Journal of Engineering Mechanics

This paper contains the description of an adaptive calculation scheme for nonlinear (elastoplastic) finite element (FE) analysis. The underlying error estimator accounts for the error in the elastic regime as well as for the one arising from plastic loading. It is based on the stress recovery scheme proposed by Zienkiewicz and Zhu in 1992. The adaptation of the FE mesh is performed by means of the h-version of mesh refinement. The advancing front method is employed for remeshing. Before restart of the analysis after mesh refinement, the transfer of variables from the old to the new mesh must be performed. Unlike as for commonly used transfer schemes, the presented mode of transfer employs stresses and displacements for the evaluation of the state variables for the new mesh. All ingredients of the adaptive calculation scheme (i.e., error estimation, mesh generation, and the transfer of variables) are extended for application to the layer concept and to curved surfaces. Both extensions are necessary for adaptive analyses of reinforced concrete (RC) shells (see companion paper).

This paper deals with the application of an adaptive calculation scheme to ultimate load analyses of reinforced concrete (RC) plates and shells. The influence of the user-prescribed accuracy on the numerical results, especially on the ultimate load, is investigated. Three examples are considered: (1) a shear wall panel; (2) a circular plate; and (3) an RC cooling tower subjected to dead load and wind load. In addition to adaptive finite element (FE) analyses, single-mesh calculations on the basis of uniformly refined meshes are performed.

Higher-order homogenization of an initial/boundary-value problem with oscillatory coefficients in one dimension is studied. Validity range and limitations of the theory are established. We show that the higher terms are necessary to account for wave dispersion but introduce secular terms that grow unbounded in time. Numerical procedures requiring superconvergent recovery of higher-order derivatives are described.

Cone-cylinder intersections are used in many shell structures including tanks, silos, pressure vessels, and piping, and internal pressurization is often an important loading condition. For the intersection of the large end of a cone and a cylinder, internal pressurization causes large circumferential compressive stresses in the intersection. These stresses can lead to failure of the intersection by either axisymmetric collapse or nonsymmetric buckling. This paper presents the first carefully conducted experimental study on these intersections. Following a brief summary of the experimental setup, the experimental results are presented together with finite-element predictions. Both experimental and numerical results show that the postbuckling behavior of internally pressurized cone-cylinder intersections is stable, but the postbuckling growth of deformations and associated strains can cause rupture failure at welds. The experimental buckling load can be closely approximated by the nonlinear bifurcation load of the perfect geometry, indicating that the effect of initial imperfections is very limited.

To simulate brittle rocks, a mixture of sand, plaster of paris, and water was used as a model material. Thin galvanized sheets were used to create joints in blocks made out of the model material. To investigate the failure modes and strength, 30 × 12.5 × 8.6 cm jointed model material blocks having different joint geometry configurations were subjected to uniaxial compressive loading. Results indicated three failure modes: (1) tensile failure through intact material; (2) combined shear and tensile failure or only shear failure on joints; and (3) mixed failure of the above two modes depending on the joint geometry. The fracture tensor component in a certain direction quantifies the directional effect of the joint geometry, including number of fracture sets, fracture density, and probability distributions for size and orientation of these fracture sets. Results obtained from the experiments were used to develop a strongly nonlinear relation between the fracture tensor component and the jointed block strength. The laboratory experiments conducted on jointed model material blocks were simulated numerically using the Universal Distinct Element Code (UDEC). With careful selection of suitable material constitutive models for intact model material and model joints, and accurate estimation and calibration of mechanical parameters of the constitutive models through a combination of laboratory testing and numerical simulations of the intact model material and model joints separately, it was possible to obtain a good agreement between the laboratory experimental and distinct element numerical results.

A new set of equations for linear elastic analysis of tall rigid-jointed frames loaded at the joints is derived. These are simultaneous difference equations involving four local kinematic quantities, with story level as the single independent variable. They may be solved explicitly for certain classes of frames of practical interest. The solution is nontrivial and employs techniques that are of general interest in the kinematic and static analysis of periodic elastic structures. Application to an eight-bay, 40-story frame under lateral loading yields topmost story drift within 6% of the exact finite-element solution. The solution represents a vertex of the subspace of kinematically admissible states. Thus, it may be used in the hypercircle formulas of Prager and Synge to obtain bounds on displacement and stress, or as a stand-alone analysis and design tool for tall planar frames. The current solution may be implemented easily in commercial spreadsheet software, offering a significant advantage to the structural analyst.

Estimates of ground deformations and liner stresses in a tunnel are usually obtained from empirical correlations or from past experience on similar tunnels. These correlations account for only a few of the significant factors, and extrapolation to other cases is questionable because similitude conditions are not generally fulfilled. In this paper, complete analytical solutions for a shallow tunnel in saturated ground are obtained. Two different drainage conditions have been considered: full drainage at the ground-liner interface, and no drainage. The solutions cover different construction processes and soil conditions: (1) dry ground; (2) saturated ground with and without air pressure; (3) with and without a gap between the ground and the liner; and (4) applicability for short term analysis (i.e., undrained excavation and liner installation) and for long term analysis. Since the ground and the liner are assumed to behave elastically, the solutions obtained are restricted to cases where ground deformations are small, such as stiff clays and rocks, or when the excavation method prevents large deformations of the ground.

The present paper aims at studying the effect of microcracks opening on the diffusion and advection processes in a saturated porous medium. It is based on a micromechanical homogenization approach. The effects of porosity and microcracks are addressed in microscopic and mesoscopic levels to yield estimates of the effective diffusion and permeability tensors. Closed-form expressions and numerical results are obtained. For instance, the effect of the crack density parameter ε on the overall properties is discussed: (1) for a given value of ε, the maximum overall diffusion coefficient decreases for increasing values of crack radius; and (2) for large crack opening, the overall permeability is mainly controlled by ε and almost independent of the applied stress and the crack radius.

Several methods have been proposed for estimating the actual tensile forces in metallic tie-rods inserted into the masonry arches and vaults of historic buildings. Static and dynamic methods based on the experimental measurement of the vertical displacements caused by concentrated loads, accelerations, and the fundamental frequencies and periods of free vibrations have been applied to arrive at a more precise evaluation of the axial tensile forces acting on the tie-rod under examination. Each of these methods, with its corresponding experimental procedure, presents different advantages and disadvantages with regard to operating procedures, equipment requirements, and accuracy range in the determination of tie-rod stress. In this paper the writers propose a simple method and experimental procedure based on a single static test. The reference structural system consists of a bending moment-resistant tie beam with unknown restraint conditions at its ends. Therefore, the proposed method does not require any assumptions when modeling the rod's extremities, nor does it discount the increase in pull induced by the transverse load as irrelevant. The relevant experimental data are represented by three vertical displacements under a concentrated load and the strain variations measured in three sections of the rod. The reliability of the method has been verified through laboratory tests using tie-rods set within a sufficiently stiff metal framework in which the tension is known through continuous monitoring by means of a load cell. The correlation of the measurements with the actual tensile strength was checked; laboratory tests show good agreement between the analytical estimates and experimental measurements.

In this paper, a simulation methodology is proposed to generate sample functions of a stationary, non-Gaussian stochastic process with prescribed spectral density function and prescribed marginal probability distribution. The proposed methodology is a modified version of the Yamazaki and Shinozuka iterative algorithm that has certain difficulties matching the prescribed marginal probability distribution. Although these difficulties are usually sufficiently small when simulating non-Gaussian stochastic processes with slightly skewed marginal probability distributions, they become more pronounced for highly skewed probability distributions (especially at the tails of such distributions). Two major modifications are introduced in the original Yamazaki and Shinozuka iterative algorithm to ensure a practically perfect match of the prescribed marginal probability distribution regardless of the skewness of the distribution considered. First, since the underlying “Gaussian” stochastic process from which the desired non-Gaussian process is obtained as a translation process becomes non-Gaussian after the first iteration, the empirical (non-Gaussian) marginal probability distribution of the underlying stochastic process is calculated at each iteration. This empirical non-Gaussian distribution is then used instead of the Gaussian to perform the nonlinear mapping of the underlying stochastic process to the desired non-Gaussian process. This modification ensures that at the end of the iterative scheme every generated non-Gaussian sample function will have the exact prescribed non-Gaussian marginal probability distribution. Second, before the start of the iterative scheme, a procedure named “spectral preconditioning” is carried out to check the compatibility between the prescribed spectral density function and prescribed marginal probability distribution. If these two quantities are found to be incompatible, then the spectral density function can be slightly modified to make it compatible with the prescribed marginal probability distribution. Finally, numerical examples (including a stochastic process with a highly skewed marginal probability distribution) are provided to demonstrate the capabilities of the proposed algorithm.

This paper presents exact axisymmetric bending solutions of circular and annular plates based on the higher-order plate theory of Levinson. The solutions are displayed in terms of the corresponding Kirchhoff (or classical thin) plate solutions. These Kirchhoff-Levinson bending relationships are derived using the mathematical similarity of the governing equations of the two plate theories and the basis of load equivalence. The relationships allow one to readily deduce the more accurate Levinson plate solutions that account for the effect of transverse shear deformation, without having to solve the more complicated Levinson plate equations.

This technical note describes prototype development of a next generation of structural testing facility referred to here as a dynamic load simulator (DLS). The DLS simulates dynamic loading environment such as wind, waves, or earthquake effects, utilizing an electric or hydraulic actuator system instead of conventional facilities such as a wind tunnel, wave tank, or shaking table. Similitude requirements or the system capacity often preclude testing of large-scale models utilizing these facilities. In conventional test facilities continuous space-time variations of aerodynamic and hydrodynamic pressure fields and inertial loads are introduced to model the effects of wind, waves, or earthquakes. On the other hand, DLS provides discrete point loads utilizing a single- or multiactuator system to produce global dynamic load characteristics by taking into account the overall spatiotemporal correlation. A suite of typical loading protocols that includes sinusoidal, random correlated Gaussian, and non-Gaussian variations are simulated and verified experimentally utilizing single and dual actuator systems.