Journal of Engineering Mechanics

This study extends the application of the Analytical Strip Method (ASM) of solution to stiffened sector plates. The plate is idealized as a system of horizontally curved plate strips and beam or rib segments rigidly connected to each other. The behavior of the system is derived by imposing the edge and continuity conditions on the closed‐form solutions of the individual plate strips and beam elements. The method is applicable to plate‐stiffener systems subjected to various loading conditions and with different boundary conditions along the straight and circular edges. The advantage of the ASM solution over the “equivalent” orthotropic plate substitute is that unequally spaced stiffeners and stiffeners of different cross‐sectional properties can be introduced in the solution. Results are presented for stiffened sectors with different edge and loading conditions.

Exact solution of reliability of structures under stochastic loadings is generally difficult. Various approximate methods have been developed based on an outcrossing rate analysis. Several first‐order and second‐order asymptotic methods are examined and compared in terms of the analytical and numerical efforts required as well as the accuracy of each method. Numerical examples are carried out, including one on the reliability of a structure with direction‐sensitive resistance under the action of vector wind force to underscore the advantage and disadvantage of each method in practical applications.

A simple incremental constitutive model for concrete materials under a general three‐dimensional quasistatic loading condition is presented. In the present formulation, the variable moduli concept is used to treat the prepeak nonlinearity, followed by the perfect plasticity concept at and beyond the peak stress to capture the dilatancy behavior of the material. The proposed model is intended for the stress states of tension‐tension, tension‐compression, and compression‐compression with a low lateral stress less than $f_c^{\prime }\text{.}$ The model predictions based on two popular failure surfaces are compared with some existing experimental results, and a good agreement is generally observed.

The nonlinear bifurcation behavior of an elastic pin‐ended strut supported laterally by a Winkler elastic foundation is studied. Attention is focused on those values of foundation stiffness at which, under axial load, the strut becomes critical with respect to two buckling modes simultaneously. A full investigation of the stability of the bifurcation points is made, and the conditions on the foundation stiffness conducive to the existence of coupled equilibrium paths are derived. The configurations and degrees of instability of the equilibrium paths, uncoupled and coupled, which branch from the critical points are found. For the most part, the bifurcation points, and the equilibrium paths which branch from them, are unstable. This suggests that the buckling load of the strut, when under compound bifurcation conditions, will be sensitive to the magnitudes of imperfections.

A boundary element formulation for thermoplastic analysis of axisymmetric bodies subjected to axisymmetric loads is developed. This formulation is implemented in a multiregion system that utilizes quadratic isoparametric shape functions to model the geometry and field variables of the boundary and domain of a body. The kernel functions are presented in an appendix and the singularities associated with these kernels are discussed. New techniques are described to calculate the coefficients associated with the singular nodes. An iterative procedure known as the initial stress algorithm is adopted for the incremental thermoplastic analysis. An advanced implementation of the algorithm includes a time‐saving feature which reduces the number of iterations needed for convergence by utilizing the past history of initial stress rates to estimate the values of the initial stress rates of the next load increment.

The endochronic theory of plasticity is modified for application to structural steel subjected to multiaxial nonproportional strainings Validity is established by comparing available experimental data with two sets of predictions by the endochronic theory (with and without modification). The modified theory appears to provide reasonably accurate prediction of the inelastic behavior of structural steel under nonproportional loading.

A simple mechanical model is developed for the dynamic response analysis of a layered soil medium. Each layer in the medium is idealized as a system of one‐dimensional vertical elastic columns interconnected by the shear springs distributed along the column. The model is applied to formulate the dynamic response of the ground and beams lying on the ground. The obtained formulation is very efficient for computation. Numerical examples are provided to demonstrate the present approach. It is found that the present m6del can adequately reproduce the dynamic behavior of a continuous foundation medium.

The present study is concerned with the membrane and bending stresses induced in a folded plate in the presence of a crack at the ridge of the folded plate. The classical method of solving dual integral equations by converting them into singular integral equations is applied for determination of stresses in a folded plate structure which is weakened by a crack. The crack is located along the ridge of the folded plate structure whose behavior is governed by the coupled set of equations pertaining to bending and stretching deformations. The presence of the crack leads to the formation of a system of dual integral equations with Cauchy kernels. These are solved numerically by applying the Chebyshev integration formula in conjunction with certain collocation techniques.

Using the finite element method, a consistent transmitting boundary is developed for the treatment of the infinite water‐sediment region in the three‐dimensional analysis of dams. The boundary can be coupled directly with the dam, water, and sediment finite elements. Applications that confirm the validity of the development and illustrate the use of the boundary are considered.

A lower bound is developed on the probability that a stationary Gaussian process exceeds a threshold during a reference period. The bound can be applied to both differentiable and non-differentiable processes. It is based on (1) a discrete time series approximation of the process; and (2) a theorem bounding the absolute value of the difference between the largest value distributions of correlated and independent stationary Gaussian series with the same marginal distributions. Several examples are considered to evaluate the usefulness of the proposed lower bound. Results suggest that the bound can be satisfactory in many engineering applications.

The definition of a corotational integral is formally introduced. Such definition is the counterpart of the definition of a corotational derivative and requires the introduction of an orthogonal tensor which corresponds to the spin entering the corotational derivative. The corotational derivatives are used to generalize the rate-form of constitutive equations from small to large deformations and rotations. Likewise, the corotational integrals substitute for the classical integrals in constitutive theories expressed in integral form, in order to extend their applicability to large deformations and rotations within an Eulerian framework. A number of existing theories such as viscoelasticity, endochronic plasticity, and functional plasticity are thus generalized by use of prope corotational integrals.