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This work deals with fracture mechanisms in quasi-brittle materials, focusing on the characterization of the Fracture Process Zone (FPZ) of specimens under tensile load. Particularly, paper was used as model material. Experiments were conducted on notched and unnotched specimens. Based on an image analysis of these observations, a stochastic finite element model was developed, using both a nonlocal stress-based approach and a discretized random field modeling of the Young's modulus. The proposed methodology allowed characterizing the damage zone and the size of the FPZ, analyzing the influence of the mesostructure, composed of flocs (fiber aggregates where the basis weight is larger than the average one) and antiflocs (complement of flocs). The area of the active FPZ and the normalized stress drop were linked using a surface energy dissipated in the active FPZ. The stress drop, until limiting value, increased with the width of the active FPZ. Finally, a relationship between the surface energy and the nonlocal internal length was established. [ABSTRACT FROM AUTHOR]

In this paper, the absolute nodal coordinate formulation (ANCF) is applied to simulate the magnetic shape memory effect. Using the absolute nodal coordinate formulation makes it possible to describe complicated or large deformation cases. The nonlinear bidirectional coupling terms between the mechanical and magnetic field are taken into account in the analysis of the single-crystalline Ni-Mn-Ga sample. A two-loop iteration procedure with variable steps is implemented to predict the magnetic-field-induced strain (MFIS) in the specimen under a changing external magnetic field and a constant auxiliary compression. In addition, the proposed approach is used to track the superelastic behavior of the magnetic shape memory alloy when subjected to a constant magnetic field. The approach effectively describes the hysteresis and superelastic phenomenon of the shape memory effect. The solution is compared here with solutions obtained using classical linear and quadratic quadrilateral elements. The deviation observed in the solution is discussed, and its cause is further clarified from a two-domain pure magnetostatic analysis of a permanent magnet. It is found that the accurate solution of such problems is associated with discontinuity of the normal component of the magnetic potential gradient across the domain interface. Special measures must be taken to make the absolute nodal coordinate formulation element compatible with the discontinuity. A mixed FEs strategy, which adopts ANCF FE in the displacement field solver and classical FE in the magnetic field solver, is proposed as an alternative option to rectify the problem, which is verified by predicting the MFIS and the dynamic mechanical response of a sample under cyclic compression. [ABSTRACT FROM AUTHOR]

In this paper, a theoretical model is established to describe the effect of nanoscale amorphization in nanocrystalline bimaterials on the dislocation emission from the tip of a collinear crack at the interface. In the description, nanoscale amorphization is formed by the splitting transition of the Grain Boundary (GB, the disclination of GBs caused by the movement of GBs). The analytical solution of the model is obtained by the elasticity complex potential solution method. In addition, the effects of nanoscale amorphization, dislocation emission angle, interfacial crack length and material constants of nanocrystalline bimaterials on the critical stress intensity factor of interfacial crack tip corresponding to dislocation emission are discussed through numerical analysis. The analysis shows that the influence of nanoscale amorphization in nanocrystalline bimaterials on the critical stress intensity factor (SIF) corresponding to dislocation emission depends on the dislocation emission angle, the position and size of the nanoscale amorphization, interface crack length and relative shear modulus. With the increase in relative shear modulus and dislocation emission angle, the normalized critical SIF decreases at first and increases afterwards. When the nanoscale amorphization size is small, the critical SIF of the dislocation is less affected, but when the size is larger, the impact becomes great. The influence of nanoscale amorphization on the dislocation emission from collinear interface crack tip is related to nanoscale amorphization and relative shear modulus. There is a critical relative shear modulus that the increase in dislocation intensity has little effect on dislocation emission. Appropriate selection of materials for the upper and lower planes can reduce the critical stress intensity factor corresponding to dislocation emission, thereby promoting the dislocation emission from interface cracks and improving the toughness of the nanocrystalline bimaterials. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dynamics and stability of a flapping flag, with emphasis on the onset of flutter instability. The mathematical model is based on the one derived in a paper by Argentina and Mahadevan (Proc Nat Acad Sci 102:1829–1834, 2005). In that paper, it is reported that the effect of vortex shedding from the trailing edge of the flag, represented by the complex Theodorsen function C, has a stabilizing effect, in the sense that the critical flow speed (where flutter is initiated) is increased significantly when vortex shedding is included. The numerical eigenvalue analyses of the present paper display the opposite effect: the critical flow speed is decreased when the Theodorsen function (i.e., vortex shedding) is included. These predictions are verified by an analytical energy balance analysis, where it is proved that a small imaginary part of the Theodorsen function, C = 1 - i ϵ , 0 < ϵ ≪ 1 , has a destabilizing effect, i.e., the critical flow speed is smaller than by the so-called quasi-steady approximation C = 1 - i 0 . Furthermore, order-of-magnitude considerations show that Coriolis and centrifugal force terms in the equation of motion, previously discarded on the assumption that they are associated with very slow changes across the flag, have to be retained. Numerical results show that these terms have a significant effect on the stability of the flag; specifically, the said destabilizing effect of the vortex shedding is significantly reduced when these terms are retained. The mentioned energy balance analysis illuminates the nature of the flutter oscillations and the 'competition', at the flutter threshold, between the different types of fluid forces acting on the flag. [ABSTRACT FROM AUTHOR]

This paper is concerned with free vibration analyses of a circular transversely isotropic elastic plate based on Reddy plate theory and modified higher-order shear deformation plate theory (MHSDT). Hamilton's principle is used to derive the equations of motion and boundary conditions of the circular plate. Natural frequencies are determined from the solution of the governing equations and boundary conditions along the circular edge. Comparisons of natural frequencies and mode shapes arising from the Mindlin plate theory, the Reddy plate theory, MHSDT, and finite element method are made for fully free and clamped circular plates. The comparison results show that MHSDT has better accuracy than the other analytical plate theories in terms of the natural frequencies and corresponding mode shapes. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error analysis is provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation, the comparison with the classical Fourier theory and the behavior of the solution in two-dimensional examples. [ABSTRACT FROM AUTHOR]

In this paper, the evaluation procedures of the natural frequency and the stress intensity factor in the opening mode are established for the Euler–Bernoulli cracked beam by using (a) a technique in the framework of the finite element method, (b) a group method of data handling (GMDH), and (c) the software ABAQUS software. In the first one, the stiffness and mass matrices of the beam are enriched according to the depth and location of the crack for the determination of the natural frequency. A discrete spring model is used to simulate the crack in the structure based on the energy release rate. The continuity conditions in a cracked element are applied to connect two sub-elements of both sides of the crack. In the second method, the natural frequency and the stress intensity factor are determined using the GMDH algorithm. Design of experiments technique is employed to create an optimum arrangement for the application in the GMDH neural network. A few case studies are examined to investigate the results of the analysis, in addition, to identify the priority and the comparison of the three methods. The procedure of the analysis explains the advantages and limitations of the finite element-based technique, the GMDH method, and ABAQUS. [ABSTRACT FROM AUTHOR]

Particle-reinforced composites (PRCs) are usually studied by some averaging or homogenization techniques. In this, the effective properties are derived by assuming that particles are dispersed within composites according to some given (probabilistic) distribution. Such approaches restrain the possibilities of studying the contribution of exact location and parameters of individual particles to the overall behavior of composites. In this paper, we attempt to fill this gap by deriving the mesoscopic model of such composites corresponding to a continuum with point inhomogeneities. We start from a fully microscopic model where the composite is regarded as a continuum with spherical inclusions. Letting the diameter of inclusions decrease to zero, material parameters of the composite are represented in terms of the Dirac distribution. The Mindlin–Reissner–von Kármán thick plate theory is considered as a particular case, and closed-form formulas are obtained for the plate stiffness coefficients. Numerical analysis of a thick composite plate reinforced over its mid-surface justifies the theoretical derivations. [ABSTRACT FROM AUTHOR]

In this paper, a refined finite element method (FEM) based on the Carrera unified formulation (CUF) is extended for stress analysis of rotors and rotating disks with variable thickness. The variational form of the 3D equilibrium equations is obtained using the principle of minimum potential energy and solved by this method. Employing the 1D CUF, a rotor is assumed to be a beam along its axis. In this case, the geometry of the rotor can be discretized into a finite number of 1D beam elements along its axis, while the Lagrange polynomial expansions may be employed to approximate the displacement field over the cross section of the beam. Therefore, the FEM matrices and vectors can be written in terms of fundamental nuclei, whose forms are independent of the order of the beam theories. The validity and capabilities of the presented procedure are investigated in a number of numerical examples, and some conclusions are reported and compared well with the analytical and 3D finite element solutions. The results obtained by the 1D CUF models are in close agreement with the reference solutions. Moreover, it is verified that the innovative procedure presented in this paper can be used as an accurate tool of structural analysis for complex rotors to reduce the computational costs. [ABSTRACT FROM AUTHOR]

The paper addresses the frequency analysis of bars with an arbitrary number of dampers, subjected to harmonically varying loads. Multiple external/internal dampers occurring at the same position along the bar, modelling external damping devices and internal damping due to damage or imperfect connections, are considered. In this context, the challenge is to handle simultaneous discontinuities of the response variables, i.e. axial force/displacement discontinuities at the location of external/internal dampers. Based on the theory of generalized functions, the paper will present exact closed-form expressions of the frequency response under point/polynomial loads, which hold regardless of the number of dampers. In addition, closed-form expressions will be derived for the exact dynamic stiffness matrix and load vector of the bar, to be used in a standard assemblage procedure for an exact frequency response analysis of 2D truss structures. Changes to consider a single damper at a given position are straightforward. Numerical applications show the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the numerical modelization of the transient dynamic response of a simply supported Euler-Bernoulli elastic beam resting on a Winkler-type foundation, under the action of a transverse concentrated load, moving at a constant velocity along the beam, displaying an harmonic-varying magnitude in time. The elastic foundation, assumed as homogeneous in space, behaves according to a bilinear constitutive law, characterized by two different stiffness coefficients in compression and in tension. A finite element method approach coupled with a direct integration algorithm is developed for efficiently tracing the nonlinear dynamic response of the beam-foundation system. An original automated procedure is set, as being apt to resolve all required space/time discretization issues. Extensive parametric numerical analyses are performed to investigate how the frequency of the harmonic moving load amplitude and the ratio between the foundation’s moduli in compression and in tension affect the so-called critical velocities of the moving load, leading to high transverse beam deflections. Analytical interpolating expressions are proposed and fitted for the achieved two-branch critical velocity trends. The present outcomes shall reveal potential practical implications in scenarios of contemporary railway engineering, especially in terms of lowering down the admissible high-speed train velocities, as for structural requirement or preventing potential passenger discomfort. [ABSTRACT FROM AUTHOR]

Tempered martensitic steels with a high chromium content are used for power plant components at elevated temperatures under creep-fatigue conditions. In order to model the complex mechanical behavior of the alloy X20CrMoV12-1, a phase mixture model is used. This model is based on the distinction of hard and soft constituents, which are connected via an iso-strain approach. Nonlinear kinematic hardening and softening effects are taken into account by introducing a backstress and a softening variable. This paper focuses on the numerical implementation of the phase mixture model, i.e., the stress update algorithm and the consistent tangent operator. For implicit time integration of the governing equations, the backward EULER method in combination with NEWTON-RAPHSON iterations is applied. The model is implemented as user material subroutine into the commercial finite element code ABAQUS. For verification, several benchmarks considering uniaxial and multi-axial stress states are presented and analyzed. Furthermore, a thermo-mechanical fatigue test based on a typical sequence of start-ups and shutdowns of power plants is simulated. [ABSTRACT FROM AUTHOR]

In this paper, the generalized differential quadrature (GDQ) method is presented for solving the nonlinear, fully intrinsic equations of geometrically exact rotating and nonrotating beams. The fully intrinsic equations of beams involve only moments, forces, velocity and angular velocity, and in these equations, the displacements and rotations will not appear explicitly. This paper presents the generalized differential quadrature method for solution of these equations. To show the accuracy, validity and applicability of the proposed generalized differential quadrature method for solving the fully intrinsic beam equations, different cases are considered. It is found that the GDQ method gives very accurate results with very few numbers of discrete points and also has very low computational cost as compared to some other conventional numerical methods and therefore this method is very efficient, accurate and fast for solving the fully intrinsic equations. [ABSTRACT FROM AUTHOR]

The medium is composed of an elliptic inclusion and many confocal elliptic layers. The crack is embedded in the elliptic inclusion. The remote loading is applied at the remote place of the matrix. Complex variable method and conformal mapping are used to study the mentioned problem. This paper provides a numerical solution for the mentioned crack problem. The continuity condition for the traction and displacement along the interface is reduced to a relation of two sets of Laurent series coefficients for the complex potentials defined in the interior or exterior to the interface. This formulation is called the matrix transfer method in this paper. From the following three conditions, the traction-free condition along creak face, the continuity condition for the traction and displacement along the interfaces and the remote loading condition, the problem is finally solved. Servable numerical examples are provided. For the exterior finite matrix case, the relevant solution is also provided. [ABSTRACT FROM AUTHOR]

In the recent literature, a growing number of research papers have been dedicated to applying the techniques of global stability and sensitivity analysis to the design of flow controls. The controls that are designed in this way are mainly passive or open-loop controls. Among those, we consider here controls that are aimed at linearly stabilizing flow configurations which would be otherwise globally unstable. In particular, a review of the literature on flow controls designed on the basis of stability and sensitivity analysis is presented. The mentioned methods can be rigorously applied to relatively simple flow regimes, typically observed at low values of the Reynolds number. In this respect, the recent literature also demonstrates a large interest in the application of the same methods for the control of coherent large-scale flow structures in turbulent flows, as, for instance, the quasiperiodic shedding of vortices in turbulent wakes. The papers dedicated to this subject are also reviewed here. Finally, all the described methods imply the solution of eigenvalue problems which are at the state-of-the-art for computational complexity. On the one hand, there are attempts to reduce the complexity of the involved computational problems by applying local stability analysis, and some examples are illustrated. On the other hand, recent advances in numerical methods, also concisely reviewed here, allow the manipulation of large eigenvalue problems and greatly simplify the development of numerical tools for stability and sensitivity analysis of complex flow models, often built using existing fluid dynamics codes. [ABSTRACT FROM AUTHOR]

In this paper, we examine the axisymmetric adhesive contact problem for a rigid circular plate and an incompressible elastic halfspace where the linear elastic shear modulus varies exponentially with depth. The analytical solution of the mixed boundary value problem entails a set of coupled integral equations that cannot be solved easily by conventional integral transform techniques proposed in the literature. In this paper, we adopt a computational scheme where the contact normal and contact shear stress distributions are approximated by their discretized equivalents. The consideration of compatibility of deformations due to the indentation by a rigid indenter in adhesive contact gives a set of algebraic equations that yield the discretized equivalents of the contacts stresses and the axial stiffness of the medium. [ABSTRACT FROM AUTHOR]

This paper provides the transfer matrix method for the solution of multiple elliptic layers with different elastic properties. In the study, the medium is composed of an elliptic inclusion and many confocal elliptic layers. In the present study, the exterior layer is a finite confocal elliptic layer. Some derivations in the present study are similar to those in Chen (Acta Mech ). However, some derivations in the present study are quite different from those in Chen (Acta Mech ). Equations for evaluating the coefficients in the Laurent series for complex potentials are suggested, which are derived from the transfer matrix and the boundary condition. A numerical example for the case of an elliptic inclusion and two confocal elliptic layers is provided in this paper. [ABSTRACT FROM AUTHOR]

The arch shape is a timeless structural solution as it has been widely used in the past but is still a common solution adopted nowadays for large spans. Structural efficiency depends primarily on optimal material exploitation, which allows us to minimize the structural volume. The paper is framed in the context of optimization of arch structures, and analytical design criteria are proposed, dealing with a specific class of deck bridges supported in the mid-span by arches. The investigation deals with a simplified structural scheme, constituted by statically determinate plane arches under self-weight and a single vertical load in the key section, exerted by the deck supports. The optimization criterion assumes a constant normal stress in all arch sections and the resulting arch shape is computed in closed form. Finally, the existence condition for the proposed solution is provided and some numerical examples are introduced. [ABSTRACT FROM AUTHOR]

The conventional Eshelby’s problems of smooth inclusions in two-dimensional space are touched in this paper. When the smooth inclusion is characterized by the Laurent polynomial, using the solution of the full-plane as basis, the solutions of a finite domain can be decomposed into a basic part and an auxiliary part. The K-M potentials, including the basic and auxiliary parts, of the circular disk, full- and half-plane problems are explicitly solved in the form of polynomials. The coefficients of the polynomials are determined by the geometric parameters characterizing the smooth inclusion and its position. The solutions for elliptical and truncated pentagram inclusions are used as examples to show the correctness and validity of the presented solutions. [ABSTRACT FROM AUTHOR]

Currently, coiling problems for an elastic rope and viscous jet have been extensively studied, but there are few theoretical studies for modeling of viscoelastic jet coiling. In this paper, we have established a continuous one-dimensional (1-D) model for a weakly viscoelastic jet of Maxwell-type, considering jet radius variation and surface tension. The 1-D model is solved numerically by the continuation method to investigate the effects of relaxation time, the falling height, and the flow rate on the coiling frequency and falling time. The numerical results mainly show that for a weakly viscoelastic jet more frequency wiggles and lower frequencies appear than for the Newtonian flow. [ABSTRACT FROM AUTHOR]

The transverse-horizontal wave propagating in a semi-infinite piezoelectric solid with hexagonal symmetry subject to initial electromechanical fields is investigated in this paper. The electromechanical boundary value problem is solved, and the phase velocity, the displacement, and the electric potential are obtained. For a metallized boundary surface, the dependency of the solution on the initial fields for several piezoelectric crystals is analyzed. These results may be proved useful to model the propagation of waves in anisotropic piezoelectric structures subject to a bias, serving as a benchmark for further numerical and experimental approaches. [ABSTRACT FROM AUTHOR]

In this paper, the Gurtin-Murdoch continuum theory is applied to develop a new continuum mechanics model for static and dynamic analyses of nanoscale rectangular plates. The relevant governing equations are established from basic principles. Analytical solutions for static and free vibration of nanoscale rectangular plates are presented for selected boundary conditions. A finite element method for the analysis of rectangular nanoplates is also developed to solve general cases that cannot be solved analytically. Expressions for stiffness and mass matrices and the load vector are derived by using a weighted residual formulation. A selected set of numerical results is presented to investigate the size-dependent static and free vibration response of plates and the influence of surface material properties and boundary conditions. [ABSTRACT FROM AUTHOR]

A crack initiates frequently at a vertex in three-dimensional joints under an external load and a thermal load. In the present paper, the stress distributions near a very small crack occurring at the vertex of the interface in a three-dimensional joint are analyzed under a tensile load using a boundary element method, and the stress intensity factor of mode II is investigated along the crack front. The joint model is composed of silicon and resin, which is modeled on a material combination in electronic devices. Three kinds of crack shape, triangular, quarter circular, and concave shapes, are supposed as a crack shape. First, the stress distributions near the vertex in the model without a crack are obtained and are used for normalizing the singular stress at the front of the crack. Dimensionless stress intensity factor for an interface crack is defined and determined from the distribution of the normalized stress. Next, the stress distribution near the intersection point of the crack front and the side surface is precisely investigated. An eigenanalysis at the intersection point is conducted, and eigenvalues yielding the stress singularity are obtained. Then, it is found that there are two values yielding the stress singularity. The stress distributions near the intersection point are expressed using the angular functions for each value yielding the singularity. Finally, it is shown that the stress intensity factor for mode II along the crack front varies following the summation of functions composed of the distance from the intersection point with the power indices of ( $${0.5 - {\lambda _1}}$$ ) and ( $${0.5 - {\lambda _2}}$$ ), where $${\lambda _1}$$ and $${\lambda _2}$$ are the orders of stress singularity at the intersection point. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the role played by the material compressibility in the oscillatory behaviour of hyperelastic spherical shells subjected to dynamic inflation. For that purpose, we carried out a comprehensive nondimensional numerical analysis using: (i) a finite differences MacCormack's scheme implemented in MATLAB, and (ii) a finite element model developed in ABAQUS/Explicit (Abaqus Explicit v6.10 user's manual, version 6.10 edn. ABAQUS Inc., Richmond, 2010). We have detected that numerical dispersion and diffusion impose limits to the capacity of the computations to describe the shock wave that emanates from the inner surface of the shell due to the application of the inflation pressure. Nevertheless, both numerical approaches capture the essential features that describe the oscillatory behaviour of the shell, including the maximum stretch of the oscillation. Using the key nondimensional groups that control the problem at hand, we have conducted a parametric study to assess the role played by nondimensional applied pressure, material compressibility, and nondimensional shell thickness in the oscillatory behaviour of the specimen. We have shown the interplay between the maximum amplitude of the oscillation and the applied pressure and obtained the critical pressure for which the oscillatory behaviour is lost, leading to an unbounded expansion of the spherical shell. Moreover, our calculations have revealed that the wave propagation within the specimen plays a key role in the dynamic response of the shell. The phase portraits used to represent the oscillatory behaviour of the spherical shell show a characteristic sawtooth form that is accentuated with the increase in material compressibility and shell thickness. [ABSTRACT FROM AUTHOR]

Simultaneous peeling of multiple strips is commonly observed particularly at small-scale detachment processes. Although theoretical treatment of this problem is addressed, numerical solution procedures for geometrically arbitrary multiple-peeling problems are still missing. In this paper, a finite element-based numerical solution procedure for 3-D large displacement multiple-peeling problems is presented. Loading/unloading of peeling strips are expressed in the form of optimality conditions, and the current positions of the peeling fronts are determined locally adapting the multiplicative decomposition and the return mapping algorithm of finite strain plasticity theories. Within an incremental-iterative solution framework, peeling fronts and the current position of other nodes are determined in a staggered way instead of using an active set-based solution algorithm. The effectiveness of the approach is demonstrated by a series of example problems including multiple peeling of an assembly of randomly oriented strips. [ABSTRACT FROM AUTHOR]

In large-eddy simulation (LES) of turbulent dispersed flows, modelling and numerical inaccuracies are incurred because LES provides only an approximation of the filtered velocity. Interpolation errors can also occur (on coarse-grained domains, for instance). These inaccuracies affect the estimation of the forces acting on particles, obtained when the filtered fluid velocity is supplied to the Lagrangian equation of particle motion, and accumulate in time. As a result, particle trajectories in LES fields progressively diverge from particle trajectories in DNS fields, which can be considered as the exact numerical reference: the flow fields seen by the particles become less and less correlated, and the forces acting on particles are evaluated at increasingly different locations. In this paper, we review models and strategies that have been proposed in the Eulerian-Lagrangian framework to correct the above-mentioned sources of inaccuracy on particle dynamics and to improve the prediction of particle dispersion in turbulent dispersed flows. [ABSTRACT FROM AUTHOR]

In this paper, the two-dimensional tractive rolling contact problem between a rigid cylinder and an orthotropic half plane is considered. A pair of singular integral equations is derived for the contact tractions using the Fourier transform technique. The governing integral equations are decoupled using the Goodman approximation and then solved numerically. Finally, the distribution of surface tractions is achieved in the contact region. This study emphasizes the significant effect of the orthotropic material parameters and the coefficient of friction on the contact tractions as well as the rolling contact characteristics for an orthotropic medium. [ABSTRACT FROM AUTHOR]

The paper focuses on the modelling and analysis of 2D solids with unilateral material constraints coupled to 1D elements with varying degree of connection between each other. Both bilateral and unilateral geometric constraints are considered, depending on the connection degree. The problem is set up, and the solution is searched for by the numerical implementation of an iterative process leading to its identification; the solution pattern follows a bi-phase minimization procedure that is realized at any step, gradually tending to satisfy all the equations and the inequalities governing the problem. Original numerical codes, specifically compiled for the problem, allow to analyse the influence of the connection on the overall behaviour of the coupled system. The presented problem finds application, as an example, in the study of non-structural brick elements, and it allows to produce some reliable prediction of the overall behaviour of a structure, which includes such elements. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic spherical cavity expansion of shock wave evolution in concrete medium described by compressible Drucker-Prager plasticity with locked hydrostat. Hugoniot jumping conditions across shock waves are fully accounted for and a complete description of the motion and stress distribution evolution is obtained for different response domains. By solving the dimensionless governing differential equations during different periods, numerical illustrations are then developed with application to an explosion scenario inside an infinite concrete medium. The parameter study indicates that the equivalent charge weight of TNT proportionally affects the shock waves evolution, while the standoff distance has an inversely proportional impact on the ultimate locked/compacted boundary area. [ABSTRACT FROM AUTHOR]

In this paper, we derive a general closed-form solution for the static, axisymmetric bending of solid and annular microstructure-dependent Mindlin plates based on the modified couple-stress theory. The solution is developed by employing a suitable change in displacement variables. The couple-stress solution contains modified Bessel functions which do not appear in the classical case. The stress distributions of the annular microstructure-dependent plate are obtained in terms of load resultants by using the general closed-form solution. Analytical and numerical examples considering solid and annular circular plates are presented. The examples include simply supported and clamped solid and annular plates subjected to a uniformly distributed load and annular plates attached to a point-loaded rigid shaft. [ABSTRACT FROM AUTHOR]

Random colored noise excitations, more close to real environmental excitations, are considered. In this paper, probabilistic solutions of nonlinear SDOF systems excited by colored noise are analyzed. With the aid of filtering method, the initial equation of motion is transferred to four coupled first-order SDEs. As a result, a Markov process of enlarged system responses comes into being, and traditional FPK equation method can be employed. However, this way makes the corresponding FPK equation become four-dimensional. In order to solve this problem, the developed and improved exponential polynomial closure (EPC) method is employed. In the solution procedure, an approximate exponential function is extended to include four state variables. Then additional unknown coefficients associated with extended state variables are produced, and the solution procedure becomes more complicated. On the other hand, since there is no exact solution, Monte Carlo simulation (MCS) is performed to verify the efficiency of the developed EPC method. Four examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Numerical results show that the developed EPC method provides good agreement with the MCS method. Moreover, the effect of bandwidth for colored noise on system responses is taken into account. [ABSTRACT FROM AUTHOR]

The boundary element method has been applied with success to linear elastic fracture mechanic problems, involving static and dynamic cases. In order to solve body force problems (e.g., gravitational forces and transient problems with velocities and accelerations), Nardini and Brebbia presented, in 1982, the dual reciprocity formulation. Originally with the intention of solving transient problems using fundamental solutions of the static formulation, the procedure was found to be very efficient in the solution of body force problems as well. Also, a Green's function corresponding to an embedded crack within the infinite medium can be introduced into the boundary element formulation as the fundamental solution. This yields accurate means of calculating only the external boundary unknown displacements and tractions and, in a post-processing scheme, determining the crack opening displacements. This paper introduces an approach that involves the numerical Green's function procedure, of Telles and coworkers, and the dual reciprocity formulation. It compares beam solutions with the simulated effect of the total weight applied as a concentrated boundary force, the actual self-weight as a body force and a frequency- and time-dependent transient Heaviside load applied to a plate with a central crack. [ABSTRACT FROM AUTHOR]

This paper introduces a new type of tuned liquid damper (TLD) having a relatively simple, easy-to-model behavior and high effectiveness in controlling structural vibrations. It consists of a traditional TLD with addition of a floating roof. Since the roof is much stiffer than water, it prevents wave breaking, hence making the response linear even at large amplitudes. The roof also facilitates the incorporation of supplemental devices with which the level of damping of the liquid vibration can be substantially augmented. This newly proposed TLD, denoted as tuned liquid damper with floating roof (TLD-FR), maintains the traditional advantages of TLDs (low cost, easy installation and tuning), but its numerical characterization is much simpler because the floating roof suppresses higher sloshing vibration modes, resulting in a system that can be represented by a single-degree-of-freedom model. An efficient numerical scheme, where the dynamic behavior of the TLD-FR is expressed as a second-order lineal system of equations, is discussed and validated by scaled experimental tests. The equations of motion of a structure equipped with a TLD-FR are then derived and manipulated to offer a unifying representation dependent upon only four model characteristics of the TLD-FR: The first three (mass, frequency and damping ratios) are common for all type of mass dampers, whereas the final one, termed efficiency index, is related to a similar parameter used to characterize liquid column dampers. Through this approach, the behavior of the proposed TLD-FR can be easily correlated with the behavior of other well-known linear mass damper devices. The relationship between these parameters and the geometrical characteristics of the TLD-FR is also examined. Finally, the identification of the optimal characteristic of the TLD-FR (natural frequency and damping) under stationary stochastic excitation is discussed. [ABSTRACT FROM AUTHOR]

In this paper, a coupled meshfree-mesh-based fluid solver is employed for flow-induced vibration problems. The fluid domain comprises of a hybrid grid which is formed by generating a body conformal meshfree nodal cloud around the solid object and a static Cartesian grid which surrounds the meshfree cloud in the far field. The meshfree nodal cloud provides flexibility in dealing with solid motion by moving and morphing along with the solid boundary without necessitating re-meshing. The Cartesian grid, on the other hand, provides improved performance by allowing the use of a computationally efficient mesh-based method. The flow equations, in arbitrary Lagrangian-Eulerian formulation, are solved by a local radial basis function in finite difference mode on moving meshfree nodes. Conventional finite differencing is used over the static Cartesian grid for flow equations in Eulerian formulation. The equations for solid motion are solved using a classic Runge-Kutta method. Closed coupling is introduced between fluid and structural solvers by using a sub-iterative prediction-correction algorithm. In order to reduce computational overhead due to sub-iterations, only near-field flow (in the meshfree zone) is solved during the inner iterations. The full fluid domain is solved during outer (time step) iterations only when the convergence at the solid-fluid interface has already been reached. In the meshfree zone, adaptive sizing of the influence domain is introduced to maintain suitable number of neighbouring particles. The use of a hybrid grid has been found to be useful in improving the computational performance by faster computing over the Cartesian grid as well as by reducing the number of computations in the fluid domain during fluid-solid coupling. The solution scheme was tested for problems relating to flow-induced cylindrical and airfoil vibration with one and two degrees of freedom. The results are found to be in good agreement with previous work and experimental results. [ABSTRACT FROM AUTHOR]

An analytical solution is developed in this paper for viscoelastic axisymmetric plane problems under stress or displacement boundary condition involving time-dependent boundary regions using the Laplace transform. The explicit expressions are given for the radial and circumferential stresses under stress boundary condition and the radial displacement under displacement boundary condition. The results indicate that the two in-plane stress components and the displacement under corresponding boundary conditions have no relation with material constants. The general form of solutions for the remaining displacement or stress field is expressed by the inverse Laplace transform concerning two relaxation moduli. As an application to deep excavation of a circular tunnel or finite void growth, explicit solutions for the analysis of a deforming circular hole in both infinite and finite planes are given taking into account the rheological characteristics of the rock mass characterized by a Boltzmann or Maxwell viscoelastic model. Numerical examples are given to illustrate the displacement and stress response. The method proposed in this paper can be used for analysis of earth excavation and finite void growth. [ABSTRACT FROM AUTHOR]

The formation of strain localization influences the stability and stiffness of the soil mass or geosystem. The thickness of shear bands provides insight into overall strength and stiffness inside the granular body, and the shear band angle gives information about the failure surface in a given soil or soil mass. Thus, it is important to be able to predict when a shear band forms and how this zone of intense deformation is located and oriented within the granular medium. A rational finite element analysis for capturing the formation and development of shear bands has been formulated by using a micropolar continuum in finite element analysis. Hardening parameters including nonsymmetric stress and length scale are implemented for a realistic stress–strain analysis. Implementation and simulations of the model will be discussed in the Part II of this research. The micro–macro structure relation for finite element analysis based on this formulation paper will be simulated in the corresponding paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper also includes two examples taken from fracture mechanics and acoustics: a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical procedure that can predict the minimum duration of a rectangular, half-cycle sine wave, linearly increasing and triangular single-pulse excitation required to overturn the rigid block resting on a moving base. Since the linearization assumption in the derivation of an analytical solution, which has already been used by Housner and other researchers, cannot be valid for a block with various slenderness ratios and dimensions, a derivation of numerical solutions which would be valid for all types of block is necessary. The proposed numerical procedure takes into account the possibility of sliding and uplifting of the block from the base. The numerical algorithm for the proposed numerical procedure in a commercial code C++ is given in the 'Appendix.' [ABSTRACT FROM AUTHOR]

The work presented in this paper discusses the transmission properties of elastic waves through multilayers of spheres which are periodically arranged in a homogeneous host material. The multilayers of spheres can have different kinds of planar defects. These defects are formed by removing one layer of spheres or by changing the radiuses or the material of scatterers in some layers. First, the reflection and transmission matrices of a single layer of spheres are obtained by the multiple scattering approaches and then the reflection and transmission matrices of multilayers of spheres are derived based on the polymerization method. Numerical examples are presented for 15 layers of spheres with one central planar defect layer or two symmetrically arranged planar defect layers. The influences of these planar defects on the frequency-dependent transmission curves are discussed. It is observed that the band gap can be widened evidently by introducing the planar defect, and the defect states appear in the band gap consequently. So the elaborately arranged planar defects are important in designing specific acoustic filters. [ABSTRACT FROM AUTHOR]

Subject of the present work is the enhancement of the buckling load of beam-type structures under a compressive force by means of active feedback control. The focus of this paper lies on experimental aspects that show the feasibility of the proposed approach. For this purpose, a cantilever beam loaded by a compressive force is considered. The compressive force is applied with the help of a cable which is fixed at the tip of the free end and passes through the foundation of the cantilever. A laser displacement sensor is used to measure the structural displacements at the beam's tip. For actuation, piezoelectric transducers are attached on each side of the cantilever beam. Two kinds of constant gain feedback control approaches are investigated on the experimental setup. The buckling load could be increased by a factor of 2.05. The experimental results agree very well with the performed numerical simulations. As a theoretical basis, a consistent theoretical formulation is presented using the Bernoulli-Euler beam theory. The formulation of the system includes also a general feedback controller with discrete displacement measurements and distributed piezoelectric patches. The influence of the controller on the buckling load, control amount by means of applied voltage and limits of the investigated active buckling control approaches are emphasized. [ABSTRACT FROM AUTHOR]

The reflection problem of the micropolar elastic waves at the non-free surface of a micropolar elastic half-space is studied in this paper. Different from the classic elastic solid, there are four kinds of elastic waves in the micropolar elastic solid and three of them are dispersive. The boundary conditions at the non-free surface of a micropolar elastic half-space are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection waves to the incident wave can be determined. Then, the reflection coefficients in terms of energy flux ratios are calculated numerically, and the normal energy flux conservation is used to validate the numerical results. At last, the influence of the boundary parameters, which reflect the mechanical behavior of the non-free surface, on the reflection energy partition of micropolar elastic waves is discussed based on the numerical results. Two cases of incident longitudinal displacement wave and incident coupled transverse displacement and transverse microrotational wave are considered. [ABSTRACT FROM AUTHOR]

This paper presents a new strategy for the numerical evaluation of 2D nearly singular integrals that arise in the solution of 3D BEM using eight-node second-order quadrilateral surface elements. The strategy is an extension of the previous sinh transformation techniques, which is used to evaluate the 1D or 2D nearly singular integrals on simple geometry elements, such as linear or planar elements. The novel feature of the proposed method is that a new distance formula is introduced here, and based on this an ingenious combination of the distance formula and the sinh transformation is developed, and hence, the rapid variation of the distance formula on the integration interval can been smoothed out. Several numerical examples involving boundary layer effect and thin-body problems in 3D potential theory are given to verify the accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic, unbounded, rotating medium due to a periodically varying heat source in the context of the linear theory of generalized thermoelasticity without energy dissipation and with energy dissipation. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material under the influence of a magnetic field are established. The Laplace-Fourier double transform technique has been used to get the solution. The inversion of Fourier transform is done by using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre's method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. The numerical estimates for displacements, temperature and stress are obtained for a hypothetical material. The solution to the analogous problem is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of rotation, non-homogeneity, damping coefficient and magnetic field on displacements, temperature and stress. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to study the effect of axisymmetric heat supply on the phenomena of diffusion in a thermoelastic thick plate of infinite extent and finite thickness. The problem is discussed within the context of the theory of generalized thermoelastic diffusion with one relaxation time. The upper and the lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using integral transform technique and a direct approach without the use of potential functions. Inversion of Laplace transforms is done by employing a numerical scheme. The mathematical model is prepared for a Copper material plate, and the numerical results are discussed and represented graphically. [ABSTRACT FROM AUTHOR]

This paper addresses the development of a novel updated Lagrangian variational formulation and its associated finite element model for the geometrically nonlinear quasi-static analysis of cantilever beams. The formulation is based on an incremental complementary energy principle. The proposed finite element model only contains nodal bending moments as degrees of freedom. The model is used for the analysis of problems modeled by the so-called elastica theory. Numerical solutions satisfying all equilibrium equations in a strong sense can be obtained for arbitrarily large displacements and rotations. A Newton-Raphson method is adopted to trace the post-buckling response. Numerical results are presented and compared with those produced by the standard total Lagrangian two-node displacement-based finite element model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that it is possible to develop a fully internally consistent model for an isotropic elastic body that has nonlinear response relations but with small strains, if one chooses to begin from a Gibbs potential (or complementary energy) rather than the classical Helmholtz potential (or strain energy). We demonstrate the practical applicability of such a model and also compare the results of exact solutions (internal pressurization of a circular cylinder and the bending of a rectangular block) for incompressible materials undergoing finite deformations with corresponding exact solutions based on small deformations. Surprisingly, the results show quite remarkable agreement up to maximum strains of nearly 20-30 %. Given that most applications of nonlinear elastic materials are in this range, the results have broad implications for the ability to consistently use small deformation nonlinear theories for a wide class of applications than hitherto considered. We also show that the nonlinear compatibility equations play a key role in determining the applicability of this approach. In particular, we show that for 3-D bodies whose dimensions are of comparable orders of magnitude (i.e., excluding rod-like or shell-like bodies), the finite deformation compatibility condition ensures that small strains and strain gradients imply small relative rotations and hence small deformations. For thin bodies (rods, plates and shells), it is well-known result that small strains do not lead to small deformations due to the possibility of large rotation gradients thus leading to other possible approximations. [ABSTRACT FROM AUTHOR]

This paper presents the treatment of elastically restrained ends for the axially, loaded beam-buckling problem for the central finite difference beam model, the microstructured beam model, and Eringen's nonlocal continuous beam model. The equivalence between the central finite difference beam model and the microstructured beam model is established herein, and these equivalent systems are regarded as belonging to one class of discrete systems since they become indistinguishable. Also, the continualized form of the discrete system is obtained by adopting the continualization method that is based on an exponential displacement function. Three approaches are then proposed for matching the discrete system with Eringen's nonlocal continuous system for the beam-buckling problem. The approaches depend on the assumption made on the constancy/or varying Eringen's small length scale coefficient e as well as which one of the discrete or continuum system is taken as the reference system. [ABSTRACT FROM AUTHOR]

This paper provides the transfer matrix method for the solution of multiple elliptic layers with different elastic properties. In the study, the medium is composed of an elliptic inclusion and many confocal elliptic layers. The conformal mapping and the continuation of analytic functions are used. In the mapping plane, the complex potentials in the inclusion and the individual layer are expressed in the form of Laurent series. The correct form of the complex potentials in the inclusion is addressed. From the continuation condition for traction and displacement along the interface, the relation between the coefficients in the Laurent series of complex potentials for two adjacent layers can be evaluated. This relation is expressed in a matrix form, and it is called the transfer matrix. Using the transfer matrixes successively and the traction condition at remote place, the problem is finally solved. Numerical examples for two cases, the two-phase case and the three-phase case, are presented. [ABSTRACT FROM AUTHOR]

For a nano-sized piezoelectric film, the surface free energy at the surface/interface will exert great effect on the behavior of nano-sized piezoelectric structures. This paper concerns the effect of surface free energy at the surface/interface of square nanofibers on the electro-mechanical behavior of a piezoelectric thin film under anti-plane shear. Combining the electro-elastic surface/interface theory, the mapping method and the generalized self-consistent method, a closed-form solution of the effective electro-elastic moduli is obtained. Numerical examples are given to illustrate quantitatively the macro-effective electro-elastic moduli under different surfaces/interfaces when the size of the square nanofibers is on the order of nanometer. The effect of shape of square nanofibers on the effective electro-elastic moduli is also examined. [ABSTRACT FROM AUTHOR]

Surface tension plays an important role in nanosized materials. In this paper, the stress field induced by surface tension around an arbitrarily shaped nanosized hole is investigated through complex variable method using truncated series, with an emphasis on the relationship between the hoop stress and the curvature of the hole's boundary curve. Our numerical results for various shapes of holes show that maximum hoop stress always appears nearby, but not exactly at the point of maximum curvature on the hole's boundary. Surprisingly, for elliptical holes with certain aspect ratios and typical non-elliptical holes (such as triangular, square and rectangular holes), our results show that hoop stress can even attain a local minimum (not a local maximum) or even the overall minimum at the point of maximum curvature. In particular, surface tension-induced hoop stress can be very large around nanosized holes. On the other hand, the surface tension-induced stress field is always localized for nanosized holes of arbitrary shapes and fades away with increasing distance from the hole. [ABSTRACT FROM AUTHOR]