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• For existence of weak solution in Signorini's contact problem in the previous works was used the Div-Curl lemma. • We follow a different and new approach applying the semigroup theory. • We prove the existence of at least one solution to the Signorini problem by using the hybrid-penalized method. • We prove uniform stabilization assuming equal wave speeds in the first and second equations of the system. • The uniqueness of the solution to Signorini's problem remains an open question. In this paper, we study Signorini's problem for a laminated Timoshenko beam with interfacial slip. We assume that the transverse displacements at the end of the beam are in the presence of two rigid obstacles (Signorini conditions). We prove the existence of solution and analyze the asymptotic behavior of the system. We use the hybrid-penalized method to show the global existence of at least one solution to Signorini's problem and finally, numerical experiments verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, we study the effect of heat conduction theories pioneered by Green and Naghdi, popularly called thermoelasticity of type Ⅲ, on the stability of laminated Timoshenko beams. Without the structural (interfacial slip) damping or any other forms of damping mechanisms, we establish an exponential stability result depending on the equality of wave velocities of the system. Our work shows that the thermal effect is strong enough to stabilize the system exponentially without any additional internal or boundary dampings. The result extends some of the developments in literature where structural damping (in addition to some internal or boundary dampings) is necessary to bring about exponential stability.

In this work, we study the effect of heat conduction theories pioneered by Green and Naghdi, popularly called thermoelasticity of type III, on the stability of laminated Timoshenko beams. Without the structural (interfacial slip) damping or any other forms of damping mechanisms, we establish an exponential stability result depending on the equality of wave velocities of the system. Our work shows that the thermal effect is strong enough to stabilize the system exponentially without any additional internal or boundary dampings. The result extends some of the developments in literature where structural damping (in addition to some internal or boundary dampings) is necessary to bring about exponential stability. [ABSTRACT FROM AUTHOR]

A shear-deformable beam theory is proposed to model the torsional behavior of laminated beams composed of variable stiffness layers. The displacement field is derived by expanding mid-surface displacements in Taylor series in width coordinate and by retaining first-order terms. Stiffness of the beam is made variable by using curvilinear fibers in layers. Variable stiffness layers are categorized into three types as symmetric, asymmetric and anti-symmetric based on their fiber paths. A displacement-based finite element method is used to solve the analytical model and to predict rotations of the beam under torsional load. Beams constructed with symmetric, antisymmetric and asymmetric variable stiffness layers are investigated for several lay-ups by both including and neglecting axial displacement terms. Acquired results are compared with the results of a finite element analysis software. It is observed that the developed model is working properly for beams with variable stiffness layers and including axial displacement terms in calculations improved the model's performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider a laminated Timoshenko beam system with frictional damping and an internal distributed delay feedback on the effective rotational angle. Under appropriate assumptions on the weight of the delay term and wave speeds of the first two equations of the system, we prove that the dissipation through the frictional damping is enough to stabilize the system exponentially. [ABSTRACT FROM AUTHOR]

In approaching the Karman the initial-boundary value problem is formulated for the dynamic elastic-plastic deformation of flexible composite beams of irregular layered-fibrous structures with account of their weakened resistance to the transverse shear. Beams consist of walls and load-bearing layers (shelves). Walls can be reinforced longitudinally or crosswise in its plane, and the shelves are reinforced in the longitudinal direction. The mechanical behavior of the component materials of the composition is described by the equations of the theory of plasticity with isotropic hardening. The explicit “cross” scheme was constructed for numerical integration of the formulated initial-boundary value problem coordinated with the step-by-step scheme and used for the simulation of elasticplastic deformation of composite material of each layer of the beam. The calculations of dynamic and quasistatic bending behavior are carried out for homogeneous and reinforced beams of I-beam cross-section. It is found that the classical theory of bending may not be acceptable to carry out such calculations for some types of metal compositions for relatively long beams. For the adequate calculation of elastoplastic deformation of composite beams of laminated-fibrous irregular structures it is necessary to use the Timoshenko theory, which takes in account the weakened resistance of the walls to the transverse shears. It is shown that in the case of dynamic loading of composite beams, the final deflections are much larger by absolute value than in the case of quasi-static loading with the same load level.

• Fracture modes partitioning for generally layered beams with hygrothermal effect. • Analytical solutions for the mode I and II fracture energies for various tests. • Residual thermal stresses effect on the fracture toughness of fiber metal laminates. • Analytical modeling of the contact problem in the end-notched flexure test. An analytical framework is presented to calculate the mode I and II components of the strain energy release rate (SERR) of a delamination between two generally layered sub-laminates, considering the residual hygrothermal stresses effect. First, the sub-laminates are modeled as Timoshenko beams, the crack tip is assumed rotationally flexible and the mode partitioning is based on the global method. Next, SERR and mode mixity are obtained for an arbitrarily loaded delaminated beam and reduced for some typical delamination fracture tests. An asymmetrically delaminated fiber metal laminate (FML) is analyzed under double cantilever beam (DCB) and end-notched flexure (ENF) configurations. For the ENF configuration, the inherent contact problem was analytically approached. We demonstrate that the thermal effect on the SERR and mode mixity of the FML, rather ignored so far in the literature, can be non-negligible. Finally, the analytical results are validated against numerical predictions using the finite element method. [ABSTRACT FROM AUTHOR]

The unsteady creep of homogeneous and metal-composite beams with irregular layered structure is considered. Beams consist of thin walls and shelves attached to them at top and bottom (bearing layers). The walls and bearing layers made of homogeneous isotropic materials. The mechanical behavior of these materials is described by a nonlinear hereditary theory of creep (Yu. Rabotnov). On the basis of the hypotheses of the Timoshenko theory with involvement of the ideas of method of steps in time the problem is formulated for the inelastic flexural deformation of such beams with account of their weakened resistance of their walls to the transverse shear. It is shown that in discrete moments of time the mechanical behavior of these materials layers obeys formally the defining relations of nonlinearelastic isotropic body with an initial stress state that is known. The secant modulus method is used for linearization of the task at each discrete time moment. Characteristics of the flexural behavior of three- and five-layer homogeneous and metal-composite beams under short-and long-term loading are studied. Statically determinate double-seat and cantilever beams are considered under the action of uniformly distributed transverse load of Heaviside type. It is found that the use of the classical theory of calculation of such beams leads to the prediction of unreasonably understated their flexibility, especially under creep conditions. In beams with reinforced bearing layers it is shown that the creep mainly develops due to the shear strain which actively accumulates in the walls of such structures.

Steady-state creep of a hybrid metal-composite laminated bending beams of irregular patterns is considered. Beams consist of walls and load-bearing layers, attached at the top and bottom (shelves). The shelves are reinforced with fibers in the longitudinal direction, and the walls are reinforced either longitudinally or cross in the plane. Under the hypotheses of the Timoshenko theory the boundary value problem is formulated for the calculation of the considered beams, which allows taking into account the weakened resistance of the walls of the transverse shifts. The simple iteration method based on the idea of the se-cant modulus method is applied for linearization of the problem. The mechani-cal behavior of reinforced and unreinforced doubleseat beams and cantilevers in conditions of steady creep under the action of uniformly distributed trans-verse load is investigated. Cross sections of beams are I-shaped. It is shown that for homogeneous I-beams, the classical Bernoulli theory does not guaran-tee the calculated results in compliance within 20% accuracy, which is consid-ered to be acceptable if the width of the shelf is comparable with the height of cross sections of beams. In the cases of metal-composite beams, the classical theory becomes generally unacceptable, because it lowers by several orders of magnitude the compliance of such structures in conditions of steady creep. It is demonstrated that the rate of shear strain, actively developing in their walls, must be considered. The consideration of these strain rates within the frame-work of the Timoshenko theory led to the discovery of new mechanisms of de-formation of laminated beams which the classical theory does not find. It is shown that the change in mechanism of deformation can occur by increasing the density of reinforcement of shelves or walls.

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general decay result. Interestingly, the result is established without any additional internal or boundary damping term and without imposing any restrictive growth assumption on the nonlinear term, provided the wave speeds of the first equations of the system are equal.

The research at hand deals with the mechanical behavior of beam-like nanostructures. Nanobeams are assembled of multiple layers of different materials and geometry giving a layered nanobeam. To properly address experimentally noticed size effects in structures of this type, an adequate nonlocal elasticity formulation must be applied. The present model relies on the stress-driven integral methodology that effectively circumvents known deficiencies of other approaches. As a main contribution, a set of differential equations and boundary conditions governing the underlaying mechanics is proposed and applied to two benchmark examples. The obtained results show the expected stiffening nonlocal behavior exhibiting most of smaller and smaller structures and modern devices.

Conventional beam elements based on the mid-plane formulation are often used to predict vibration frequencies of beams. Recently published work on the vibration of functionally graded materials (FGM) beams shows that if the positions of immovable end supports are at a different plane to the middle-plane, beam elements based on mid-plane formulation will yield inaccurate results. This paper extends this work further by critically examining the effect of end support positions along the height of the beam in the context of vibration analysis. A formulation for vibration analysis of beams based on reference-plane formulation is proposed. In order to verify the proposed formulation, we considered FE modelling of beams based on generalized beam elements, composite shell elements and 3D solid elements that are able to accurately capture the effect of end support height position on vibration frequencies. Two vibrating beam examples are considered. The first problem deals with a single layer beams and the second problem deals with a double layer beam. Both problems are analyzed using the proposed method and FE models based on generalized beam elements, composite shell elements and 3D solid elements for different end support conditions and heights. Single layer beam was also modelled in FE using conventional beam elements. The results clearly showed that if one uses conventional beam elements for vibration analysis of beams, the results will not be accurate if immovable end supports are applied at an eccentricity to the mid-plane. Vibration frequencies predicted from the proposed reference-plane formulation were shown to agree well with the results from FE models based on generalized beam elements, composite shell elements, and 3D solid elements. [ABSTRACT FROM AUTHOR]

The article carried a generalization of the technical theory of pure bending uniform prismatic beam of constant thickness and height in case of viscoelastic laminated composite beam. Used hereditary theory of viscoelastic creep uniformly aging bodies. Calculated averaged by Voigt and Reuss values of deformation parameters of the composite beam in pure bending.The effective instantaneous elastic modulus and instantaneous radius of curvature of the neutral layer of a flexible beam. Discovered that the Hill’s effective values of instantaneous elastic modulus for bending of a beam and for uniaxial tension / compression viscoelastic composite rods are the same.

This paper investigates the possibility of energy harvesting using Fiber Reinforced Plastic beams under cyclic loading. The behaviour of E-glass fiber/epoxy and Hemp fiber/epoxy laminated beams reinforced with piezoelectric fibers is examined by evaluating their bending strain and deflection. An optimum stacking sequence for all types of reinforcement: E-glass fibers, hemp fibers, and piezoelectric fibers, is suggested such that energy harvesting potential is maximized while failure and damage accumulation remain at low levels. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the FEM solution of laminated plates and shells that nowadays are mostly done by low order solid or shell finite elements enriched by stress or strain fields, or by specific kinematics dedicated to the analysis of such structures. We introduce a triangular based prismatic finite element of any approximation order capable of solving from very thin to very thick laminated plates and shells, with the following properties: (i) locking-free behavior; (ii) good stress distribution even for complex materials; (iii) geometrically exact description of large displacements; and (iv) geometry dedicated to evaluate plates and shells (laminated or not) free of problems due to distorted meshes or ill-conditioned systems as thickness decreases. This triangular based prismatic finite element can also be employed in laminated beams, holding the same properties. The proposed element uses total Lagrangian description based on positions, and its performance regarding the claimed properties is demonstrated in several examples. [ABSTRACT FROM AUTHOR]

Free vibration characteristics and buckling behaviors of generally laminated composite beams subjected to the concentrated axial force and various classical end conditions are investigated in this paper. The analysis is based on a unified higher-order shear deformation beam theory. The Poisson effect, axial force, extensional deformation, bending deformation, shear deformation, and rotary inertia are all incorporated in the formulation. The dynamic stiffness method is employed to perform the exact vibration and buckling analyses of laminated composite beams. The dynamic stiffness matrix is developed from the complete analytical solutions of the homogeneous governing differential equations. Numerical results for the natural frequencies and buckling loads of particular laminated beams are presented and compared with previously published results. The effects of shear deformation, axial force and end condition on the natural frequencies, buckling loads and/or mode shapes of the laminated beams are thoroughly analyzed. [ABSTRACT FROM AUTHOR]

A través del Laboratorio Nacional de Productos Forestales de la Universidad de Los Andes (Mérida, Venezuela) se realizaron los ensayos de flexión estática, según la Norma ASTM D-198-84, para la determinación de los esfuerzos de diseño de 18 vigas de madera laminada de pino caribe encoladas con adhesivo de isocianato (MDI). Las mismas fueron fabricadas íntegramente en la única industria de madera laminada existente, hasta el presente, en Venezuela. Estas vigas laminadas se dividieron en dos tipos, 9 estaban constituidas por láminas completas de madera y las otras 9 estaban constituidas por láminas de madera seccionadas y unidas por medio de la técnica del finger joint; dentro de cada uno de estos tipos se prepararon tres vigas laminadas con anchos distintos (65 mm , 95 mm y 125 mm), siendo sus alturas y sus largos iguales (270 mm y 3500 mm respectivamente). Al comparar los resultados obtenidos con valores de vigas laminadas de pino radiata de Chile, y pino resinoso de Argentina se logró determinar, que los valores de Esfuerzo Límite Proporcional, Módulo de Ruptura y Módulo de Elasticidad para todas las vigas estudiadas, estaban por debajo. El análisis morfológico de todas las vigas, definió que éstas presentaron grandes deficiencias en la calidad física de la madera y las líneas de cola, y por igual, en el proceso de fabricación. Estos factores, son la principal causa de los bajos valores obtenidos. Se recomienda, en esta primera etapa de la industria, mejorar los aspectos técnicos señalados, para aumentar la resistencia y calidad estructural de las vigas laminadas encoladasStatic flexion tests of eighteen glued-laminated timber of caribean pine glued with isocyanate-based adhesives (MDI) were carried out following ASTM- D198-84 standards at the National Laboratory of Forest Products of "La Universidad de los Andes" (Mérida, Venezuela). These beams were fabricated, in their entirety, by the only company that develops glued-laminated (GLULAM) timber in Venezuela. The glued-laminated timber was divided into two groups of nine. The first group consisted of GLULAM timber made from whole beams of wood, while the second was composed of sectioned wood that had been finger-joined and later made into GLULAM beams. Each group was divided into three subgroups with glued-laminated timber of widths 65mm, 95mm and 125mm, but with a common height of 270mm and a length of 3500mm. The values obtained for stress at proportional limit, modulus of rupture and the modulus of elasticity for all the beams studied were less than those reported for glued-laminated timber from Chilean radiata pine and Argentinean resinous pine. Morphology studies performed on all the studied beams revealed that they presented great deficiencies in the physical quality of the wood, glue lines, and fabrication process. These factors are responsible for the low-performance of the test samples. It is recommended, in this first stage of the industry, that the mentioned technical aspects be improved so that resistance and structural quality of glued-laminated timber is in turn enhanced

This paper is devoted to the static analysis of laminated beams with both compact and thin-walled cross-sections. The kinematic models are obtained by means of the Carrera Unified Formulation (CUF), which is a hierarchical formulation leading to very accurate and computationally efficient finite element (FE) models. According to the latest developments in the framework of CUF, it is possible to easily adopt both equivalent-single-layer and layer-wise approaches, by expanding the unknown kinematic variables on the beam cross-section with either Taylor-like or Lagrange-like polynomials, respectively. A number of laminated beam structures are analysed and particular attention is given to laminated single- and multi-cell cross-section beams with open and closed contours. Moreover, in order to demonstrate the effectiveness of the proposed refined elements, the results in terms of displacements and stresses are compared with solid FE solutions and, when possible, with the results available from the research literature. [ABSTRACT FROM AUTHOR]

A través del Laboratorio Nacional de Productos Forestales de la Universidad de Los Andes (Mérida, Venezuela) se realizaron los ensayos de flexión estática, según la Norma ASTM D-198-84, para la determinación de los esfuerzos de diseño de 18 vigas de madera laminada de pino caribe encoladas con adhesivo de isocianato (MDI). Las mismas fueron fabricadas íntegramente en la única industria de madera laminada existente, hasta el presente, en Venezuela. Estas vigas laminadas se dividieron en dos tipos, 9 estaban constituidas por láminas completas de madera y las otras 9 estaban constituidas por láminas de madera seccionadas y unidas por medio de la técnica del finger joint; dentro de cada uno de estos tipos se prepararon tres vigas laminadas con anchos distintos (65 mm , 95 mm y 125 mm), siendo sus alturas y sus largos iguales (270 mm y 3500 mm respectivamente). Al comparar los resultados obtenidos con valores de vigas laminadas de pino radiata de Chile, y pino resinoso de Argentina se logró determinar, que los valores de Esfuerzo Límite Proporcional, Módulo de Ruptura y Módulo de Elasticidad para todas las vigas estudiadas, estaban por debajo. El análisis morfológico de todas las vigas, definió que éstas presentaron grandes deficiencias en la calidad física de la madera y las líneas de cola, y por igual, en el proceso de fabricación. Estos factores, son la principal causa de los bajos valores obtenidos. Se recomienda, en esta primera etapa de la industria, mejorar los aspectos técnicos señalados, para aumentar la resistencia y calidad estructural de las vigas laminadas encoladas. Abstract Static flexion tests of eighteen glued-laminated timber of caribean pine glued with isocyanatebased adhesives (MDI) were carried out following ASTM- D198-84 standards at the National Laboratory of Forest Products of “La Universidad de los Andes” (Mérida, Venezuela). These beams were fabricated, in their entirety, by the only company that develops glued-laminated (GLULAM) timber in Venezuela. The glued-laminated timber was divided into two groups of nine. The first group consisted of GLULAM timber made from whole beams of wood, while the second was composed of sectioned wood that had been finger-joined and later made into GLULAM beams. Each group was divided into three subgroups with glued-laminated timber of widths 65mm, 95mm and 125mm, but with a common height of 270mm and a length of 3500mm. The values obtained for stress at proportional limit, modulus of rupture and the modulus of elasticity for all the beams studied were less than those reported for glued-laminated timber from Chilean radiata pine and Argentinean resinous pine. Morphology studies performed on all the studied beams revealed that they presented great deficiencies in the physical quality of the wood, glue lines, and fabrication process. These factors are responsible for the low-performance of the test samples. It is recommended, in this first stage of the industry, that the mentioned technical aspects be improved so that resistance and structural quality of glued-laminated timber is in turn enhanced.

This paper presents a new class of refined beam theories for static and dynamic analysis of composite structures. These beam models are obtained by implementing higher-order expansions of Chebyshev polynomials for the three components of the displacement field over the beam cross-section. The Carrera Unified Formulation (CUF) is adopted to obtain higher-order beam models. The governing equations are written in terms of fundamental nuclei, which are independent of the choice of the expansion order and the interpolating polynomials. Static and free vibration analysis of laminated beams and thin-walled boxes has been carried out. Results obtained with the novel Chebyshev Expansion (CE) model have been compared with those available in the literature. For comparison, Taylor-like Expansion (TE) and Lagrange Expansion (LE) CUF models, commercial codes, analytical and experimental data are exploited. The performances of refined beam models in terms of computational cost and accuracy in comparison to the reference solutions have been assessed. The analysis performed has pointed out the high level of accuracy reached by the refined beam models with lower computational costs than 2D and 3D Finite Elements. [ABSTRACT FROM AUTHOR]

In this study we present an alternative finite element formulation to solve two-dimensional laminated and functionally graded bar elements with continuum transverse stress distribution. The considered structural elements are long or short and the strain level can be large. Thus, it is necessary to consider a hyperelastic constitutive model capable of representing large strains. Enhancements - regularization of the Reissner-Mindlin kinematics and the zigzag effect - are developed to impose continuous transverse shear stress. The regularized Reissner-Mindlin kinematics is important for both laminated and functionally graded materials, while the zigzag enhancement is important only for laminates. The formulation is developed considering laminated bars; however, as the number of laminas is unlimited and keeps the number of degrees of freedom; functionally graded materials are directly represented. An additional degree of freedom is considered for large strains, improving the element volumetric performance. The formulation is validated comparing the proposed kinematics with literature results. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with time-dependent behavior of a simply-supported laminated functionally graded (FG) beam with viscoelastic interlayer. The viscoelastic interlayer is modeled as an arbitrary linear viscoelastic material and the elastic modulus of each graded layer varies with the thickness as an arbitrary function, respectively. Closed-form solutions of interface shear stress, axial displacement, transverse displacement and axial stress of the beam under an arbitrary time-dependent load are obtained in Laplace transformed shape. For a simple model, the viscoelastic interface is modeled as a viscoelastic material using Standard Linear Solid model and the elastic modulus of each graded layer exhibits linear variation through the thickness under a constant distributed uniform load. Analytical solutions are derived by inversing Laplace transform which are verified by finite element analysis using software MSC.Marc. [Copyright &y& Elsevier]

Abstract: This paper deals with the geometrically non-linear static and dynamic analysis of functionally graded (FG) beams under combined effect of thermal fields and mechanical excitations integrated with a pair of sensor layers for structural monitoring. The sensor layers are considered to be made of the functionally graded piezoelectric (FGP) materials. The material properties of the host FG beam and FGP sensors are assumed to be graded in the thickness direction according to a power law distribution. The von Karman type geometric non-linearity and the first-order shear deformation theory are used to formulate the governing equations of motion utilizing the Hamilton principle. The solution of coupled non-linear partial differential equations in spatial and time domains is obtained using the hybrid generalized differential quadrature method–Newmark algorithm–Newton–Raphson iterative scheme. A set of parametric study is conducted to show the influence of geometric non-linearity, material parameters and temperature field on the static and dynamic responses of piezoelectric FG beams subjected to impulsive loads. Due to the absence of similar results in the specialized literature, it is expected that the results of this research will be instrumental toward an optimal design of piezoelectric FG structures for static and dynamic structural health monitoring purpose. [Copyright &y& Elsevier]

Abstract: A method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated beam structures is presented. The novelty of this method is the use of one-dimensional finite elements to discretize the geometry of the beam. The key property of this beam element, named LRZ [1], is the possibility to capture the relative displacement between consecutive layers which occurs during delamination. The fracture mode that the LRZ element is capable to predict is mode II. In order to capture the relative displacement using the LRZ element it is necessary to adapt the RZT theory as presented in this paper. The mechanical properties of the layers are modeled using a continuum isotropic damage model [2]. The modified Newton–Raphson method is used for solving the non-linear problem. The RZT theory, the LRZ finite element and the isotropic damage model are described in the paper. Also, the implicit integrations algorithm is presented. The performance of the LRZ element is analyzed by studying the delamination in a beam for two different laminates, using the plane stress solution as a reference. [Copyright &y& Elsevier]

Abstract: A linear static analysis of composite beams is presented in this work. Simply supported, cross-ply laminated beams are examined. Beams with different values of length-to-thickness ratio subjected to bending loadings are considered. Carrera’s Unified Formulation is adopted to derive several hierarchical theories. The kinematic field is imposed above the cross-section via a N-order polynomials approximation of the displacements unknown variables. The governing equations and boundary conditions are variationally obtained through the Principle of Virtual Displacements. A closed form, Navier-type solution is adopted. Thanks to this formulation, quasi three-dimensional strain and stress fields can be obtained. Classical beam models, such as Euler–Bernoulli’s and Timoshenko’s, are obtained as particular cases. Results are validated in terms of accuracy and computational costs towards three-dimensional FE models implemented in the commercial code ANSYS. Numerical investigations show that good results are obtained as long as the appropriate expansion order is used. [Copyright &y& Elsevier]

Abstract: The exact dynamic stiffness matrix of a uniform laminated composite beam based on trigonometric shear deformation theory is developed in this paper. A refined laminated beam constitutive equation is derived that takes into account the breadth direction strains. The dynamic stiffness matrix is formulated directly in an exact sense by solving the governing differential equations of motion that describe the deformations of laminated beams according to the trigonometric shear deformation theory, which includes the sinusoidal variation of the axial displacement over the cross-section. The derived dynamic stiffness matrix is then used in conjunction with the Wittrick–Williams algorithm to compute the natural frequencies and mode shapes of the composite beams. The results obtained from the present theory are compared with those available in the literature wherever possible. [Copyright &y& Elsevier]

The present paper is concerned with the thermal post-buckling behaviors of magneto-electro-elastic laminated beams. Timoshenko beam theory accompanying the von Kármán geometric nonlinearity is considered to model the beams. Temperature and magneto-electric fields are obtained based on satisfying the interfacial continuity conditions and corresponding boundary conditions, and then introduced into the stress-strain constitutive relationships. Afterwards, three governing equations of motion are established with respect to the generalized kinematical variables according to Hamilton's principle, and solved by the generalized differential quadrature method and pseudo-arc length continuation technique. The numerical results aim at the studies on thermal post-buckling paths, post-buckling vibration characteristics and magneto-electric potential responses, the effects on which the lay-up modes, thermal load types and magneto-electric fields exert are discussed. [ABSTRACT FROM AUTHOR]

Static flexion tests of eighteen glued-laminated timber of caribean pine glued with isocyanate-based adhesives (MDI) were carried out following ASTM-D198-84 standards at the National Laboratory of Forest Products of "La Universidad de los Andes" (Mérida, Venezuela). These beams were fabricated, in their entirety, by the only company that develops glued-laminated (GLULAM) timber in Venezuela. The glued-laminated timber was divided into two groups of nine. The first group consisted of GLULAM timber made from whole beams of wood, while the second was composed of sectioned wood that had been finger-joined and later made into GLULAM beams. Each group was divided into three subgroups with glued-laminated timber of widths 65mm, 95mm and 125mm, but with a common height of 270mm and a length of 3500mm. The values obtained for stress at proportional limit, modulus of rupture and the modulus of elasticity for all the beams studied were less than those reported for glued-laminated timber from Chilean radiata pine and Argentinean resinous pine. Morphology studies performed on all the studied beams revealed that they presented great deficiencies in the physical quality of the wood, glue lines, and fabrication process. These factors are responsible for the low-performance of the test samples. It is recommended, in this first stage of the industry, that the mentioned technical aspects be improved so that resistance and structural quality of glued-laminated timber is in turn enhanced. [ABSTRACT FROM AUTHOR]

Based on the two-dimensional theory of elasticity, a new approach combining the state space method and the differential quadrature method is presented in this paper for freely vibrating laminated beams. Applying the differential quadrature method to the state space formulations along the axial direction of the beam, new state equations about state variables at discrete points are obtained. Using matrix theory, the solution can be easily derived, which can very conveniently deal with the continuity conditions. Frequency equation governing the free vibration of laminated beams is then derived and the natural frequencies are obtained. No other assumption on deformations and stresses along the thickness direction is introduced, so that the present method is efficient for laminated beams with arbitrary thickness. It also can cope with arbitrary boundary conditions without applying Saint-Venant’s principle. Numerical examples of multi-layered beams and sandwich beams are performed. Results are verified by comparing them with the published results obtained from various finite element methods and shear beam theories. [Copyright &y& Elsevier]

Three analytical one-dimensional linear elastic models of composite laminated beams are considered – composite Bernoulli-Euler beam (BE), composite Timoshenko beam (T) and multilayer sandwich beam model (MS). They are compared with results obtained via finite element method for a two-dimensional model in plane stress state. Overall system stiffness is verified with experimental data obtained for two statical configurations – three-point bending and four-point bending. The first configuration concerned 8 types of three-panel cross-laminated timber (CLT) beams accounting for various materials and thickness of timber panels as well as various materials and thickness of adhesive layer, while the second one concerned 5 types of two-panel aluminium laminated beams accounting for different thickness of adhesive layer. Simplified multilayer sandwich model is found to be in good accordance with FEA results and with experimental data, while simple BE and T models are shown to provide erroneous estimates. [ABSTRACT FROM AUTHOR]

The research at hand deals with the mechanical behavior of beam-like nanostructures. Nanobeams are assembled of multiple layers of different materials and geometry giving a layered nanobeam. To properly address experimentally noticed size effects in structures of this type, an adequate nonlocal elasticity formulation must be applied. The present model relies on the stress-driven integral methodology that effectively circumvents known deficiencies of other approaches. As a main contribution, a set of differential equations and boundary conditions governing the underlaying mechanics is proposed and applied to two benchmark examples. The obtained results show the expected stiffening nonlocal behavior exhibiting most of smaller and smaller structures and modern devices. [ABSTRACT FROM AUTHOR]

The formulation of an enriched hierarchical one-dimensional finite element suitable to analyze the rheological behavior of thick arbitrarily laminated beams is presented. The formulation is based on the Equivalent Single Layer (ESL) theory and was developed to allow the use of any high-order beam shear deformation theory (HBST) in a unified approach. A generalized Maxwell model was implemented to analyze the time-dependent behavior of the composite. The finite element employs local Lagrange and Hermitian support functions enriched with orthogonal Gram-Schmidt polynomials and is free of shear locking. The enriched macro elements can be used with very coarse meshes and the precision can be controlled without generating a new mesh. The formulation has been validated with numerical examples of symmetric and non-symmetric laminated beams using the three-dimensional finite element program PLCD. [ABSTRACT FROM AUTHOR]