Journal of Engineering Mechanics

The theory of ponding instability of inflated imperfect spherical membranes subjected to a central load is considered. The equilibrium of the imperfect spherical cap is analyzed and the expression relating the critical central weight to the imperfection geometry and the properties of the membrane for the onset of collapse is derived. Some comparisons of the present results with experimental data (12,13) are carried out and it is concluded that imperfections in the test models (12,13) were responsible for the discrepancies between theoretical predictions and the experimental findings.

Finite element models of crack‐line wedge‐loaded, double cantilever beam (CLWL‐DCB) fracture specimens were used in their generation mode to evaluate the crack tip opening displacements (CTOD) associated with a fracture process zone preceding the macrocrack tip in such specimens. The crack tip locations of the macrocrack and the fracture process zone were determined experimentally and used as input conditions for these generation analyses. The crack opening resistance along the process zone was then adjusted to achieve consistency in the computed CTOD. This modified finite element model was then used with reasonable success in the propagation analysis of stable crack growth in concrete CLWL‐DCB fracture specimens.

This paper presents a stochastic analysis of a tapered column subjected to gravity as well as horizontal and vertical earthquake accelerations. The normal mode approach is used. The approach considers the effect of both non‐uniformity in column configuration and axial loading on mode shapes and natural frequencies. The earthquake accelerations are modeled as non‐stationary Gaussian random processes with either white or non‐white power spectra. This allows the statistical moments of column responses to be solved from a set of first order ordinary differential equations derived from the theory of Markov process. Both time histories of responses and spatial distribution of maximum responses along the elevation of the column are presented. Exact analytical sequences can be applied to handle problems of nonuniform columns.

A method is proposed for the analysis of mode I and mixed mode crack propagation in concrete. It is based on a hybrid technique which uses finite elements to represent the uncracked specimen, and distributed dislocations to represent the crack. Consequently, no remeshing of the finite elements is required after crack propagation. This method is improved and further developed to make it applicable to concrete by incorporating the nonlinear traction transfer characteristics in a crack in concrete. By incorporating expressions obtained from previous studies to represent the aggregate interlock and imperfect debonding (i.e., tensile softening) in the crack, the major sources of nonlinearity caused by cracking are accounted for. Crack propagation in a single edge notched beam, subjected to four point bending, is modeled correctly, while the predicted reduction in load corresponds satisfactorily with the experimentally obtained results.

A new sixth order technical theory for the bending of beams is presented, which includes the influence of transverse normal strain. Appropriate boundary conditions are delineated. Application to the bending of a simple beam verifies improvement over shear deformation solution.

One of the few analytical methods available for the analysis of flexure of plates with large deflections is the perturbation method, the main feature of which is the representation of a dependent variable as a power series in a constant (perturbation) parameter. In the geometrically nonlinear theory of axisymmetric circular plates, the central deflection, edge rotation, load and (1-ν), where ν is Poisson's ratio, all have been used in the role of the perturbation parameter. The asymptotic solutions thus obtained indicate the (1-ν²) is a suitable perturbation parameter for the analysis of loosely clamped circular plates with finite axisymmetric deflections. In order to demonstrate the utility of this new parameter, an analysis of a unifromly loaded circular plate with movable clamped edge is carried out. Furthermore, deviating from the usual practice of obtaining the necessary linearized equations from the nonlinear differential equations of Kirchoff's theory, the derivations make use of the energy integrals. The first two differential equations of the linear infinite system coincide with Berger's equations.