Journal of Engineering Mechanics

An isotropic plasticity model for soil is presented that introduces a number of significant modifications into an existing bounding‐surface model for clay to extend the range of application to sand, offering a simple unified treatment for soil. The paper focuses on the modeling of sands. The new features are both radial and deviatoric mapping rules to define the loading surface, a nonassociated flow rule incorporating a subelliptic plastic potential surface, and the presence of a kinked critical‐state line. Unlike many existing macroscopically based models, loose and dense states of a specific sand are not given different sets of material constants since the two states are linked by means of an “effective” normal consolidation line. Thus, for instance, sand in a dense state is considered very heavily overconsolidated in the normal mean effective‐stress range. After presenting the normalized triaxial formulation in full and discussing the calibration procedure, comparisons are made between the model's simulations and compression test data from established drained and undrained triaxial experiments up to failure on loose and dense sand over a wide range of confinements.

This study considers the periodic forced vibration of nonlinear hysteretic system. Multiharmonic steady‐state responses of a general hysteretic system adopting the Bouc‐Wen differential model, subjected to arbitrary periodic excitation, are analyzed by the Galerkin/Levenberg‐Marquardt method. The frequency/ time domain alternation and the fast Fourier transform (FFT) techniques are introduced in this frequency domain solution procedure. The frequency‐controlled and amplitude‐controlled algorithms are simultaneously formulated to obtain complete, probably multivalued, frequency response curves. This approach gives possible harmonic, superharmonic, and subharmonic responses of the Bouc‐Wen hysteretic system. The response characteristics of softening, hardening, and quasilinear hysteretic systems are studied through numerical computations. The proposed procedure is also extended to analyze the periodic vibration of degrading hysteretic system with amplitude‐dependent stiffness deterioration. In addition, a verification is given by comparing with the results obtained by a numerical integration procedure.

The present study involves two aspects associated with the steady‐state performance of the versatile Bouc‐Wen hysteretic model. First, influence of the model parameters on steady‐state responses and hysteresis loops of the single‐degree‐of‐freedom (SDOF) hysteretic system is studied by the proposed Galerkin/ Levenberg‐Marquardt (GLM) method. The dynamic behavior corresponding to five kinds of hysteresis loops is identified. Second, the steady‐state characteristics of the Bouc‐Wen hysteretic model used for representing inelastic constitutive laws are recognized. As endochronic constitutive relationship, this smooth hysteretic model may locally violate the Drucker's (or Ilyushin's) stability postulate of plasticity when the steady‐state hysteresis loops are exhibited with intermediate unloading‐reloading. The study is emphasized on the energy dissipation properties in small unloading‐reloading cycles starting at an arbitrary deformation previously reached. The extent of local violation of the Drucker's postulate under steady‐state circumstances is observed through numerical analysis. The mitigation of this violation is addressed by parameter studies.

This paper studies the effects of spatial variations of multiple earthquake ground excitations on responses of in‐plane circular incompressible arches. The responses of arches subjected to both correlated horizontal and vertical multiple excitations are calculated. The ground‐motion spatial correlations are modeled by an empirically obtained coherency‐loss function. The multiple input effects on arches having different properties are studied by varying the arch span length and material properties. The effects of multiple horizontal and vertical excitations on arch antisymmetric and symmetric modes are discussed. The responses of arches subjected to the combined horizontal and vertical excitations are also discussed. The quasi‐static responses caused by the partially correlated multiple input are calculated and their effects on the total structural responses are analyzed. Also calculated are the responses of arches subjected to the various simplified input such as the conventionally used uniform input or multiple input with phase shifts only. The effects of those assumptions on the total arch responses are studied. Some conclusions about the multiple input effects on arches are drawn.

Mixed formulation of the hp version of the finite‐element method is developed in the case of rotational shells subjected to axisymmetric and asymmetric loads. The circumferential variations of moments and displacements are expressed in terms of Fourier series expansions. Integrals of Legendre polynomials are used as shape functions for approximating the variation of deflections and moment resultants in the meridional direction. The arbitrary meridional curve of the shell is represented by Legendre polynomials. Reissner's variational principle is used in setting up the mixed matrices and vectors. Body residuums and unbalanced nodal fractions are used as error indicators. A number of rotational shell problems with steep stress gradients are considered and the efficacy of using mesh refinements in the hp mode is evaluated.

The stochastic response of a beam excited by moving loads with random amplitude is presented. The force arrivals at the beam are assumed to constitute a Poisson process of events. The input process is considered as a filtered Poisson process, as the response of a linear undamped oscillator excited by a superposition of two Poisson white noise processes. By means of the extension of the Itô's differential rule to the case of delta correlated input processes, the cumulant differential equations of every order of the response process are obtained. These equations are first‐order linear differential equations with constant forcing function and a closed‐form solution of the nonstationary stochastic response is provided. A numerical application of a bridge subjected to traffic flow has been performed by means of the proposed approach. The results are provided in terms of cumulants up to the fourth order and a comparison with those obtained by means of a Monte Carlo simulation is presented.

This paper presents a comprehensive analytical and numerical treatment of two‐dimensional dynamic response of a dissipative poroelastic half‐plane under time‐harmonic internal loads and fluid sources. General solutions for poroelastodynamic equations corresponding to Biot's theory are obtained by using Fourier integral transforms in the x‐direction. These general solutions are used to solve boundary‐value problems corresponding to vertical and horizontal loads, and fluid sources applied at a finite depth below the surface of a poroelastic half‐plane. Explicit analytical solutions corresponding to above‐boundary‐value problems are presented. The solutions for poroelastic fields of a half‐plane subjected to internal excitations are expressed in terms of semiinfinite Fourier type integrals that can only be evaluated by numerical quadrature. The integration path is free from any singularities due to the dissipative nature of the elastic waves propagating in a poroelastic medium, and the Fourier integrals are evaluated by using an adaptive version of the trapezoidal rule. The accuracy of present numerical solutions are confirmed by comparison with existing solutions for ideal elasticity and poroelasticity. Selected numerical results are presented to portray the influence of the frequency of excitation, poroelastic material properties and types of loadings on the dynamic response of a poroelastic half‐plane. Green's functions presented in this paper can be used to solve a variety of elastodynamic boundary‐value problems and as the kernel functions in the boundary integral equation method.

A method for computing probabilities of failure of structural components and systems is proposed. The approach is based on a radial‐space division technique in conjunction with automatic generation of unit centerline vectors. Based on this technique, the standard normal space is divided into active and passive subdomains. The probability contribution of each active subdomain to the total probability of failure is estimated by approximating the actual limit‐state hyper‐surface with a hypersphere segment centered on the actual hypersurface. The proposed method can solve with relatively high accuracy both component and system reliability problems involving nonlinearities and multiple extremum points of the probability density on the limit‐state hypersurface. A number of numerical examples involving linear and nonlinear performance functions of components and systems are presented. The results are in good agreement with exact solutions, probability bounds, multinormal approximations, and/or Monte Carlo simulations.

In the present paper we address the question of whether localized failure due to elastoplastic bifurcation can be captured within the fixed‐mesh approach. To this end, the theoretical framework of localization analysis of elastoplastic solids is revisited, and examples of weak discontinuities are presented for an elastic perfectly plastic Huber‐Mises material with focus on plane stress. The prominent role of finite‐element design (standard displacement versus enriched formulation) and orientation (aligned versus misaligned geometry) is demonstrated first at the element level, when a single element is uniformly stretched to the yield limit and subjected to localization at all Gauss points. The weak localization test probes the directional properties of the finite element when spatial discontinuities in the strain field are to be captured. This element test is subsequently extended to the structural level and is illustrated with the eigenanalysis of a flat steel bar that is uniformly stretched to the yield limit in uniaxial tension. The effect of mesh alignment is examined with a layer of finite elements that is gradually rotated towards the spatial discontinuity of elastoplastic bifurcation analysis.

The main objective of the present research is to develop a rational model to predict the elastic modulus of fiber‐reinforced, quasibrittle matrices such as cement and ceramic matrices. Generally, the elastic modulus of a two‐phase composite is predicted from the mechanical properties and proportions of the two components. Here a new approach is introduced in which the interfacial layer surrounding the fiber, viewed as a third phase with zero volume, is modeled as an imperfect bond with mechanical properties similar to or different from the surrounding matrix. Based on this assumption, new upper‐ and lower‐bound solutions for the elastic modulus of aligned short‐fiber composites are analytically derived assuming either a uniform applied stress or a uniform applied strain; the two solutions are combined to achieve an average modulus of aligned short‐fiber composite. The usual lower‐bound solution for the modulus of elasticity of a fiber composite with the fiber normal to the axis of loading is modified to account for matrix porosity as affected by the presence of fibers. It is finally suggested that the elastic modulus of random short‐fiber composites be taken as an average of the values obtained for the aligned and normal fiber values.