# Showing papers in "Acta Mechanica in 2015"

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TL;DR: In this article, a non-classical sinusoidal plate model is developed on the basis of modified strain gradient theory, which takes into account the effects of shear deformation without any shear correction factors and also captures the size effects due to additional material length scale parameters.

Abstract: A new non-classical sinusoidal plate model is developed on the basis of modified strain gradient theory. This model takes into account the effects of shear deformation without any shear correction factors and also can capture the size effects due to additional material length scale parameters. The governing equations and corresponding boundary conditions for bending, buckling, and free vibration analysis of the microplate are derived by implementing Hamilton’s principle. Analytical solutions based on the Fourier series solution are presented for simply supported square microplates. A detailed parametric study is performed to demonstrate the influences of thickness-to-length scale parameter ratio, length-to-thickness ratio, and shear deformation on deflection, critical buckling load, and fundamental frequencies of microplates. It is observed that the effect of shear deformation becomes more significant for smaller values of length-to-thickness ratio.

189 citations

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TL;DR: A comprehensive overview of advances with regard to SMA composites and devices utilizing them is pursued, with emphasis on identifying the characteristic responses and properties of these material systems as well as on comparing the various modeling methodologies for describing their response.

Abstract: Following their discovery in the early 1960s, there has been a continuous quest for ways to take advantage of the extraordinary properties of shape memory alloys (SMAs). These intermetallic alloys can be extremely compliant while retaining the strength of metals and can convert thermal energy to mechanical work. The unique properties of SMAs result from a reversible diffussionless solid-to-solid phase transformation from austenite to martensite. The integration of SMAs into composite structures has resulted in many benefits, which include actuation, vibration control, damping, sensing, and self-healing. However, despite substantial research in this area, a comparable adoption of SMA composites by industry has not yet been realized. This discrepancy between academic research and commercial interest is largely associated with the material complexity that includes strong thermomechanical coupling, large inelastic deformations, and variable thermoelastic properties. Nonetheless, as SMAs are becoming increasingly accepted in engineering applications, a similar trend for SMA composites is expected in aerospace, automotive, and energy conversion and storage-related applications. In an effort to aid in this endeavor, a comprehensive overview of advances with regard to SMA composites and devices utilizing them is pursued in this paper. Emphasis is placed on identifying the characteristic responses and properties of these material systems as well as on comparing the various modeling methodologies for describing their response. Furthermore, the paper concludes with a discussion of future research efforts that may have the greatest impact on promoting the development of SMA composites and their implementation in multifunctional structures.

150 citations

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TL;DR: In this paper, the authors consider viscous, heat-conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions and derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy.

Abstract: We consider viscous, heat-conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity—instead of the classical partition into so-called fluxes and driving forces—the apparent antisymmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared with the speed of sound, the Maxwell–Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case, this approximation via a scale separation argument is no longer possible. We introduce the new concept of entropy invariant model reduction, leaving the entropy production unchanged under the reduction from partial momentum balances to a single mixture momentum balance. This results in an extension of the Maxwell–Stefan equations to chemically active mixtures with an additional contribution to the transport coefficients due to the chemical interactions.

98 citations

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TL;DR: In this paper, a new Timoshenko beam model is developed using a modified couple stress theory and a surface elasticity theory, which leads to the simultaneous determination of the equations of motion and complete boundary conditions.

Abstract: A new Timoshenko beam model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and complete boundary conditions for a Timoshenko beam. The new model contains a material length scale parameter accounting for the microstructure effect in the bulk of the beam and three surface elasticity constants describing the mechanical behavior of the beam surface layer. The inclusion of these additional material constants enables the new model to capture the microstructure-and surface energy-dependent size effect. In addition, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current model, unlike existing Timoshenko beam models. The new beam model includes the models considering only the microstructure dependence or the surface energy effect as limiting cases and recovers the Bernoulli–Euler beam model incorporating the two effects as a special case. Also, the current model reduces to the classical Timoshenko beam model when the microstructure dependence, surface energy and Poisson’s effect are all suppressed. To demonstrate the new model, the static bending and free vibration problems of a simply supported beam are analytically solved by directly applying the general formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko beam model. In addition, the differences in both the deflection and rotation predicted by the two models are very large when the beam thickness is small, but they are diminishing with the increase of the beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new model is higher than that given by the classical model, with the difference between them being significantly large for very thin beams. These predicted trends of the size effect in beam bending at the micron scale agree with those observed experimentally.

85 citations

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TL;DR: In this paper, a finite element analysis of functionally graded plates based on a general third-order shear deformation plate theory with a modified couple stress effect and the von Karman nonlinearity is carried out to bring out the effects of couple stress, geometric non-linearity and power-law variation of the material composition through the plate thickness on the bending deflections of plates.

Abstract: Finite element analysis of functionally graded plates based on a general third-order shear deformation plate theory with a modified couple stress effect and the von Karman nonlinearity is carried out to bring out the effects of couple stress, geometric nonlinearity and power-law variation of the material composition through the plate thickness on the bending deflections of plates. The theory requires no shear correction factors. The principle of virtual displacements is utilized to develop a nonlinear finite element model. The finite element model requires C
1 continuity of all dependent variables. The microstructural effects are captured using a length scale parameter via the modified couple stress theory. The variation of two-constituent material is assumed through the thickness direction according to a power-law distribution. Numerical results are presented for static bending problems of rectangular plates with various boundary conditions to bring out the parametric effects of the power-law index and length scale parameter on the load–deflection characteristics of plates with various boundary conditions.

83 citations

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TL;DR: In this paper, the authors explored the influence of flexoelectricity on the electromechanical coupling behavior of a simply supported picolectric nanoplate by using the Kirchhoff plate theory.

Abstract: Flexoelectricity, representing the coupling between electrical polarizations and strain gradients, should be taken into account in the analysis of electromechanical responses of nanostructures where large strain gradients are expected. In this paper, we will explore the influence of flexoelectricity on the electromechanical coupling behavior of a simply supported piezoelectric nanoplate by using the Kirchhoff plate theory. The governing equations and corresponding boundary conditions are deduced from Hamilton’s principle, and the analytical solutions are obtained for the deflection and natural frequency. The results indicate that the deflections predicted by the present model are smaller than those calculated by the classical one which only considers piezoelectricity, while the frequencies exhibit the opposite trend. In addition, the flexoelectric effect is more prominent for thinner plates; the differences of the deflections or frequencies between the two models are gradually diminishing with an increase in the plate thickness. The current work may contribute to the understanding of the higher-order electromechanical coupling mechanism. Moreover, the modified plate model can be utilized to accurately design novel piezoelectric nanoplate-based sensors in nanoelectromechanical systems.

81 citations

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TL;DR: In this paper, a novel extended 4-node quadrilateral finite element (XCQ4) based on a consecutive interpolation procedure (CIP) with continuous nodal stress for accurately modeling singular stress fields near crack tips of two-dimensional (2D) cracks in solids is presented.

Abstract: A novel extended 4-node quadrilateral finite element (XCQ4) based on a consecutive-interpolation procedure (CIP) with continuous nodal stress for accurately modeling singular stress fields near crack tips of two-dimensional (2D) cracks in solids is presented In contrast to the traditional approaches, the approximation functions constructed based on the CIP involve both nodal values and averaged nodal gradients as interpolation conditions Our objective is to exhibit a pioneering extension of the recently developed CQ4 element enhanced by enrichment to precisely model 2D elastic crack problems, taking advantages of the strengths and making use all the desirable features of both techniques, the CIP and the local enriched partition of unity method The stress intensity factors (SIFs) are estimated using the interaction integral The accuracy and performance of the proposed XCQ4 and its numerical properties are illustrated by numerical examples, considering both single and mixed-mode problems with complicated configurations Compared with reference solutions available in the literature and the conventional XQ4 results, it is found that the accuracy of the XCQ4 is high Studies on the convergence rate of the SIFs in relative errors also reveal a better performance of the XCQ4 over the classical XQ4 The fracture parameters are found to be stable for different areas of integration paths around the crack tip Further applications of the developed XCQ4 to other complex problems are potential

72 citations

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TL;DR: In this article, the authors investigated the bifurcation behavior of a heated conical shell made of a through-the-thickness functionally graded material and obtained properties of the shell based on a power law form across the thickness.

Abstract: Bifurcation behavior of heated conical shell made of a through-the-thickness functionally graded material is investigated in the present research. Properties of the shell are obtained based on a power law form across the thickness. Temperature dependency of the constituents is also taken into account. The heat conduction equation of the shell is solved based on an iterative generalized differential quadrature method (GDQM). General nonlinear equilibrium equations and the associated boundary conditions are obtained using the virtual displacement principle in the Donnell sense. The prebuckling solution of the shell is obtained under the assumption of linear membrane deformations. The stability equations are extracted via the concept of the adjacent equilibrium criterion. A semi-analytical solution employing the GDQM and trigonometric expansion is implemented to solve the stability equations. Numerical results of the present research are compared and validated with the known available data through the open literature. Some parametric studies are conducted to investigate the influences of various involved parameters, such as the cone semi-vertex angle, boundary conditions, power law index of composition rule, length to thickness ratio, and the radius to thickness ratio.

65 citations

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TL;DR: In this article, a forced vibration analysis of a microplate subjected to a moving load is presented, which is based on the modified couple stress theory in conjunction with Kirchhoff-love plate theory.

Abstract: This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff–Love plate theory. The equations of motion of the problem are derived using Lagrange’s equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

62 citations

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TL;DR: In this article, the size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified couple stress theory and the resulting initial boundary value problem is of fourth order, and it is solved employing the analog equation method.

Abstract: The size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified couple stress theory. For a three-dimensional orthotropic body, three additional material length scale parameters should be involved in the modified couple stress theory (with respect to the three shear moduli). However, in this study and without restricting the generality, we assume that the 2D couple stress state of the orthotropic micro-plate is described solely by only one material length scale parameter in accordance with the in-plane shear modulus. Furthermore, this reasonable assumption allows us to compare qualitatively the results with those obtained by the nonlocal elasticity theory, which also uses only one material length scale parameter to capture the size effect. Using Hamilton’s principle, the governing equilibrium equation of the micro-plate and the associated general boundary conditions are derived in terms of the deflection. The resulting initial boundary value problem is of fourth order, and it is solved employing the analog equation method. Example problems are presented for orthotropic skew micro-plates, and useful conclusions are drawn from the investigation of their micron-scale response. Some of the findings detected in studying the microstructure vibratory response of orthotropic skew micro-plates, based on the modified couple stress theory, are also verified by those obtained by the nonlocal elasticity theory. Nevertheless, a new important finding is that both the frequency and critical load parameters increase by increasing the material length scale parameter of the modified couple stress theory, which is in direct contradiction to that of the nonlocal elasticity theory where these parameters decrease by increasing the nonlocal parameter.

60 citations

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TL;DR: In this paper, the effect of carbon nanotube (CNT) waviness on the active constrained layer damping (ACLD) of the laminated hybrid composite shells is investigated.

Abstract: In this article, we investigate the effect of carbon nanotube (CNT) waviness on the active constrained layer damping (ACLD) of the laminated hybrid composite shells. In particular, the effect of CNT waviness has been studied for the case of a novel nano-tailored composite—continuous fuzzy fiber-reinforced composite (FFRC). The distinctive feature of the construction of the FFRC is that the uniformly spaced straight or wavy CNTs are radially grown on the circumferential surfaces of carbon fibers. The constraining layer of the ACLD treatment is considered to be made of vertically or obliquely reinforced 1–3 piezoelectric composite material. A three-dimensional finite element model has been developed to study the damping characteristics of the laminated FFRC shells integrated with the patches of ACLD treatment. Our results reveal that (i) the planar orientation of CNT waviness has a significant influence on the damping characteristics of the laminated FFRC shells, (ii) damping characteristics of the symmetric cross-ply, and antisymmetric angle-ply laminated FFRC shells are improved if CNT waviness is coplanar with the longitudinal plane of the carbon fiber, and (iii) for the antisymmetric cross-ply laminated FFRC shells, the performance of the ACLD patches becomes maximum for attenuating the fundamental mode when CNT waviness is coplanar with the transverse plane of the carbon fiber.

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TL;DR: In this article, the authors derived the governing equations of the conical shell by using the first-order shear deformable shell model and taking into account the size parameter through couple stress theory.

Abstract: In this paper, the governing equations of the conical shell are derived by using the first-order shear deformable shell model and taking into account the size parameter through couple stress theory. In order to obtain the governing equations, Hamilton’s principle is used and the equations of shell motion with partial differentials are derived along with classical and non-classical boundary conditions. Finally, the free vibration of the single-walled carbon nanocone (SWCNC) is scrutinized through examples. The SWCNC is modeled as simply supported, and the Galerkin method is used to solve the vibration problem. The results of the new model are compared with those of the classical theory, which point to the conclusion that the classical model is a special case of couple stress theory. Results also reveal that nanoshell rigidity in the couple stress theory is greater than that in the classical theory, which leads to an increase in natural frequencies. Moreover, the study investigates the effect of the size parameter on nanoshell vibration for different lengths and apex angles.

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TL;DR: A new method combining the Kriging model with OIMCS is proposed, based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA.

Abstract: Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box (p-box) model. Although tremendous efforts have been devoted to propagating random or p-box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.

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TL;DR: In a numerical example, the dynamic response of a single-span steel bridge subjected to a high-speed train is analyzed showing the efficiency of the proposed approach and the importance of considering rail irregularities for a reliable prediction of the acceleration response.

Abstract: For analyzing the dynamic interaction problem of a train passing a railway bridge with high speed, a substructure approach is presented taking into account the influence of rail irregularities. Modal analysis provides a description of the finite element bridge model in modal space with a small number of degrees of freedom. The train is modeled as a sequence of multibody mass–spring–damper systems. A linear interaction model in the context of a component mode synthesis method is used for coupling the two substructures. In a numerical example, the dynamic response of a single-span steel bridge subjected to a high-speed train is analyzed showing the efficiency of the proposed approach. The results of this example demonstrate the importance of considering rail irregularities for a reliable prediction of the acceleration response.

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TL;DR: In this paper, the dynamics of a Birkhoffian system with fractional derivatives is studied and a general method for constructing a fractional dynamical model of the actual problem is presented.

Abstract: In this paper, we present a new fractional dynamical theory, i.e., the dynamics of a Birkhoffian system with fractional derivatives (the fractional Birkhoffian mechanics), which gives a general method for constructing a fractional dynamical model of the actual problem. By using the definition of combined fractional derivative, we present a unified fractional Pfaff action and a unified fractional Pfaff–Birkhoff principle, and give four kinds of fractional Pfaff–Birkhoff principles under the different definitions of fractional derivative. And then, by using the fractional Pfaff–Birkhoff principles, we establish a series of fractional Birkhoffian equations with different fractional derivatives and construct the tensor representation of autonomous fractional Birkhoffian equations. Further, we study the relationship among the fractional Bikhoffian system, the fractional Hamiltonian system and the fractional Lagrangian system and give the transformation conditions. And furthermore, as applications of the fractional Birkhoffian method, we construct five kinds of fractional dynamical models, which include the fractional Lotka biochemical oscillator model, the fractional Whittaker model, the fractional Hojman–Urrutia model, the fractional Henon–Heiles model and the fractional Emden model.

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TL;DR: In this paper, the effect of axisymmetric heat supply on the phenomena of diffusion in a thermoelastic thick plate of infinite extent and finite thickness is discussed within the context of the theory of generalized thermo-elastic diffusion with one relaxation time.

Abstract: 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.

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TL;DR: In this paper, the stochastic natural frequencies of laminated composite conical shells using a surrogate model (D-optimal design) approach were derived for finite element analysis with uncertainty due to variation in angle of twist.

Abstract: The present study portrays the stochastic natural frequencies of laminated composite conical shells using a surrogate model (D-optimal design) approach. The rotary inertia and transverse shear deformation are incorporated in probabilistic finite element analysis with uncertainty due to variation in angle of twist. A sensitivity analysis is carried out to address the influence of different input parameters on the output natural frequencies. Typical fiber orientation angle and material properties are randomly varied to obtain the stochastic natural frequencies. The sampling size and computational cost are exorbitantly reduced by employing the present approach compared to direct Monte Carlo simulation. Statistical analysis is presented to illustrate the results. The stochastic natural frequencies obtained are the first known results for the type of analyses carried out here.

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TL;DR: In this paper, a Timoshenko beam finite element is developed based on the strain gradient theory and employed to evaluate the mechanical behavior of microbeams used in microelectromechanical systems.

Abstract: The classical continuum theory not only underestimates the stiffness of microscale structures such as microbeams but is also unable to capture the size dependency, a phenomenon observed in these structures. Hence, the non-classical continuum theories such as the strain gradient elasticity have been developed. In this paper, a Timoshenko beam finite element is developed based on the strain gradient theory and employed to evaluate the mechanical behavior of microbeams used in microelectromechanical systems. The new beam element is a comprehensive beam element that recovers the formulations of strain gradient Euler–Bernoulli beam element, modified couple stress (another non-classical theory) Timoshenko and Euler–Bernoulli beam elements, and also classical Timoshenko and Euler–Bernoulli beam elements; note that the shear-locking phenomenon will not happen for the new Timoshenko beam element. The stiffness and mass matrices of the new element are derived in closed forms by following an energy-based approach and using Hamilton’s principle. It is noted that unlike the classical beam elements, the stiffness matrix of the new element has a size-dependent nature that can capture the size-dependent behavior of microbeams. The shape functions of the newly developed beam element are determined by solving the equilibrium equations of strain gradient Timoshenko beams, which brings about a size-dependent characteristic for them. The new beam element is employed to evaluate the static deflection of a microcantilever, and the results are compared to the experimental data as well as the results obtained by using the classical beam element and the couple stress plane element. The new beam element is also implemented to calculate the static deflection, vibration frequency, and pull-in voltage of electrostatically actuated microbeams. The current results are compared to the experimental data as well as the classical FEM outcomes. It is observed that the results of the new element are in excellent agreement with the experimental data while the gap between the experimental and classical FEM results is significant.

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TL;DR: In this paper, the authors proposed a new formulation for active vibration control of a rectangular plate based on the optimal positions/orientations of piezoelectric actuators/sensors attached to the plate.

Abstract: The purpose of this study is to suggest a new formulation for active vibration control of a rectangular plate based on the optimal positions/orientations of piezoelectric actuators/sensors attached to the plate. The free vibration and modal properties are derived by using Rayleigh–Ritz and the transient response by assumed modes methods based on the classical plate theory. Three criteria are proposed for optimal location of piezoelectric patches attached to the simply supported plate. In other words, the optimal positions/orientations of piezoelectric patches can be determined based on spatial controllability/observability gramians of the structure, as well as the consideration of residual modes to reduce the spillover effect. These criteria are used to achieve the optimal fitness function defined for a genetic algorithm optimizer to find the optimal locations/orientations of piezoelectric sensors/actuators. To control the vibrations of the plate, a negative velocity feedback control algorithm is designed. The results of simulations indicate that by locating piezoelectric patches in the optimal positions, the depreciation rate of the structure increases and the amplitudes of the plate vibrations reduce effectively. The effect of number of piezoelectric devices on the active damping property of the system is also analyzed.

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TL;DR: In this article, a stochastic micromechanical framework for multiphase composites is proposed to characterize the probabilistic behaviors of effective properties of composite materials, and a new simulation framework, consisting of univariate approximation for multivariate function, Newton interpolations, and Monte Carlo simulation, is developed to quantitatively evaluate the stochiastic characteristics of the effective properties.

Abstract: A stochastic micromechanical framework for multiphase composites is proposed to characterize the probabilistic behaviors of effective properties of composite materials. Based on our previous work, the deterministic micromechanical model of the multiphase composites is derived by introducing the strain concentration tensors. By modeling the volume fractions and properties of constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the inherent randomness of effective properties among different specimens. A new simulation framework, consisting of univariate approximation for multivariate function, Newton interpolations, and Monte Carlo simulation, is developed to quantitatively evaluate the stochastic characteristics of the effective properties of composites. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, and the Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the effective properties of multiphase composites. Finally, the effects of the correlation between the constituents’ material parameters are discussed based on our proposed stochastic micromechanical model, which shows that the negative correlation between Young’s modulus and Poisson’s ratio of the constituents can enhance the effective properties of the composites.

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TL;DR: In this paper, a new approximate universal solution for the normal contact between frictionless spherical surfaces is established by combining analytical and numerical methods, which can be universally used to calculate the pressure distribution of conformal and non-conformal contact.

Abstract: Elastic spherical contact, especially conformal contact, is a widely encountered problem in mechanical design and wear analysis, but corresponding universal methods do not exist. A new approximate universal solution for the normal contact between frictionless spherical surfaces is established by combining analytical and numerical methods. The proposed model is not limited to an elastic half-space and can be universally used to calculate the pressure distribution of conformal and non-conformal contact. The validity and universality of the model were verified by a large number of three-dimensional finite element analyses of different materials and structures. With the new model, users can investigate the complex relationships between key parameters, such as maximum contact pressure, radius of contact region, normal load radii, and radial clearance, and apply this understanding in design and wear analysis of products with spherical contact surfaces, such as bearings.

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TL;DR: In this article, the authors analyzed the effects of Young's modulus uncertainty on the static response of the Timoshenko beam under uniformly distributed load and derived approximate explicit expressions of the lower bound and upper bound of the interval response.

Abstract: Response variability of Timoshenko beams with uncertain Young’s modulus subjected to deterministic static loads is analyzed. The uncertain material property is idealized within a non-probabilistic context by using an interval field model recently proposed by the first two authors. Such a model is able to quantify the dependency between adjacent values of an interval uncertainty by means of a real, deterministic, symmetric, nonnegative, bounded function conceived as the non-probabilistic counterpart of the autocorrelation function characterizing random fields. In order to analyze the effects of Young’s modulus uncertainty on the static response of the Timoshenko beam, a finite difference discretization of the coupled interval ordinary differential equations of equilibrium is performed. Then, approximate explicit expressions of the lower bound and upper bound of the interval response are derived. Numerical results showing the effects of interval material uncertainty on the static response of a simply supported beam under uniformly distributed load are presented.

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TL;DR: In this article, nonlinear free vibration and primary/secondary resonance analyses of shape memory alloy (SMA) fiber reinforced hybrid composite beams with symmetric and asymmetric lay-up are investigated.

Abstract: In this paper, nonlinear free vibration and primary/secondary resonance analyses of shape memory alloy (SMA) fiber reinforced hybrid composite beams with symmetric and asymmetric lay-up are investigated. The simplified Brinson constitutive model and cosine phase transformation kinetics are utilized to simulate the behavior of the SMA materials and calculate the recovery stress. In order to predict the behavior of the smart laminated beam, Euler–Bernoulli beam theory and nonlinear von-Karman strain field are employed. Two types of micromechanical models, namely Voigt and Reuss models are considered. The Galerkin procedure together with the elliptic function and multi timescales method is adopted to obtain analytical solutions for the nonlinear free vibration and primary/secondary response phenomena. Numerical results reveal that some of the geometrical and physical parameters such as the SMA volume fraction, the amount of prestrain in the SMA fiber, orientation of composite fiber, vibration amplitude and temperature are important factors affecting the free vibration characteristic in the pre/post-buckled region, and primary and secondary resonance of the laminated beams reinforced with SMA fibers. The analytical solutions and results are reported for the first time and can serve as benchmark for researchers to validate their numerical and analytical methods in the future.

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TL;DR: In this paper, the Stokes' hypothesis for a Newtonian fluid is reconsidered, and a possible explanation is given of the fact that, in spite of its evidently weak physical justification, it permits to obtain good results for the description of most compressible flows.

Abstract: The so-called Stokes’ hypothesis for a Newtonian fluid is reconsidered, and a possible explanation is given of the fact that, in spite of its evidently weak physical justification, it permits to obtain good results for the description of most compressible flows. The explanation stands upon a closer analysis of the effect of the terms of the complete stress tensor in which the viscosity coefficients appear. An alternative formulation of the hypothesis is proposed, which also permits to clearly identify the very particular flow conditions in which it cannot justify the experimental evidence.

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TL;DR: In this paper, a new time-variant reliability measurement based on a non-probabilistic interval process model is proposed, in which the time-varying uncertain variables at any time as intervals and define the corresponding auto-covariance function and correlation coefficient function to characterize the correlation between limit states at different times.

Abstract: The study on reliability of an aging structure requires taking into account the influence of time Typical approaches for performing time-variant reliability assessment are always based upon the random process model, where the dynamic distributions of uncertain parameters are determined by a substantial number of samples In this paper, a new time-variant reliability measurement based on a non-probabilistic interval process model is proposed, in which we describe the time-varying uncertain variables at any time as intervals and define the corresponding auto-covariance function and correlation coefficient function to characterize the correlation between limit states at different times By combining with the set-theory approach and the classical first-passage theory, a new non-probabilistic model of safety evaluation for time-dependent structures is established, and its measure index is then analytically calculated The proposed model of time-variant reliability is suitable for both the cases of stationary process and non-stationary process Moreover, the Monte Carlo method is also presented as a means of verification The comparison between the presented model and the Monte Carlo-based model is eventually carried out on two application examples; the usage, efficiency and accuracy of the developed approach can be demonstrated

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TL;DR: In this article, the authors employed the Brazilian disk with a central dumbbell-shaped slit with two key-shaped ends and made of PMMA to perform mixed mode I/II brittle fracture experiments on keyhole notches for various notch lengths and radii and, also, different mode mixity ratios.

Abstract: The Brazilian disk specimen weakened by a central dumbbell-shaped slit with two key-shaped ends and made of PMMA is employed to perform mixed mode I/II brittle fracture experiments on key-hole notches for various notch lengths and radii and, also, different mode mixity ratios. The load-carrying capacity of the specimen resulting from the test machine at the onset of sudden fracture is theoretically predicted by means of a well-known brittle fracture criterion, namely the local strain energy density criterion. A good agreement is found to exist between the theoretical and the experimental results.

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TL;DR: In this paper, the authors provide important information to engineering designers, introducing exact linking relationships between elastic Euler-Bernoulli beam response and fractional visco-elastic Timoshenko beam response.

Abstract: The Euler–Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler–Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a fractional constitutive law has to be considered. In this context, it has been provided that if the homogeneous beam correspondence principle also holds, then the study of a fractional visco-elastic Euler–Bernoulli beam may be derived from the elastic one. As mentioned before, when dealing with visco-elasticity the Timoshenko beam model is more appropriate than Euler–Bernoulli’s one, and this paper provides important information to engineering designers, introducing exact linking relationships between elastic Euler–Bernoulli beam response and fractional visco-elastic Timoshenko beam response. Ready-to-use tables and a straightforward formulation have been provided leading to significant analysis cost savings and improved quality.

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TL;DR: In this article, a model for the elastic response of a thermo-responsive hydrogel subjected to swelling under an arbitrary deformation with finite strains is developed for modeling the behavior of the hydrogels.

Abstract: A model is developed for the elastic response of a thermo-responsive hydrogel subjected to swelling under an arbitrary deformation with finite strains. The constitutive equations involve the stress–strain relation, the nonlinear diffusion equation for water molecules, the heat conduction equation, and the Allen–Cahn equation for a scalar order parameter (proportional to the concentration of hydrophilic segments in polymer chains). Material constants are found by fitting equilibrium mass uptake diagrams for macro- and microgels under unconstrained and constrained swelling in the vicinity of the volume phase transition temperature. Quantitative agreement is demonstrated between the experimental data and the results of simulation. The effect of composition of hydrogels (concentrations of monomers and cross-linker) on adjustable parameters is analyzed numerically.

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TL;DR: In this article, the authors investigated the nonlinear buckling and post-buckling problems of functionally graded stiffened toroidal shell segments surrounded by an elastic medium under torsion based on an analytical approach.

Abstract: The nonlinear buckling and post-buckling problems of functionally graded stiffened toroidal shell segments surrounded by an elastic medium under torsion based on an analytical approach are investigated. The rings and stringers are attached to the shell, and material properties of the shell are assumed to be continuously graded in the thickness direction. The classical shell theory with the geometrical nonlinearity in von Karman sense and the smeared stiffeners technique are applied to establish theoretical formulations. The three-term approximate solution of deflection is chosen more correctly, and the explicit expression to find critical load and post-buckling torsional load-deflection curves is given. The effects of geometrical parameters and the effectiveness of stiffeners on the stability of the shell are investigated.

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TL;DR: In this paper, a self-consistent size-dependent theory for viscous flows is proposed, which allows for the possibility of couple-stresses, along with general non-symmetric forces.

Abstract: There can be no doubt as to the importance of vortical motion in fluid mechanics. Yet, very little attention is given typically to the balance law of angular momentum and to its role in defining the fundamental character of stress, which as a result is usually assumed as a symmetric tensor. Here, we allow for the possibility of couple-stresses, along with general non-symmetric force–stresses, and develop a self-consistent size-dependent theory within the context of classical continuum mechanics. This development relies upon the identification of the following key components for the dynamic response of three-dimensional fluid continua: (i) fundamental, uniquely defined kinematical measures of flow, (ii) an independent set of energy conjugate variables, (iii) the corresponding permissible natural and essential boundary conditions, and (iv) a non-redundant set of body-force and inertial contributions. Based upon this formulation, one can recognize that the previous couple-stress theory for fluids suffers from some inconsistencies, which may have restricted its applicability in the study of viscous flows. After presenting the general formulation of the new consistent theory, we specialize for incompressible viscous flow and consider the problem of generalized Poiseuille flow within this size-dependent fluid mechanics. Finally, we conclude that the theory presented here may provide a basis for a broad range of fluid mechanics applications and for fundamental studies of flows at the finest scales for which a continuum representation is valid.