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A novel quadrature element for performing plane stress elastoplastic analysis is introduced in this paper. Differing from the popular finite-element method, the quadrature-element method (QEM) first evaluates the integration in the weak-form statement of the problem by an integral quadrature scheme, and then approximates the differentiation at the discrete integration points by the differential quadrature analog. As a result, the QEM avoids construction of shape functions and obtains higher-order elements easily by just increasing the order of integration. The usage of higher-order elements leads to more accurate solutions and coarser geometric meshes without detriment to the computational scale because the number of degrees of freedom is maintained. In addition, the element nodes in the QEM are the same as the integration points that possess physical meanings such as strains and stresses, which is crucial in the elastoplastic analysis for determining the elastic/plastic state of the nodes. A straightforward elastoplastic quadrature-element formulation is developed. Incremental-iterative and return mapping solution schemes are adopted to implement the quadrature element for the elastoplastic analysis. Numerical examples are presented to demonstrate the effectiveness and high accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

Wave propagation in elastic solids is analyzed by a space-time discontinuous Galerkin quadrature element method. First, the space-time quadrature element is conveniently formulated based on the space-time discontinuous Galerkin formulation. This method treats both the spatial and temporal domains in a unified manner, enabling it to handle not only structured space-time meshes but also unstructured ones. It effectively captures discontinuities or sharp gradients in the solution. To transform the formulation into a system of algebraic equations, the Gauss-Lobatto quadrature rule and the differential quadrature analog are utilized. High-order elements are constructed simply by increasing the order of integration and differentiation without the laborious construction of shape functions. Then, dispersion analysis is conducted for one- and two-dimensional elements. The analysis reveals that as the Courant number decreases, the total dispersion error monotonically converges to the spatial dispersion error, which can be reduced by increasing the element order. Additionally, high-order elements nearly eliminate numerical anisotropy in different directions. Finally, several numerical examples of elastic wave propagation validate the method's effectiveness and high accuracy. [ABSTRACT FROM AUTHOR]

Yield-line theory is accepted as a method for the design of reinforced concrete structures in many codes. Many guidelines have been provided to find the most possible failure mechanism and the lowest upper solution. Slabs equally reinforced in two normal directions, which fail in a fan mechanism under concentrated load, have been studied and ultimate bearing capacity for this kind of slab has been presented. Up to date, the ultimate bearing capacity of unequally reinforced slabs under concentrated load, so-called orthotropic slabs, has not been solved. This paper made an effort to solve this problem. Expression for ultimate bearing capacity of orthotropic reinforced concrete slab under concentrated load is derived in a polar system according to the principle of virtual works. On the basis of the variation principle, the equation of negative yield line is established, which gives the lowest upper solution. The equation of negative yield line for orthotropic reinforced concrete slab under concentrated load is found to be a symmetric and closed curve with determinate shape but indeterminate radius. The ultimate bearing capacity is dominated by bending or punching shear of slab, depending on the depth and the reinforcement ratio of the slab. [ABSTRACT FROM AUTHOR]

Carbon nanotube reinforced composites offer enhancements in fracture properties since the reinforcing nanotubes provide a bridging mechanism to resist crack growth. In this paper, a study of crack bridging by nanotubes in a nanotube-reinforced polymer composite is presented. The process of crack bridging is idealized as normal pullout of the participating nanotubes from the polymer matrix. The resistance to crack growth due to bridging is taken as the aggregate of the resistance offered by all the nanotubes, ignoring any interaction among the nanotubes themselves. The pullout of a single nanotube from the polymer matrix is modeled as an axisymmetric, nearly one-dimensional problem. This is done by assuming that fracture along the nanotube–polymer interface is dominated by shear openings, and that the nanotube behaves as a rigid body. When the polymer is a linear elastic material, the force–displacement relation for pullout is obtained as a function of dimensionless variables representing the interfacial fracture energy and the pullout length scale. Applying the correspondence principle, the elastic results are extended to the case where the polymer is a linear viscoelastic material with a single relaxation time. The force–displacement relation is then a function of the viscoelastic properties of the polymer and the pullout velocity as well. Using these results, the apparent enhancement in the fracture energy of the composite is obtained. This provides a guideline to design these composites for desired fracture properties in terms of the interfacial strength of the nanotube–polymer interface and the volume fraction of the nanotubes. Results of numerical simulations of nanotube pullout are compared to the predictions of the analytical model. [ABSTRACT FROM AUTHOR]

The linear elastic analysis of in-plane and out-of-plane loaded masonry walls is still significant under service loads and is required by codes of practice, therefore the knowledge of the homogenized mechanical properties of masonry is of relevant interest. The aim of this paper is to discuss the problem of the out-of-plane loaded masonry walls in detail and to assess the accuracy and reliability of different homogenization approaches presented in the technical literature, with particular interest in recent explicit formulas obtained through an asymptotic model (as reported by Cecchi and Sab in 2002). Several meaningful comparisons are presented for different types of new and historical masonry structures currently employed in Italy. The validation of the analytical models is carried out by means of a three-dimensional (3D) finite-element (FE) out-of-plane homogenization. A final structural comparison among analytical models, FE out-of-plane homogenization, and a computationally expensive heterogeneous 3D FE model is discussed for a simply supported square panel laterally loaded. [ABSTRACT FROM AUTHOR]

Deals with the issues concerning the symmetry of the tangent stiffness matrix for spatial elastic beam elements and frames. Asymmetry of element tangent stiffness matrices; Space dome example; Importance of the nature of internal bending moments.

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]

The accuracy of the optimally blended spectral-element method for wave propagation in a homogeneous transversely isotropic elastic medium was investigated. A nonstandard quadrature rule obtained by combining Gauss quadrature rule and Gauss–Lobatto–Legendre quadrature rule was used to compute elementary matrixes. The mass and stiffness matrixes were represented as the triple tensor-product of elementary matrixes as second-order tensors. The solution of the eigenvalue problem representing the semidiscretized version of elastic wave equation for plane harmonic wave propagation was obtained using the Rayleigh quotient approximation technique. The resulting eigenvalues subsequently were used to estimate the phase and group velocity of three bulk waves. The variations of the errors in these velocities of the bulk waves with the number of grid points per wavelength were depicted graphically. These variations were shown for different polynomial orders and various angles of deviation from the symmetry axis. The effect of a change in the order of time discretization on error variation also was shown. The solution obtained by the optimally blended spectral-element method was found to be more accurate than that from the classical spectral-element method for low-order polynomials. The improvement in solution accuracy was demonstrated through dispersion analysis. [ABSTRACT FROM AUTHOR]

In general, the response of a system coupled with a vibration absorber is obtained by incorporating only elastic analysis under different loading conditions. However, the elastoplastic analysis is carried out for blast-resistant structures such as monolithic and composite sandwich panels. The present study delineates the nonlinear elastoplastic analysis of two steel plates sandwiched with mechanical elements (spring-dashpot-inerter)–based dynamic vibration absorber (DVA) subjected to a uniformly distributed blast load on one of its surfaces. The assembly of two steel plates interconnected with spring–dashpot elements is modeled as an equivalent two-degree-of-freedom (2DOF) system incorporating nonlinear elastoplastic material properties. The equivalent mass, resistance, and load are computed using transformation factors. The displacement response of the equivalent 2DOF system is compared with a finite element (FE)–based numerical model of the assembly. The influence of inserting an inerter between two plates is investigated by considering three configurations of dynamic vibration absorber and varying certain parameters such as stiffness, damping coefficient, and inertance. It was observed that in terms of deformation and force transmitted to the back plate, the configuration of the inerter in series with a dashpot element performed better than the simple spring–dashpot arrangement. The internal resistance of the front plate governs the performance of different configurations of DVA, which was demonstrated by changing the thicknesses of the plates. The influence of nonlinearity on the dynamics of the system was investigated. [ABSTRACT FROM AUTHOR]

A constitutive model based on hyperelasticity is proposed to capture the resilient (elastic) behavior of granular materials. Resilient behavior is a widely accepted idealization of the response of unbound granular layers of pavements, following shakedown. The coupling property of the proposed model accounts for shear dilatancy and pressure-dependent behavior of the granular materials. The model is calibrated using triaxial resilient test data obtained from the literature. A statistical comparison is made between the predictions of the proposed model and a few of the prominent models of resilient response. The proposed coupled hyperelastic model yields a significantly better fit to the experimental data. It also offers a computational efficiency when implemented in a classical nonlinear finite elemental framework. [ABSTRACT FROM AUTHOR]

Presents information on a study that discussed the generalized bending of a large plate with a circular elastic inclusion. Overview of Reissner's theory of bending of elastic plates; Details on plate differential equations in polar coordinates; Solutions.

Presents a study which proposed a combined stiffness matrices of an elastic foundation and shell element to simplify the analysis of an asymmetric tank on an elastic foundation subjected to a non-axisymmetric load. Shell stiffness formulation of axisymmetric shell element under nonaxisymmetric load; Transfer matrix method used; Numerical example.

In this paper, the finite deformations of laminated rubber bearings are analyzed by employing a one-dimensional model consistent with the framework of three-dimensional finite elasticity. In such a context, the equilibrium deformations are governed by a nonlinear system of differential equations involving unknown scalar functions of the axial coordinate. It is shown how to obtain the pure bending and the simple extension of the bearing as exact solutions of the equilibrium problem. Moreover, for each of these two cases, the corresponding relation between the significant kinematical parameter and the load sustaining the deformation is established. Small deformations of the bearing superimposed on a finite compression are also considered. In particular, stability of the finitely stressed state and structural response for superimposed small shear and bending are investigated. [ABSTRACT FROM AUTHOR]

In this work, a simple and effective finite element-boundary integral equation (FE-BIE) approach for the static analysis of elastic beams and frames in bilateral frictionless contact with an elastic half-plane is extended to include the case of material nonlinearity. Elastic-perfectly plastic behavior is assumed for the supported structure and in particular for the foundation beam. Potential plastic hinges are placed along structural elements and modeled as nonlinear semirigid connections characterized by a rigid-plastic moment-rotation relationship. Incremental, load-controlled analyses of beams and frames resting on an elastic half-plane with several potential plastic hinges along the structural members are then performed. Numerical examples illustrate the effectiveness of the model in determining the stiffness degradation of the structure for increasing loads, together with ultimate loads and collapse mechanisms. [ABSTRACT FROM AUTHOR]

The analysis of microheterogeneous materials exhibiting eigenstressed and/or eigenstrained phases requires an estimation of eigenstrain influence tensors. Within the framework of continuum micromechanics, we here derive these tensors from extended Eshelby-Laws matrix-inclusion problems, considering, as a new feature, an auxiliary matrix eigenstress. The auxiliary matrix eigenstress is a function of all phase eigenstresses and, hence, accounts for eigenstress interaction. If all material phases are associated with one and the same Hill tensor, the proposed method degenerates to the well-accepted transformation field analysis. Hence, the proposed concept can be interpreted as an extension of the transformation field analysis toward consideration of arbitrarily many Hill tensors, i.e., as an extension toward heterogeneous elastic media comprising inclusion phases with an arbitrary ellipsoidal shape and with arbitrary spatial orientation. This is of particular interest when studying heterogeneous media consisting of constituents with nonspherical phase shapes, e.g., cement-based materials including concrete, or bone. As for polycrystals studied by means of the self-consistent scheme, the auxiliary matrix eigenstress turns out to be equal to the eigenstresses homogenized over the representative volume element (RVE), which is analogous to the self-consistent assumption that the auxiliary stiffness is the average stiffness of the RVE. The proposed method opens the door for micromechanics-based modeling of a great variety of composite phase behaviors characterized by eigenstresses or eigenstrains, e.g., thermoelasticity, poroelasticity, drying-shrinkage, as well as general forms of inelastic behavior, damage, fatigue, and fracture. [ABSTRACT FROM AUTHOR]

We present and compare two different methods for numerically solving boundary value problems of gradient elasticity. The first method is based on a finite-element discretization using the displacement formulation, where elements that guarantee continuity of strains (i.e., C1 interpolation) are needed. Two such elements are presented and shown to converge: a triangle with straight edges and an isoparametric quadrilateral. The second method is based on a finite-element discretization of Mindlin’s elasticity with microstructure, of which gradient elasticity is a special case. Two isoparametric elements are presented, a triangle and a quadrilateral, interpolating the displacement and microdeformation fields. It is shown that, using an appropriate selection of material parameters, they can provide approximate solutions to boundary value problems of gradient elasticity. Benchmark problems are solved using both methods, to assess their relative merits and shortcomings in terms of accuracy, simplicity and computational efficiency. C1 interpolation is shown to give generally superior results, although the approximate solutions obtained by elasticity with microstructure are also shown to be of very good quality. [ABSTRACT FROM AUTHOR]

A computational analysis method is presented to investigate the potential energy of fully nonlinear framed structures and other energy characteristics due to earthquake ground motions. The overall potential energy is directly related to the stiffness of the structure, and it consists of three components in a fully nonlinear system: (1) strain energy representing the storing energy that is associated with the linear elastic portion of the structural response; (2) higher-order energy representing the energy associated with the geometric nonlinear effect of the overall structural response, which is derived from finite element method; and (3) plastic energy representing the energy dissipated by material inelasticity of the structure, and it is being derived analytically. The merit of proposed analysis method lies in the uncoupling of geometric nonlinearity and material inelasticity effects before solving for the equation of motion, and this leads directly to the analytical representations of each energy form. Both plastic energy and higher-order energy based on single-degree-of-freedom system are studied in detail to demonstrate the beauty of the proposed analysis method. In addition, a method of generating energy density spectra is also proposed, which is useful to enhance the understanding energy characteristics in seismic analysis. Finally, a five-story frame is used as a numerical example to illustrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

A theoretical approach to determine the tilting stiffness of a rectangular elastic layer bonded between two rigid plates is presented. On the basis of two kinematics assumptions, the governing equation for the mean pressure is derived from the equilibrium equations. Using the approximate shear boundary condition, the mean pressure is solved and the tilting stiffness of the bonded rectangular layer is then established in an explicit single-series form. Whereas the finite element method can be applied to calculate the stiffness, the series solution provides a convenient way for parametric studies. Through the obtained pressure expressions, the horizontal displacements are derived from the corresponding equilibrium equations, from which the shear traction on the bonding surface can be found. The error of using the approximate shear boundary condition is negligible for the tilting stiffness, but becomes significant for the horizontal displacements and bonding shear stresses near the edges of the rectangular layers. [ABSTRACT FROM AUTHOR]

A constitutive law for fiber-reinforced concrete materials consisting of an elastic perfectly plastic model for compression and an elastic-constant postpeak response for tension is presented. The material parameters are described by using Young’s modulus and first cracking strain in addition to four nondimensional parameters to define postpeak tensile strength, compressive strength, and ultimate strain levels in tension and compression. The closed-form solutions for moment-curvature response are derived and normalized with respect to their values at the cracking moment. Further simplification of the moment-curvature response to a bilinear model, and the use of the moment-area method results in another set of closed-form solutions to calculate midspan deflection of a beam under three- and four-point bending tests. Model simulations are correlated with a variety of test results available in literature. The simulation of a three- and four-point bending test reveals that the direct use of uniaxial tensile response underpredicts the flexural response. [ABSTRACT FROM AUTHOR]

The force analogy method which has been proven to be very efficient in dynamic analysis of inelastic structures is here introduced for the first time into the field of stochastic dynamic analysis for inelastic structures. This stochastic force analogy method (SFAM) maintains the advantage of the high efficiency in the numerical computation of the force analogy method in dynamic analysis. According to the SFAM, the variance covariance functions of inelastic dynamic responses, such as displacement, velocity, inelastic displacement of the entire moment-resisting framed structures, and plastic rotation at individual plastic hinge location, can be produced for structures subject to random excitation. Detailed theoretical development of the SFAM is derived, and a simple numerical example using a single degree of freedom system is presented. The reasonability of the proposed method is validated by the good agreement between the results from the proposed SFAM and those obtained from Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

An improved form of a recently derived energetic-statistical formula for size effect on the strength of quasibrittle structures failing at crack initiation is presented and exploited to perform stochastic structural analysis without the burden of stochastic nonlinear finite-element simulations. The characteristic length for the statistical term in this formula is deduced by considering the limiting case of the energetic part of size effect for a vanishing thickness of the boundary layer of cracking. A simple elastic analysis of stress field provides the large-size asymptotic deterministic strength, and also allows evaluating the Weibull probability integral which yields the mean strength according to the purely statistical Weibull theory. A deterministic plastic limit analysis of an elastic body with a through-crack imagined to be filled by a perfectly plastic “glue” is used to obtain the small-size asymptote of size effect. Deterministic nonlinear fracture simulations of several scaled structures with commercial code ATENA (based on the crack band model) suffice to calibrate the deterministic part of size effect. On this basis, one can calibrate the energetic-statistical size effect formula, giving the mean strength for any size of geometrically scaled structures. Stochastic two-dimensional nonlinear simulations of the failure of Malpasset Dam demonstrate good agreement with the calibrated formula and the need to consider in dam design both the deterministic and statistical aspects of size effect. The mean tolerable displacement of the abutment of this arch dam is shown to have been approximately one half of the value indicated by the classical deterministic local analysis based on material strength. [ABSTRACT FROM AUTHOR]

Initial imperfections of columns are often assumed to have the shape of the first buckling mode. In this technical note, the imperfection has the shape of the second mode. An elastica analysis is performed, and numerical results are obtained for two cases with the use of a shooting method. For the example of a pinned column, bifurcation occurs at a load slightly higher than the critical load for the perfect system. With further increase in load, the deflection changes smoothly from an antisymmetric shape with one node to a shape with no nodes. For the cantilevered-column example, a limit point occurs just beyond the critical load for the perfect system, and the equilibrium shape jumps from one state to another. As the load is increased further, the deflection passes smoothly to the other side of the column and loses its inflection point. [ABSTRACT FROM AUTHOR]

Error propagation analysis of an implicit pseudodynamic algorithm has been developed for linear elastic systems. However, these error propagation results might not be applicable to nonlinear systems. Since the pseudodynamic testing method aims at investigating the nonlinear behavior of a seismically loaded structure it is important to perform the error propagation analysis of the implicit pseudodynamic algorithm for nonlinear systems. A technique to conduct the nonlinear error propagation analysis of an implicit pseudodynamic algorithm is constructed and is illustrated by analyzing the constant average acceleration method. Theoretical results reveal that the numerical and error propagation properties for nonlinear systems are generally inherited from those of linear elastic systems although some properties are affected by the step degree of nonlinearity. It is verified that the most important property of unconditional stability is preserved for nonlinear systems for a complete pseudodynamic test procedure even if the convergence error is present. It is concluded that error propagation for the improved implementation is superior to that of the direct implementation and is consistent with that developed for linear elastic systems. [ABSTRACT FROM AUTHOR]

The aim of this work is the study of masonry behavior by means of a homogenized model in several perturbative parameters. The difficulty in the mechanical modeling of masonry depends on its discrete character, as such, masonry is composed of blocks between which mortar is laid. Moreover, the building procedure leads to head and bed joint stiffnesses which may be different. Within the limits of the hypotheses of the model, the capacity of the homogenization method to grasp these features was investigated in this study. The homogenization model proposes a constitutive identification between the masonry and a standard continuum. Moreover, the introduction of two perturbative parameters enables one to grasp the influence of variations in the relative thickness of the joints with respect to the dimensions of the blocks, and of variations in the deformability of the latter on the constitutive homogenized functions. On a structural level, for a sample case, the capacity of the homogenized continuous model to describe the characteristic aspects of the behavior of masonry has been investigated by comparison with a discrete model. [ABSTRACT FROM AUTHOR]

Presents a study which analyzed the overall collapse of the World Trade Center buildings in New York City on September 11, 2001. Elastic dynamic analysis; Analysis of inelastic energy dissipation; Conclusions.

Presents a study which derived a set of equations for linear elastic analysis of tall rigid-jointed frames loaded at the joints. Description of the problem; Characteristic states and difference equations for displacements; Description of the piecewise uniform frame; Solution of boundary conditions for uniform frame.

Presents information on a study which examined the asymmetric low-velocity impact of a finite layer of elastically supported beams. Dynamic beam theory solution; Static beam theory solution; Conclusions.

Focuses on a study which analyzed the buckling of a heavy elastic column loaded by a concentrated force at the top. Formulation of boundary conditions; Numerical results of critical load parameters; Critical load parameters for Bernoulli-Euler column.

Presents information on a study which examined the problem of a 1D elastic distributed system coupled with a moving linear oscillator. Problem formulation; General solution procedures; Numerical method; Numerical results.

Presents information on a study which focused on a method based on the Mindlin-Deresiewicz displacement field solution for obtaining the force-displacement relationship for a contact between two elastically similar bodies. Contact force-displacement relations; Conclusions.

The authors presented a solution of beams on nonuniform elastic foundations based on Green's function. Although the formulation is impeccable from a mathematical point of view, it is conducted in the opposite way of the finite element approach, which constitutes the most widely used procedure to obtain complex structural solutions. In order to take advantage of existing software without changing the stiffness method coded in most structural programs it is preferable to develop the stiffness matrix contribution of the continuous elastic foundation provided by a Winkler type of soil with variable modulus along the beam element.

The authors thank professor Deschapelles for his discussion, which informs readers about other and more detailed approaches to the subject of beams on elastic foundations. A comprehensive listing of references concerning this well-developed topic was obviously beyond the scope of a brief note. It may be worthwhile to point out that the methodology employed by these authors, namely, a Green's functions formulation, can be applied under suitable circumstances to a wide range of structural geometries.