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Highly flexible plate structures are subjected to various loading and edge conditions in many engineering applications, such as in the aerospace and civil industries. In this paper, the post-buckling response of rectangular plates subjected to axial and shear loadings is investigated by employing the Carrera Unified Formulation (CUF). As in previous works, only isolated plates have been considered, regardless of the effects of the stiffeners and boundary conditions imposed by the surroundings. However, in this research, different plate models are implemented, and the effects of boundary conditions imposed by the stiffeners are evaluated precisely. Comprehensive assessments are provided for the geometrically nonlinear equilibrium curves of the plate structures using the Newton–Raphson linearization method with the path-following constraint. Furthermore, the comparisons of different geometrically nonlinear assumptions according to the full Green–Lagrange nonlinear model and von Kármán nonlinear plate theory are presented. The importance of strain–displacement relationships and stiffeners' effects in the nonlinear response of plate structures is highlighted. As a result, the accuracy and effectiveness of the presented CUF-2D model are demonstrated. [ABSTRACT FROM AUTHOR]

Traditional studies that applied the viscoelastic continuum damage (VECD) model to asphalt materials were mostly accompanied by uniaxial tests whose specimen size requirement provided challenges for mixtures cored from thin asphalt layers. In this paper, an analysis methodology is presented for determining the pseudostrains and damage characteristic curves of asphalt mixtures from both the horizontal (for tension) and vertical (for compression) axes of the indirect tension (IDT) specimen simultaneously. To validate this methodology, laboratory tests were conducted on asphalt specimens in the IDT mode. Complex modulus tests were conducted at various temperatures and frequencies to allow for the construction of a dynamic modulus master curve, which, in turn, was used to obtain the relaxation modulus. In addition, constantcrosshead strength tests were conducted at two temperatures (10 and 20C) to evaluate the behavior of the asphalt specimens under growing damage. The results of the laboratory study revealed that the damage characteristic curve obtained for compression was located above its counterpart for tension. It also was found that the material showed more favorable damage characteristics at 10C than at 20C for both tension and compression and that the damage characteristic curves obeyed the time-temperature superposition principle, which is consistent with the uniaxial test results. These results indicate that the VECD model can be applied to the biaxial IDT test for characterizing tensile and compressive damage characteristic curves simultaneously. [ABSTRACT FROM AUTHOR]

Long slender elastic structures, such as railroad tracks, pipelines, and pavements, may experience buckling owing to axial compressive forces developed in them as a result of thermal or other effects, and in many cases these structures can be simplified as a beam on an elastic foundation. This paper presents an investigation of the critical buckling and postbuckling of such an elastic structure on a nonlinear foundation that has softening and restabilizing effects. The method of minimization of the total potential energy of the beam-foundation system is invoked to develop a differential equation of equilibrium and a differential equation of critical buckling (or bifurcation) of the beam. The analysis shows that critical buckling may be in a symmetric or in an antisymmetric mode, depending on the length of the beam, and when the length is extremely large, the two buckling modes are indistinguishable. The equations of the postbuckling equilibrium of the beam are highly nonlinear. To elucidate the response of the beam, a multiple-scale perturbation technique as used in modal analysis and a numerical solution based on a shooting technique are developed. It is shown that the postbuckling equilibrium of the beam has two stages after its critical buckling: a postbuckling localization stage that is unstable, and a subsequent postbuckling snaking stage characterized by a zigzag of the equilibrium configuration, and this snaking stage is dependent on the relative effects of the softening and restabilizing parameters. Comparisons of the perturbation solutions with the results of the numerical formulation show that the former semianalytical technique is accurate in the initial stages of postbuckling during which localization develops, but not in the subsequent snaking stage. The effect of the foundation parameters is also investigated in the paper. [ABSTRACT FROM AUTHOR]

Ductile fracture of metals resulting from large amplitude inelastic reverse straining has been the predominant reason for the failure of structural components under extreme loadings. This kind of fracture, characterized by only a few reverse cycles with large precrack plastic strain, is often termed ultra-low cycle fatigue (ULCF). Ductile failure of metals has recently been recognized to be a function of stress triaxiality and Lode angle parameter. In this paper, a new fracture model with full consideration of stress triaxiality and Lode angle parameter as well as the cutoff regions is proposed from the extension of its equivalence for monotonic loading in the parallel paper. The underlying mechanism and determination of the cutoff region boundary is well-defined and discussed. Additionally, the effect of load excursion on shifting the boundary of the cutoff region and the subsequent damage evolution is assessed. The nonlinearity of damage evolution is also studied and well-characterized. The developed criterion is evaluated against data extracted from a series of multistress states cyclic experimental results, and excellent correlations between the proposed model and experimental results are achieved. Comparison between the proposed model and other existing models is made, and favorable results are shown for the proposed model. The presented model can be used for predicting the potential for ULCF failure in alloys. [ABSTRACT FROM AUTHOR]

Studies of the bearing capacity of footings usually do not take into account the effect of the intermediate principal stress. In practice, the intermediate principal stress has certain influences on the strength of geomaterials (e.g., rock and soil) or concrete. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua ( FLAC) and the united strength theory (UST) to investigate the influence of the intermediate principal stress on the bearing capacity of strip and circular footings. A series of numerical solutions are presented to determine the vertical bearing capacity of strip and circular footings using an elastic-perfectly plastic constitutive model following UST and the associative flow rule. First, the bearing capacity of flexible and strip footings according to UST and other criteria are compared. Second, three bearing capacity factors (, , and ) are evaluated for strip and circular footings subjected to centered vertical loads with rough interfaces. A certain influence of the intermediate principal stress on the bearing capacity of strip and circular footings was detected based on UST and the associative flow rule. It was found that the intermediate principal stress has more influence on the bearing capacity of a strip footing than the bearing capacity of a circular footing. It was also found that the bearing capacity factor is more significantly influenced by the intermediate principal stress than are the factors and . The influence of the intermediate principal stress on three bearing capacity factors for strip and circular footings analyzed in this paper has been obtained using the elastic-perfectly plastic constitutive model based on UST. [ABSTRACT FROM AUTHOR]

It is important to generalize constitutive models from the triaxial compression state to the three-dimensional stress state for soils. However, there are some deficiencies in the existing methods, e.g., the using failure criteria method, the generalized shear stress ratio method, and the shape function approach using Lode's angle or reduced Lode's angle, for generalizing either isotropic or anisotropic constitutive models. For example, the critical state curve may be misshapen and the yield surface will appear to be curvature discontinuous if the constitutive model is generalized with the shape function approach using reduced Lode's angle. The transformed stress (TS) space has been proposed in the authors' former work based on the spatially mobilized plane (SMP), the Lade's, and the generalized nonlinear strength criterion. In this paper, the TS method based on an arbitrary failure criterion is proposed. It is a simple approach to generalize constitutive models without introducing any extra parameters. Another important work in this paper is using the TS method to generalize anisotropic models. It was found that (1) the processes for generalizing anisotropic models and isotropic models are the same, i.e., the proposed method can be directly used to generalize anisotropic models without any modification; (2) the deficiencies of other methods for generalizing constitutive models can be eliminated with the TS method (for instance, the yield surfaces appear to be curvature continuous after generalization, and the critical state curves of the generalized models are consistent with the adopted failure criteria); and (3) it is demonstrated by the comparison between the predictions and test results that the TS method is better than the shape function approach using Lode's angle in describing the soil behaviors in the general stress state. In this paper, the modified Cam clay model is taken as an example for the discussion. [ABSTRACT FROM AUTHOR]

This paper considers the case of a relatively large number of parallel columns that buckle simultaneously. The close proximity between columns results in the possibility of contact between adjacent columns as buckling proceeds, and this brings with it some interesting observations on load-carrying capacity. Some experimental results verify the theoretical development based on the versatility of high-fidelity 3D printing, but also highlights the difficulty of applying purely axial loading. The sensitive nature of initial geometric imperfections (slight lack of straightness) and load eccentricity strongly influence postbuckled contact, load-carrying capacity, and, as the number of columns is increased, a statistically based evaluation of anticipated behavior is explored and ultimately found to be unrealistic. [ABSTRACT FROM AUTHOR]

Multistable structural members are extensively used in various fields, including microelectromechanical systems (MEMS) actuation, sensing, and energy harvesting. The multistable configuration of elements can be obtained through their elastic postbuckling response. Under quasi-static excitations, the snap-through transitions of buckled elements constitute a useful tool to generate high-rate excitations for piezoelectric transducers. Yet, more efficient energy harvesting and accurate sensing requires that buckling events happen at specific loading levels. This paper investigates the control of snap-through events by using beam assemblies. Multiple bilaterally constrained beams were arranged in parallel and subjected to axial displacement–controlled loading. Experimental studies show that snap-buckling transitions can be controlled by changing the geometry of the assembled beams. An analytical model was developed to investigate the effect of system parameters on its postbuckling response. Results show that transitions are mainly controlled by the beams' thicknesses and lengths. By tuning both parameters, the system can be designed to snap at a desired axial displacement. In this paper, the assemblies were designed to transition at equally spaced axial displacements. However, other displacement combinations can be achieved. [ABSTRACT FROM AUTHOR]

The formulation of and solution to the problem of the free vibrations of a geometrically nonlinear column, supported at the loaded end by a spring with linear characteristics, are discussed in the paper. Transversal free vibrations around a rectilinear form of static equilibrium are considered in this work. The considered system was subjected to a generalized load with a force directed toward the positive pole. The boundary problem was formulated using Hamilton's principle and the straightforward expansion method. A series of numerical simulations were conducted using the mathematical model. The characteristic curve in the plane of load versus natural frequency was assigned to different parameters of the considered system. Experimental research was carried out to confirm the accuracy of the assumed mathematical model. The research relied on modal analysis and the determination of the natural frequency of the system for chosen values of an external load. [ABSTRACT FROM AUTHOR]

As a global problem for reinforced concrete structures located in a chloride and/or carbon dioxide-laden environment, reinforcing steel corrosion in concrete costs approximately $100 billion per annum worldwide for maintenance and repairs. The continual demands for greater load for infrastructure exacerbate the problem. This paper attempts to examine the whole process of longitudinal cracking in concrete structures under the combined effect of reinforcement corrosion and applied load. A model for residual stiffness of cracked concrete is derived using the concept of fracture energy. It is found that the corrosion rate is the most important single factor that affects both the time-to-surface cracking and crack width growth. The paper concludes that the developed model is one of very few theoretical models that can predict with reasonable accuracy the crack width on the surface of reinforced concrete structures under such a combined effect. The developed model can be used as a tool to assess the serviceability of corrosion-affected concrete infrastructure. Timely repairs have the potential to prolong the service life of reinforced concrete structures. [ABSTRACT FROM AUTHOR]

In this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members (0<(hmax-hmin)/hmax<1), the solution to the boundary value problem is obtained in the form of a Frobenius’ series, which is shown to converge in the interior of the domain and at the boundary if and only if 0<(hmax-hmin)/hmax<1/2. Therefore, for 1/2<=(hmax-hmin)/hmax<1 the Frobenius’ series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems. [ABSTRACT FROM AUTHOR]

For exposed subsea pipelines, lateral buckles are usually artificially triggered as an accommodation technique to release thermal expansion by providing temporary flotation with controlled spacing. With the given buoyancy load, the pipeline will be uplifted initially and will then buckle laterally under a certain thermally induced axial load, which is called the bifurcation load. Previous studies have analyzed this problem and modeled the uplifted pipeline as a fixed-fixed end beam, assuming the lateral seabed stiffness is infinite. However, the lateral seabed stiffness is usually low because the seabed is formed from soft soils. Using analytical methods, this paper investigates the buoyancy load required to trigger lateral buckles along a pipeline, considering a seabed with finite elastic stiffness, and provides suggestions for the buoyancy design with an elastic-plastic seabed model using an example of finite-element analysis. It was found that the seabed condition significantly influenced the flotation design. [ABSTRACT FROM AUTHOR]

In the present paper, stress intensity factor (SIF) analyses and fatigue-crack-growth simulations of corner cracks emanating from loaded pinholes of attachment lugs in structural assemblies are carried out for different load cases. A three-dimensional (3D) symmetric Galerkin boundary-element method (SGBEM) and FEM alternating method is developed to analyze the nonplanar growth of these surface cracks under general fatigue. The 3D SGBEM-FEM alternating method involves two very simple and coarse meshes that are independent of each other: (1) a very coarse FEM mesh to analyze the uncracked lug, and (2) a very coarse SGBEM mesh to model only the growing crack surface. By using the SGBEM-FEM alternating method, the nonplanar growth of cracks in 3D (surfaces of discontinuity) up to the failure of structures are efficiently simulated, and accurate estimations of fatigue lives are made. The accuracy and reliability of the SGBEM-FEM alternating method are verified by comparing them to other FEM solutions, as well as experimental data for fatigue-crack growth available in the open literature. The SIF calculations, crack surface evolutions, and fatigue-life estimations are all in good agreement with other detailed FEM solutions and experimental observations. It is noted that for fracture and fatigue analyses of complex 3D structures such as attachment lugs, a pure FEM requires several hundreds of thousands or even millions of elements, whereas the present 3D SGBEM-FEM alternating method requires only up to 1,000 FEM elements and SGBEM elements. It thus demonstrates that the present SGBEM-FEM alternating method, among the many Schwartz-Neumann-type alternating methods developed in the past 20-30 years are suitable for analyzing fracture and fatigue-crack propagation in complex 3D structures in a very computationally efficient manner, as well as with very low human labor costs. [ABSTRACT FROM AUTHOR]

This paper describes the wave-propagation behavior of multilayered structures and proposes an optimization procedure for designing layered stress wave attenuators. Two types of stress wave attenuators were investigated, straight and nonstraight configurations, and their wave behaviors were analyzed using the concept of longitudinal waves in rods and flexural waves in Timoshenko beam formulations. The underlying concept in this research relies on the reflection and transmission of waves at different types of discontinuities, such as boundaries, impedance mismatches, and angled joints. Therefore, the effects of these discontinuities were explored thoroughly, and their attenuation capacity was investigated using explicit formulas. These concepts then were used to develop a heuristic optimization procedure to obtain efficient layered stress wave attenuators by properly tuning the length and material of each layer. It was assumed that the stress wave attenuators were subjected to impulsive transient loadings with similar duration as that of blast waves. The results obtained demonstrate that it is very difficult to attenuate the amplitude of transient loadings with the duration of blast waves in structures using straight layered configurations having small thickness, whereas symmetric nonstraight architectures can be rather effective for achieving the desired attenuation of impulsive loadings. [ABSTRACT FROM AUTHOR]

Mathematical modeling of the nonlinear triaxial behavior and damage of such a complex material as concrete has been a long-standing challenge in which progress has been made only in gradual increments. The goal of this study is a realistic and robust material model for explicit finite-element programs for concrete structures that computes the stress tensor from the given strain tensor and some history variables. The microplane models, which use a constitutive equation in a vectorial rather than tensorial form and are semimultiscale by virtue of capturing interactions among phenomena of different orientation, can serve this goal effectively. This paper presents a new concrete microplane model, M7, which achieves this goal much better than the previous versions M1-M6 developed at Northwestern University since 1985. The basic mathematical structure of M7 is logically correlated to thermodynamic potentials for the elastic regime, the tensile and compressive damage regimes, and the frictional slip regime. Given that the volumetric-deviatoric (V-D) split of strains is inevitable for distinguishing between compression failures at low and high confinement, the key idea is to apply the V-D split only to the microplane compressive stress-strain boundaries (or strain-dependent yield limits), the sum of which is compared with the total normal stress from the microplane constitutive relation. This avoids the use of the V-D split of the elastic strains and of the tensile stress-strain boundary, which caused various troubles in M3-M6 such as excessive lateral strains and stress locking in far postpeak uniaxial extension, poor representation of unloading and loading cycles, and inability to represent high dilatancy under postpeak compression in lower-strength concretes. Moreover, the differences between high hydrostatic compression and compressive uniaxial strain are accurately captured by considering the compressive volumetric boundary as dependent on the principal strain difference. The model is verified extensively in the companion paper. [ABSTRACT FROM AUTHOR]

In many cases, an arch may have in-plane elastic end restraints provided by the connected structures or elastic foundations, which may influence the elastic lateral-torsional buckling of the arch. However, little research of the lateral-torsional buckling of arches with elastic end restraints has been reported in the open literature. This paper analytically investigates the lateral-torsional buckling of pin-ended circular arches having in-plane elastic rotational end restraints under a uniform radial load. The analytical solutions for the prebuckling behavior of such an arch show that the uniform radial load produces combined axial compressive and bending actions in the arch and that the axial compressive force produced by the uniform radial load is approximately uniform along the arch axis. It is found that the stiffness of elastic rotational end restraints has significant effects on the magnitude and distribution of the axial compressive forces and bending moments. The axial compressive force decreases with an increase of the stiffness of rotational end restraints. The analytical solution for the lateral-torsional buckling load of the arch is derived, which accounts for the effects of rotational end restraints. It is found that the effects of the stiffness of rotational end restraints on the lateral-torsional buckling load are profound. The buckling load increases with an increase of the stiffness of the end restraints. It is demonstrated by comparisons with the finite-element results that the analytical solution provides good predictions for the lateral-torsional buckling load of both shallow and deep arches having in-plane rotational end restraints. [ABSTRACT FROM AUTHOR]

The phenomenon of dynamic instability is investigated in this paper for a beam constrained at its end sections by viscoelastic (Kelvin-Voigt) translational and rotational supports, additionally affected by a certain degree of damage, to understand the influence of viscoelasticity and damage in its response under a dynamic axial load. A calculation procedure is developed to investigate the regions of dynamic instability of such a constrained beam by using an exact approach for solving the unloaded case and by applying it to the well-known solution for the boundary frequency domains of the dynamic problem. Damage is supposed to affect the elastic response of the restraints and to follow the scalar isotropic model. With respect to viscoelasticity, the time variable is treated as a parameter to account for the different timescales, according to the two transient phenomena: viscoelasticity and instability caused by an external dynamic load. The regions of dynamic instability for several configurations of the constraints are shown as three-dimensional diagrams in which the aforementioned regions contained in the plane described by the dynamic component of the periodic load and the frequency of the same load are shown here to vary in time and with respect to the level of damage of the constraints. In particular, the first three natural frequencies of the beam for each studied configuration have been taken into account. As expected, for each natural frequency and each configuration, the instability domains settle into asymptotic values ascertaining that the presence of damage in time increases the instability of the beam, since it is proved to move the domains toward lower, more easily reachable values of the external load frequency. [ABSTRACT FROM AUTHOR]

An experimental investigation on the axial load capacity of fixed-end pretwisted steel bars of rectangular solid cross sections is described in this paper. The fixed-end bar test conducted in this study includes bars with both ends griped and embedded in cylindrical slips. More than 200 specimens are considered in this study containing bars with four different cross sections, widths of 20 mm or 30 mm and thicknesses of 3 mm or 6 mm, and three different lengths of 300, 400, and 500 mm. The samples are twisted beyond their elastic limit using torque machine and then subjected to axial load using a compression MTS machine. A set of twisting angles ranges between 0 and 225° is considered for each length. Three samples are tested for each angle then the average of the results is calculated. It is proven experimentally that the permanent twists have influenced the axial strength and the static performance of the pretwisted bars. This improvement is supported by the considerable increase in the critical buckling loads of the bars for certain angles of twists. Multiple regression analysis (MRA) is also conducted using the experimental results to develop mathematical models capable of predicting the critical loads of the tested bars. Results indicate that, with a minimal processing of data, MRA could predict well the critical loads of the pretwisted bars within 99% confidence interval. [ABSTRACT FROM AUTHOR]

This paper presents a coupled approach using an artificial neural network (ANN) and the finite difference method (FDM) that has been developed to predict the distribution of axial load along fully grouted standard cable bolts in the field using laboratory pullout test data. A back-propagation training algorithm was used in ANN to determine axial loads in the cables tested in the laboratory. The ANN component of the computational model was trained using two different types of data sets. At first, the ANN was trained to predict the axial loads in a series of short cables grouted with Portland cement at a specific water-to-cement ratio and subjected to different radial confining stiffness values. Next, the ANN model was trained for an expanded case to include the influence of lateral confining stress on the distribution of axial load in the cable reinforcement. Finally, the ANN model was implemented into a widely used, FDM-based geotechnical software (FLAC). The accuracy of the ANN–FDM model is demonstrated in this paper against measured data from laboratory and field tests. The analysis approach introduced in this study is a valuable computational tool that can be used to determine the axial load distribution in long standard cable bolts, which are commonly installed to stabilize rock masses in various geotechnical, transportation, and mining applications. [ABSTRACT FROM AUTHOR]

Top tensioned strings and beams are often used in civil and marine applications. Typically these members have constant cross sections, and a pronounced, usually linear, tension variation, due to the effects of gravity. In this paper simple, approximate formulas for the natural frequency of such strings are derived, based on asymptotic techniques, while for the tensioned beam case approximate closed-form results are developed by the Wentzel–Kramers–Brillouin method. Both derivations are shown in reasonable detail. While similar work is known for a beam with varying axial tension this is believed to be the first time that a single analytic expression is developed for the full length of the beam. A simple example in which the bottom tension is only 9% of the top tension is analyzed for cases with and without bending stiffness, and the solutions have been compared to the exact solution for the string case and to the results from three finite-element programs for the beam case. The accuracy was found to be very good, even in this situation, in which the tension variation is large. [ABSTRACT FROM AUTHOR]

This paper presents the free vibration analysis of axially loaded rotating cross-ply laminated cylindrical shells with the consideration of the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to the rotation. The Ritz method is employed for the solution of this problem. Adopting the trigonometric series as the admissible displacement functions, a set of frequency characteristics equations is derived. The frequency characteristic analysis for shells of simply supported boundary conditions is examined and the frequency characteristics of various lamination schemes are investigated. The results from the present analysis are compared with the available solutions to validate its accuracy. [ABSTRACT FROM AUTHOR]

In this paper the influence of bimoment, induced by external axial loads, on the global buckling of thin-walled Z-section beams, subjected to different boundary conditions, is studied. Since bimoment varies along the beam axis, the problem of torsional and torsionalflexural buckling of thin-walled beams is defined by linear homogeneous differential equations of the second-order theory with a variable coefficient. To obtain the buckling load numerically, a finite-difference method is employed for discretizing the governing differential equations. To verify the validity and the accuracy of this study, numerical solutions are presented and compared with those calculated by simulation software. [ABSTRACT FROM AUTHOR]

In the absence of geometrical constraints, ductile fracture has been identified as the predominant mode of failure for structural elements under extreme loads, the prediction of which still represents considerable challenges. Ductile fracture of metals has only recently been recognized to be dependent on both stress triaxiality and Lode angle parameter. In this study, a new fracture model that is dependent on both stress triaxiality and Lode parameter is proposed. The developed model is proposed for the case of monotonic loading and is applicable to a wide range of stress states. The extension of the model to reverse loading, with complex loading history, is addressed in a parallel paper. The developed criterion is evaluated against data extracted from a series of multistress states monotonic experimental results for various metals, and a strong correlation is evident between the proposed model and experimental results in the entire range of the tested stress states. A detailed parametric study is conducted in order to show the effect of the model's parameters on the fracture map. Comparative study among popular ductile fracture criteria and the proposed model in their prevailing ranges is also performed. The results show that the newly developed criterion, featuring only three parameters, does not lag behind its counterparts in any stress triaxiality ranges. [ABSTRACT FROM AUTHOR]

The nonlinear analysis of shape memory alloy (SMA) hybrid composite beams under in-plane thermal load is presented in this paper. The properties of the constituents are assumed to be temperature dependent. The initial imperfection of the beam is also taken into account as an initial deflection function prior to heating. Geometrical nonlinearity is formulated in the von Karman sense. It is assumed that the kinematics of the beam obeys the Timoshenko first-order beam theory and the SMA fibers follow the one-dimensional Brinson constitutive law. These basic assumptions are inserted into the static version of the virtual displacements principle to derive the nonlinear equilibrium equations. The resulting system of equations is uncoupled and solved exactly. Closed-form expressions are presented to trace the equilibrium path of the beam as a function of the uniform heating parameter. It is shown that, in special cases, the induced tensile recovery stress of the SMA fibers may stabilize an imperfect beam that has bent during heating. [ABSTRACT FROM AUTHOR]

In this paper, the moment-curvature behavior of a steel column under constant axial loading is implemented into a computationally efficient one-dimensional finite-element approach, utilizing Timoshenko beam theory, to determine the dynamic response of steel columns subjected to blasts. Then, a new single-degree-of-freedom (SDOF) approach is provided for determining pressure impulse curves for steel columns under constant axial loading. This SDOF approach relies on the newly defined concept of the reduced resistance-deflection function to accurately simulate the effects and the global instability failure mechanism, which are both caused by the axial load. The aforementioned finite-element approach is then used to thoroughly validate the newly proposed SDOF approach for deriving pressure impulse curves. It is shown that, despite the inherent simplicity of the approach, the newly proposed SDOF approach provides accurate and reliable results. [ABSTRACT FROM AUTHOR]

Double-beam systems have found many applications in civil and mechanical engineering. Extensive works of research have been conducted on the investigation of double-beam systems in which some have studied the vibration characteristics of general double-beam systems without considering the effect of axial load, whereas others investigated the vibration and buckling of axially loaded double-beam systems with classical boundary conditions. A few previous studies have considered a general axially loaded double-beam system, but none of them have provided a general solution to calculate the critical buckling load of the system with arbitrary boundary conditions. In the present study, free vibration and buckling of an axially loaded double-beam system, which was composed of two nonidentical beams with generalized boundary conditions, were analytically studied by using the Euler–Bernoulli beam theory. A semianalytical method was proposed to calculate the natural frequencies and mode shapes of the system, and an explicit formula was derived to determine the critical buckling load of the system. Parametric investigations were performed to study the influences of the connecting stiffness of the interlayer and axial loads on the dynamic characteristics and critical buckling load of the system. Results show that the proposed method can be used for free vibration and buckling analyses of generalized double-beam systems subjected to axial loads. [ABSTRACT FROM AUTHOR]

This paper presents finite-element (FE) analysis to study the axial load capacity of pretwisted steel bars of rectangular cross sections. The FE simulations are conducted using the commercial software ABAQUS. The FE simulations include bars of 20- and 30-mm width, 3- and 6-mm thicknesses, and three different lengths of 300, 400, and 500 mm. The bar ends are gripped and embedded in cylindrical slips. A set of twisting angles, ranging between 0 and 270° with an increment of 15°, is considered for each length. Geometric imperfections as well as actual elastic-plastic behaviors have been implemented in nonlinear FE models. The column strengths, load-shortening curves as well as failure modes, were predicted. The FE model is initially verified by comparing the buckling capacity and mode of the simulated straight bars with the experiments and the AISC code. The bars are then twisted beyond their elastic limit, unloaded to remove elastic recovery, and subjected to axial displacement. FE simulations showed that the permanent twists have influenced the axial strength and the static performance of the pretwisted bars. This improvement is supported by the considerable increase in the critical buckling loads of the bars, particularly at twisting angles ranged between 15 and 90°. Two analytical models capable of predicting the critical elastic and inelastic loads were developed using the FE results and utilizing multiple regression analysis for permanent angles of twist up to 90°. Multiple regression analysis models were shown to accurately predict the buckling loads within a 90% or more confidence interval. [ABSTRACT FROM AUTHOR]

Classical shear beam theory does not consider the rotation of cross sections. This paper studies the free vibration of axially loaded shear beams carrying lumped masses at elastically supported ends where rotational motion of the cross section is taken into account. By using asymptotic analysis of the Timoshenko beam theory, a unified analytical approach for dealing with free-vibration problems of nonclassical shear beams subjected to axial compressive or tensile force according to Engesser's model is presented. A simple characteristic equation is derived for axially loaded shear beams with translational and rotational springs and with attached lumped end masses. The resulting frequency equation is compared with the classical one. A condition causing the nonclassical shear beams to collapse to the classical ones is found. Natural frequencies are evaluated and mode shapes are given explicitly. The influences of the spring coefficients, axial loads, and rotational inertia on the natural frequencies are expounded. The frequency equations of shear beams with typical ends such as free-free and free-pinned ends can be recovered from the present study as special cases. [ABSTRACT FROM AUTHOR]

In this paper, stability analysis of thick annular sector plates under mechanical and thermal loads based on third-order shear deformation theory (TSDT) is investigated. The equilibrium and stability equations based on TSDT are obtained and solved analytically by doing some mathematical manipulation. Then, for nine possible boundary conditions, the buckling load and temperature are calculated and compared with those obtained using different plate theories. As the results show, for boundary conditions that include simply supported and clamped edges, the minimum value for buckling load and temperature is predicted by first-order shear deformation theory (FSDT) and maximum value is predicted by classical plate theory (CPT). Also, for boundary conditions containing free edges, the value obtained by TSDT is larger than that obtained using CPT and FSDT for some values of thickness/length ratio. It is worthy to mention that the results obtained from CPT for boundary conditions containing free edges in a wide range of thickness/length ratio are acceptable. [ABSTRACT FROM AUTHOR]

Concrete-filled fiber-reinforced polymer (FRP) tubes (CFFTs) have been introduced as a new system for piles, columns, and poles. A simple moment connection based on direct embedment of the CFFT into concrete footings or pile caps, without using dowel-bar reinforcement, has been proposed by the authors. Robust analytical models to predict the critical embedment length (Xcr) were also developed and experimentally validated. In this paper, a comprehensive parametric study is carried out using the models developed earlier along with a newly developed closed-form model for the general case of axial loading, bending, and shear applied to the CFFT member. The parameters studied are the diameter (D), thickness (t), length outside the footing (L), and laminate structure of the FRP tube, as well as the tube-concrete interface bond strength (τmax), concrete compressive strength in the CFFT (fct′) and footing (fc′), and the magnitude and eccentricity of axial compressive or tensile loads. It was shown that increasing D, L/D, τmax, and fc′ of the footing, or the axial compression load, reduces (X/D)cr, whereas increasing t and fct′ of the CFFT, the fraction of longitudinal fibers in the tube, or the axial tension load, increases Xcr. As the axial load eccentricity increases, Xcr reduces for tension loads and increases for compression loads until both cases converge asymptotically to the same Xcr value, essentially that of pure bending. [ABSTRACT FROM AUTHOR]

In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition. [ABSTRACT FROM AUTHOR]

This paper presents a robust analytical model for a moment connection of concrete-filled fiber reinforced-polymer (FRP) tubes (CFFTs) to concrete footings. The CFFT connection is based on a simple approach of direct embedment into the footing, thereby eliminating the need for connection rebar or mechanical devices. The CFFT is externally subjected to lateral and axial loads, resembling practical applications such as piles affixed to pile caps, bridge columns, or utility poles. The model adopts the concepts of equilibrium, deformations compatibility, and nonlinear concrete stress-strain behavior. It also employs a “bond stress-slip” relation that can be obtained from simple push-through tests on some of the commercially used tubes. The model can predict the critical embedment length Xcr, which is the minimum length required to achieve material failure of the CFFT outside the footing, and bond failure inside the footing, simultaneously. If the actual embedment length is less than Xcr, bond failure occurs prematurely at a lower strength that can also be predicted by the model. The model was verified using experimental data and showed that Xcr was only 0.7 of the diameter for that case. A sensitivity parametric analysis was carried out that led to some approximations. Based on which, a simple closed-form expression was established for Xcr in the case of lateral loading only. [ABSTRACT FROM AUTHOR]

This paper considers load transfer from an axially loaded long elastic bar into a multilayered poroelastic half-space. The problem is analyzed by decomposing the bar-half-space system into an extended half-space governed by Biot’s theory of poroelasticity and a one-dimensional fictitious bar. The interaction problem is formulated in the Laplace transform domain. Vertical displacement of the bar is approximated by an exponential series with a set of arbitrary functions. The arbitrary functions are determined by using a variational method. The vertical displacement influence function of a multilayered half-space subjected to a buried uniform vertical patch load is required in the variational formulation. The required influence function is obtained by employing a previously developed exact stiffness matrix method. Time domain solutions are computed by using a numerical Laplace inversion scheme. Selected numerical results are presented to portray the influence of the bar length–radius ratio, layer configuration, poroelastic material parameters, and loading time history on the time dependent response of a bar. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the dynamic instability of different elastic-plastic beams subjected to transverse pulse load. Two types of beam dynamic instability, i.e., symmetrical and asymmetrical instabilities, are studied. The unstable responses of the elastic-plastic beams are illustrated by investigating the modal participation factors of the lowest nine vibration modes, which are determined by inverse derivation of the numerically simulated beam deflection response. The critical pulse loads for the beam symmetrical and asymmetrical instabilities are obtained with respect to different load durations. Characteristic diagrams for beams with different boundary conditions and subjected to different type pulse loads are given. The present study conforms that not only axial compressive load induces instability of slender members, but also transverse pulse load results in instability of elastic-plastic beams. [ABSTRACT FROM AUTHOR]

The behavior of Hostun RF sand on proportional strain paths at low confining pressures (20 to 100 kPa) is considered in this paper. In such paths, a constant dilation rate is imposed during shear. The usual features of pore pressure increase (contracting material) or decrease (dilating material) are here observed depending upon whether the imposed dilation rate is respectively greater or smaller than the “natural” dilation rate at failure (as measured in a drained test). Particular attention is given to the static liquefaction phenomenon, which is seen to occur for loose as well as dense sand provided the imposed dilation rate is large enough to lead to a continuous pore pressure increase during shear. Instability tests performed at low confining pressures on proportional strain paths show that the instability line is strain path dependent. It does not coincide with the peak deviator stress line in proportional strain paths tests, in general, but does coincide with the line d2W=0 (nil second increment of total work). [ABSTRACT FROM AUTHOR]

This paper addresses the development of a nonconforming axisymmetric quadrilateral variable-node element which is designated as NAQV. The NAQV element is an improved version of the axisymmetric quadrilateral variable-node (AVQ) element by adding nonconforming modes selectively. Both NAQV and AQV elements are effectively used in overcoming some problems in connecting the different layer patterns in the adaptive h refinement on a quadrilateral mesh. The use of elements with variable nodes eliminates the necessity of imposing displacement constraints on irergular (hanging) nodes in order to enforce the interelement compatibility. Therefore, the NAQV and AQV elements can be used effectively in the local mesh refinement for the axisymmetric structures which have stress concentrations. As verified through some numerical tests, the NAQV element shows excellent performance and can be used in the analysis of practical problems. [ABSTRACT FROM AUTHOR]

An accurate nonlinear hygrothermal-electro-elastic (HTEE) buckling analysis of piezoelectric fiber-reinforced composite cylindrical shells subjected to the coupled loading effects of axial compression and hydrostatic pressure was established by considering the nonuniform prebuckling effect. Nonlinear governing equations were derived based on higher-order shear deformation theory and Novozhilov's nonlinear shell theory. Accurate critical buckling stresses and pressures and explicit buckling modes for both axisymmetric and nonaxisymmetric buckling were obtained by the Galerkin method. A comparison between the new prediction and existing results is presented and excellent agreement is reported. A comprehensive parametric study of geometric parameters, end conditions, distribution patterns, and hygrothermal-electric multiphysical fields on the buckling behavior of HTEE composite cylindrical shell is also analyzed and discussed. [ABSTRACT FROM AUTHOR]

This work investigated the effective structural and functional behavior of shape-memory alloy (SMA)-based triply periodic minimal surface foams based on the Schwarz primitive (P-foams) using finite-element analysis (FEA) and numerical homogenization methods. The effect of relative density and applied temperature on the homogenized mechanical behavior of the SMA foam, including its superelasticity, and the evolution of the effective martensite volume fraction with the applied load was investigated considering axial and shear loading cases. In contrast to dense SMA, the effective martensite volume fraction in the considered foam was found to vary exponentially with the strain in the case of monotonic loading, asymptotically approaching 1 as the strain increased indefinitely. Moreover, the effective superelasticity of the SMA P-foam was found to be facilitated by decreased temperature and relative density. The onset of phase transformation for the P-foam under various loading scenarios was shown to be well approximated using an extended Hill loading surface. [ABSTRACT FROM AUTHOR]

Ramming paste is a carbonaceous porous material used in Hall-Héroult cells. It is baked in place under varying loads. To model the cell mechanical behavior during its lifespan, it was necessary to develop a constitutive law that included ramming paste creep behavior. Athreedimensional (3D) nonlinear viscoelastic-viscoplastic constitutive law was devised and developed to model the primary and secondary creep stages of baked paste. The model consisted of two parts (i.e., viscoelastic and viscoplastic). Each creep mechanism was based on the existence of a dissipative potential for the hydrostatic and deviatoric parts. Analytical solutions were presented for linear creep behavior. For the nonlinear case, the deviatoric part of the viscoelastic behavior could be obtained numerically, and all other parts analytically. Finally, model parameters were identified for paste baked and tested at different temperatures. A pattern search algorithm was used to optimize the model parameters. A comparison of the results gained from the model with experimental results showed that the devised model well represented the nonlinear viscoelastic-viscoplastic behavior of the paste baked at 250C and tested at room temperature. In addition, the model was able to predict the qualitative creep behavior of the paste baked at 350, 560, and 1,000C and tested at 300, 300, and 25C, respectively. [ABSTRACT FROM AUTHOR]

Provides information on a study which investigated the frictional damping properties of axially loaded metallic cables made from one layer of wires helically wrapped around a central wire. Linear model of simple straight strand; Modeling of interwire contact with friction; Hysteretic model of axially loaded simple straight strand; Discussion of numerical results.

Part 1. Presents information on a study which discussed a beam element for shear behavior modeling and its axial force interaction and bending of reinforced concrete beams and columns. Mechanisms of shear deformation; Features of fiber beam element; How are forces and stiffness achieved in shear deformation; Benefits of beam element solution; Summary.

Unreinforced portland-cement concrete exhibits a nonlinear relationship between applied stress and observed strain, even though the strains are at magnitudes that warrant the infinitesimal strain approximation (i.e., the norm of the displacement gradient is appropriately small). Previous efforts to model this nonlinear response of concrete express a dependence of stress on the deformation gradient (via the infinitesimal strain). However, models derived from the class of Cauchy elastic bodies do not allow a nonlinear relationship between the stress and linearized strain. Nonlinear constitutive relations that are implicit relations between the stress and a proper measure of strain, or nonlinear expressions of an appropriate measure of strain as a function of stress, lead to a logical linearization procedure wherein the linearized strain can be a nonlinear function of the stress. Using such a constitutive model, the authors accurately characterize both axial strain and circumferential strain in concrete that occurs under axial compression, up to the peak compressive stress (i.e., the failure stress). The phenomenological coefficients of the constitutive models are given predictive power via correlation with compressive strength and the air content of the ten concrete mixtures (comprising 23 concrete cylinders) that were experimentally tested under unconfined uniaxial compression. [ABSTRACT FROM AUTHOR]

The estimation of the deflection of glass panels under wind pressure is important in designing external facades of buildings.A direct method to compute the large deflections of glass panels under uniform loads such as wind pressure is presented. The model allows for derivation of the load-deflection response of square or rectangular multilayered glass panels subject to uniform loads. The boundary conditions examined are those of four-point discontinuous supports or continuous supports along the four sides. With some assumptions on bending and membrane action of flat glasses, simple analytical expressions were derived from the elastic theory. Viscoelastic effects for multilayered glass panels with a thin interlayer of PVB were taken into account by introducing a time-dependent equivalent thickness, as suggested in the literature. The mechanical model based on the structural behavior of equivalent beams is also able to account for the flexural and membrane actions. Different experimental results available in the literature and relative to flexural tests on out-of-plane loaded, large-scale panels made of laminated structural glass were utilized to validate the model. The model was compared satisfactorily with numerical results obtained by using nonlinear FEMs and with existing analytical models. In almost all cases, the comparison was satisfactory, and the proposed model provides a useful design instrument that allows one to determine the minimum thickness of multilayered glass panels while respecting maximum allowable deflection and strength criteria. [ABSTRACT FROM AUTHOR]

A generalized theory for the viscoelastic behavior of bitumen is presented. The mathematical model incorporates strain rate and temperature dependency as well as nonmonotonic loading and unloading with shape recovery. The model is phenomenological in nature. It can be calibrated using a relatively limited set of experimental parameters that are obtainable by uniaxial tests. It is shown that the mathematical model can be represented as a special nonlinear form of the Burgers model. This facilitates the derivation of numerical algorithms for solving the constitutive equations. A numerical scheme is implemented in a customized material model subroutine in a finite-element analysis (FEA) program. Simulation results are compared with the results of uniaxial and indentation tests on bitumen. [ABSTRACT FROM AUTHOR]

The use of a membrane to mitigate the extreme pressure loads on the roof of a surface-mounted prism is investigated. The fluid-structure interaction problem is solved by coupling the unsteady Navier-Stokes equation with the membrane equation. The minimum number of membrane modes required for the solution is determined through a convergence study. The results show that this passive control technique can be used to reduce the extreme pressure coefficients by approximately 25%. This reduction is explained by investigating the effects of the membrane on the flow field. [ABSTRACT FROM AUTHOR]

The present investigation deals with the nonlinear stability behavior of cross-ply laminated composite circular cylindrical shells subjected to partial and complete edge loading along with uniform external pressure. The shell is modeled using Donnell's shell theory including the first-order shear deformation theory (FSDT). The analysis uses the simply supported boundary condition (at , , ). The equations governing the nonlinear stability behavior of cylindrical shells are derived in terms of displacements () and rotations (, ). The applied partial edge loading is expressed in terms of Fourier series, and stress distributions within the cylindrical shell are determined by prebuckling analysis. The study uses multiterm Galerkin's method along with the Newton-Raphson method to solve the governing partial differential equations of the shell nonlinear stability. With the help of numerical investigations, the authors present the number of modes required for the postbuckling analysis and the influence of initial geometric imperfections on the equilibrium path in the presence of partial edge loading. They have developed a simple algorithm based on potential theory to locate the exact location of bifurcation and limit points on the equilibrium path using the bisection method. [ABSTRACT FROM AUTHOR]

Buckling and vibration characteristics of thin, symmetrically laminated, elliptical composite plates under initial in-plane edge loads and resting on Winkler-type elastic foundation are presented based on the classical laminated-plate theory. The governing equations were obtained from the variational approach and solved by the Ritz method. Extensive numerical data are provided for the first three natural frequencies as a function of in-plane load, and critical buckling loads as a function of aspect ratio for various classical edge conditions (free, clamped, and simply supported). Moreover, the effects of fiber orientation on the natural frequencies and buckling loads of laminated angle-ply plates, with stacking sequence of , were studied for chosen foundation parameter. Selected deformation buckling mode shapes are illustrated. The accuracy of calculations was checked by performing good convergence studies, and the correctness of results is established by comparison to existing results in the literature and FEM data. [ABSTRACT FROM AUTHOR]

Analytical solutions have been derived for the onset of strain localization in a broad class of unsaturated elastic-plastic porous materials based on Bishop's definition of effective stress. Critical hardening moduli for constant water content and drained loadings were found to be further gradual simplifications of the critical hardening modulus for an undrained loading. In addition, the solutions were found to reduce to the previously found solutions for fully saturated and monophasic porous materials by adequately adjusting bulk moduli of the pore fluids. This finding demonstrates that the mechanics of fully saturated and monophasic soils is the special simpler case of the mechanics of unsaturated soils. A diagnostic tool for detection of the inception of strain localization was developed by implementing the aforementioned solutions into a constitutive driver for a bounding surface plasticity model. The tool was used to further illustrate the strain localization behavior of unsaturated Bourke silt from the Bourke region of New South Wales, Australia, subjected to undrained, constant water content and drained loadings. [ABSTRACT FROM AUTHOR]

The optimum design of an additional intermediate support is investigated for raising the fundamental natural frequency of a beam or column subjected to compressive axial loadings. First, the criterion that constitutes the general characteristic equation of the optimal attachment position is explicitly provided so that an objective value of the fundamental frequency can be achieved with the minimum restraint stiffness of the intermediate support. Then, the optimum design of an intermediate support is performed for three illustrative beams of different classical boundary conditions to demonstrate the effects of the compressive axial loads. Numerical results show that the axial load can remarkably influence the support design of its optimum position and minimum stiffness when using it to increase the beam fundamental frequency. [ABSTRACT FROM AUTHOR]

The analytical treatment of normal, rocking, and torsional forced time-harmonic vibrations of a rigid circular disk in a transversely isotropic full-space is revisited. A complete discussion on frequently used contact assumptions of adhesive and smooth models is given, and the effects of different contact models on the results of each vibration mode are discussed. With the aid of appropriate dynamic Green's functions, the in-plane mode of vibration of the disk is treated analytically for the first time, and the results are expressed in terms of the solution of a Fredholm integral equation. For all four vibration modes, the relations for the contact stress, the resultant force acting on the disk, and the dimensionless compliance factor are given. The available closed-form results in the literature corresponding to the static loading are exactly recovered as the limiting cases of the current study. Furthermore, the results are verified with the special case of an isotropic full-space. By virtue of the contour integration technique as well as the residue theorem, a robust numerical integration technique is proposed to overcome the difficulties in numerical evaluation of the semiinfinite integrals appearing in the obtained Fredholm integral equations of all four modes of vibration. Some plots are provided to present the lateral, vertical, and rocking compliance factors for different transversely isotropic materials. The effects of material anisotropy on the results are also highlighted. [ABSTRACT FROM AUTHOR]