens were subjected to direct impact with different projectile velocities and quantified their deformation response with high speed stereo-photography together with 3D digital image correlation.
84 citations
TL;DR: A recently developed phase-field model of fracture equipped with anisotropic crack driving force to model failure phenomena in soft biological tissues at finite deformations is presented, applicable to both rate-dependent or rate-independent brittle and ductile failure modes.
Abstract: This work presents a recently developed phase-field model of fracture equipped with anisotropic crack driving force to model failure phenomena in soft biological tissues at finite deformations. The phase-field models present a promising and innovative approach to thermodynamically consistent modeling of fracture, applicable to both rate-dependent or rate-independent brittle and ductile failure modes. One key advantage of diffusive crack modeling lies in predicting the complex crack topologies where methods with sharp crack discontinuities are known to suffer. The starting point is the derivation of a regularized crack surface functional that [Formula: see text]-converges to a sharp crack topology for vanishing length-scale parameter. A constitutive balance equation of this functional governs the crack phase-field evolution in a modular format in terms of a crack driving state function. This allows flexibility to introduce alternative stress-based failure criteria, e.g., isotropic or anisotropic, whose maximum value from the deformation history drives the irreversible crack phase field. The resulting multi-field problem is solved by a robust operator split scheme that successively updates a history field, the crack phase field and finally the displacement field in a typical time step. For the representative numerical simulations, a hyperelastic anisotropic free energy, typical to incompressible soft biological tissues, is used which degrades with evolving phase field as a result of coupled constitutive setup. A quantitative comparison with experimental data is provided for verification of the proposed methodology.
80 citations
TL;DR: In this article, the authors studied the instability of solution as the initial energy is negative while under an appropriated (and realistic) condition, they proved existence and uniqueness of solution using semi-group theory.
Abstract: This paper is concerned with the theory of thermoelastic dipolar bodies which have a double porosity structure. In contrast with previous papers dedicated to classical elastic bodies, in our context the double porosity structure of the body is influenced by the displacement field, which is consistent with real models. In this setting, we show instability of solution as the initial energy is negative while under an appropriated (and realistic) condition, we prove existence and uniqueness of solution using semi-group theory.
78 citations
TL;DR: In this article, a modified Fourier-Ritz approach was developed to study the free in-plane vibration for the orthotropic circular, annular and sector plates with general boundary conditions, and several auxiliary closed-form functions were added to the standard Fourier cosine series to obtain a robust function.
TL;DR: In this paper, Lagrangian Perturbation Theory (LPT) and its regularization in the Eective Field Theory (EFT) approach are compared. But the LPT displacement with the same phases as a corresponding N-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra.
Abstract: We study Lagrangian Perturbation Theory (LPT) and its regularization in the Eective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a correspondingN-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra. We reliably detect a non-vanishing leading order EFT coecient and a stochastic displacement term, uncorrelated with the LPT terms. This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors or transients in our simulations. This term constitutes a limit to the accuracy of perturbative descriptions of the displacement field and its phases, corresponding to a 1% error on the non-linear power spectrum atk = 0:2hMpc 1 at z = 0. Predicting the displacement power spectrum to higher accuracy or larger wavenumbers thus requires a model for the stochastic displacement.
TL;DR: In this article, a higher-order structural theory is presented to accurately evaluate the natural frequencies of laminated composite shells, and a new kinematic model is developed starting from the theoretical framework given by a unified formulation.
Abstract: The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.
TL;DR: In this paper, a 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented.
Abstract: In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton
TL;DR: In this article, a solution method capable of treating static bending and free vibration problems involving thermally loaded functionally graded annular and circular micro-plates is introduced, which is based on modified couple stress theory.
TL;DR: In this article, a stable nodal integration method with strain gradient (SNIM-SG) is proposed for dynamic problems using linear triangular and tetrahedron element, except for considering the smoothed strain into the calculation of potential energy functional as NS-FEM.
Abstract: A stable nodal integration method with strain gradient (SNIM-SG) for curing the temporal instability of node-based smoothed finite element method (NS-FEM) is proposed for dynamic problems using linear triangular and tetrahedron element. In each smoothing domain, except for considering the smoothed strain into the calculation of potential energy functional as NS-FEM, a term related to strain gradient is taken into account as a stabilization term. The proposed SNIM-SG can achieve appropriate system stiffness in strain energy between FEM and NS-FEM solutions and obtains quite favorable results in elastic and dynamic analysis. The accuracy and stability of SNIM-SG solution are studied through detailed analyzes of benchmark cases and practical engineering problems. In elastic-static analysis, it is found that SNIM-SG can provide higher accuracy in displacement field than the reference approaches do. In free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that SNIM-SG solution strengths the original relatively soft NS-FEM, and SNIM-SG is confirmed to obtain fairly accurate natural frequency values in various examples. All in all, SNIM-SG cures the flaws of NS-FEM and enhances the dominant of nodal integration. Thus, the efficacy of the presented formulation in solving solid mechanics problems is well represented and clarified.
TL;DR: In this article, a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated was presented, and the axial displacement field was constructed with only 5 unknowns, as against 6 or more in other higher-order shear and normal deformation theories.
Abstract: This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (ez ≠ 0), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.
TL;DR: In this article, a finite element model for the dynamic analysis of sandwich laminated plates with a soft core and composite laminated face layers, as well as piezoelectric sensor and actuator layers is presented.
TL;DR: In this paper, a modified Fourier-Ritz approach has been adopted to analyze the free vibration of axially loaded laminated composite beams with arbitrary layup and general boundary conditions, which include classical boundaries, elastic boundaries, and their combination.
Abstract: In this paper, a modified Fourier–Ritz approach has been adopted to analyze the free vibration of axially loaded laminated composite beams with arbitrary layup and general boundary conditions, which include classical boundaries, elastic boundaries, and their combination. The influences of Poisson effect, axial deformation, couplings among extensional, bending and torsional deformations, shear deformation, and rotary inertia are incorporated in the formulation. In this present method, regardless of boundary conditions, the displacements and rotation components of the beam are invariantly expressed as a standard Fourier cosine series and several auxiliary closed-form functions. These auxiliary functions are introduced to eliminate any potential discontinuities of the original displacement function and its derivatives, throughout the whole beam including its ends, and to effectively enhance the convergence of the results. Since the displacement field is constructed to be adequately smooth in the whole soluti...
TL;DR: In this paper, the authors present an analytical solution for the buckling and free vibration analysis of laminated beams by using a refined and generalized shear deformation theory which includes the thickness expansion.
TL;DR: In this article, a discontinuous Galerkin method (DGM) for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults is proposed.
Abstract: We have formulated and implemented a discontinuous Galerkin method (DGM) for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults. The approach is based on the interior-penalty formulation of DGM, and the fractures are simulated using the linear-slip model, which is incorporated into the weak formulation by including an additional term that is similar to the penalty term but uses the fracture compliance instead of an arbitrary penalty parameter. We have calibrated our results against an analytic solution of fracture-induced anisotropy for a set of elongated horizontal fractures, and we have evaluated numerical examples that simulate the reflection and transmission of waves at a fracture and at fracture interface waves. This method can further be used with models containing intersecting fractures and multiple fracture sets in 2D or 3D domains.
11 Nov 2016
TL;DR: In this paper, a strain gradient theory is used to study free vibration, wave propagation and tension analyses of a sandwich micro/nano rod made of piezoelectric materials under electric potential.
Abstract: Strain gradient theory is used to study free vibration, wave propagation and tension analyses of a sandwich micro/nano rod made of piezoelectric materials under electric potential. The structure is resting on a Pasternak's foundation medium. Love's rod model is used for derivation of displacement field. The piezoelectric face sheets are subjected to two-dimensional electric potential including an applied voltage at top of plate and a cosine term along the thickness direction. Hamilton's principle is used to derive governing equations of motion in terms of axial displacement and electric potential. Three distinct behaviors of the present problem including free vibration, wave propagation and tension analyses are performed. Some important numerical results are presented in detail to capture the effect of materials length scales and applied voltage on the different behaviors of microrod.
TL;DR: In this paper, the deformation solution of functionally graded (FG) plates with variation of material stiffness through their length using higher order shear deformation theory (HSDT) including stretching effects is presented.
Abstract: This paper presents the deformation solution of functionally graded (FG) plates with variation of material stiffness through their length using higher order shear deformation theory (HSDT) including stretching effects. The present theory accounts for both the shear deformation and thickness stretching effect by a sinusoidal variation of the displacement field across the thickness. Equations of motion are derived from Hamilton's principle, and the relevant governing equations of elasticity are solved with a power law distribution of material property (material stiffness) to derive the analytical solution of the deflection of the FG plate. The problem is then modelled using the finite element method (FEM). The resultant analytical solutions are verified against the finite element (FE) solutions. The FE solutions are obtained using linear hexahedral solid elements with spatially graded property distribution (at different Gauss points), which is implemented by a user material subroutine (UMAT) in the ABAQUS FE software. It can be concluded that the present exact formulation is not only accurate, but also simple in predicting the bending of FG plates. Also, this study can be applied to find the optimum material distribution to produce controlled-stiffness distribution in FG plates corresponding to prescribed characteristics. Moreover, the good agreement found between the exact solution and the numerical simulation demonstrates the effectiveness of graded solid elements in the modelling of FG plate deflection under bending.
TL;DR: In this article, the Sublaminate Generalized Unified Formulation (S-GUF) is used for bending analysis of thin and thick composite plates, including monolithic and sandwich structures.
TL;DR: In this article, the displacement field of a composite laminated plate is defined by the first-order shear deformation theory (FSDT), and a brief theoretical description of the advanced meshless techniques extended to the analysis of composite plates, considering a weak-form approach combined with the FSDT is presented.
TL;DR: In this paper, an analytical solution is presented to predict ground movement induced by a nonuniformly deforming circular tunnel in a heavy elastic halfplane, which can serve as a simple tool for predicting a reasonable ground settlement profile in the preliminary design of tunnels.
Abstract: An analytical solution is presented to predict ground movement induced by a nonuniformly deforming circular tunnel in a heavy elastic half-plane. Simple expression is proposed to describe the nonuniform soil deformation around the tunnel. The tunnel-deforming components (i.e., ground loss, ovalization, vertical translation) can be determined by the solution-inherent mechanism and by fitting from measured field data. The effects of tunnel-deforming components on the resulting displacement field are discussed. Case studies from various ground conditions were used to check the capacity and applicability of the proposed solution. Although elasticity is a rough representation of the soil behavior, the proposed analytical solution can serve as a simple tool for predicting a reasonable ground settlement profile in the preliminary design of tunnels.
TL;DR: Numerical results show that the FSEM can be effectively applied to vibration analysis of the coupled shell structures and the effects of geometric parameters and boundary conditions on the frequencies are investigated.
Abstract: This paper presents a Fourier spectral element method (FSEM) to analyze the free vibration of conical-cylindrical-spherical shells with arbitrary boundary conditions. Cylindrical-conical and cylindrical-spherical shells as special cases are also considered. In this method, each fundamental shell component (i.e., cylindrical, conical, and spherical shells) is divided into appropriate elements. The variational principle in conjunction with first-order shear deformation shell theory is employed to model the shell elements. Since the displacement and rotation components of each element are expressed as a linear superposition of nodeless Fourier sine functions and nodal Lagrangian polynomials, the global equations of the coupled shell structure can be obtained by adopting the assembly procedure. The Fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution. Numerical results show that the FSEM can be effectively applied to vibration analysis of the coupled shell structures. Numerous results for coupled shell structures with general boundary conditions are presented. Furthermore, the effects of geometric parameters and boundary conditions on the frequencies are investigated.
TL;DR: In this paper, a one-dimensional (1D) higher-order exact formulation for linearized buckling analysis of beam-columns is introduced, and the displacement field is expressed as a generic N-order expansion of the generalized unknown displacement field.
Abstract: This article introduces a one-dimensional (1D) higher-order exact formulation for linearized buckling analysis of beam-columns. The Carrera Unified Formulation (CUF) is utilized and the displacement field is expressed as a generic N-order expansion of the generalized unknown displacement field. The principle of virtual displacements is invoked along with CUF to derive the governing equations and the associated natural boundary conditions in terms of fundamental nuclei, which can be systematically expanded according to N by exploiting an extensive index notation. After the closed form solution of the N-order beam-column element is sought, an exact dynamic stiffness (DS) matrix is derived by relating the amplitudes of the loads to those of the responses. The global DS matrix is finally processed through the application of the Wittrick-Williams algorithm to extract the buckling loads of the structure. Isotropic solid and thin-walled cross-section beams as well as laminated composite structures are an...
TL;DR: In this article, a coupled wave-mode approach for the determination of wave dispersion characteristics in structurally advanced periodic structures is presented, which combines two scales of model order reduction, at the unitcell level, component mode synthesis (CMS) provides the displacement field associated with local resonances of the periodic structure, while the free wave propagation is considered using a spectral problem projection on a reduced set of shape functions associated with propagating waves, thus providing considerable reduction of the computational cost.
TL;DR: In this paper, the virtual crack closure integral technique (VCCT) is formulated in the framework of cell-based smoothed finite element (CS-FEM) for evaluating stress intensity factors and for modeling the crack propagation in solids.