Journal of Engineering Mechanics

Beam‐column elements in which plastic hinges may form are commonly used for elastic‐plastic analysis of frames. The concept of a zero‐length plastic hinge (lumped plasticity) is a mathematical abstraction, because it implies infinite strains. Nevertheless, the concept is convenient computationally, and can be sufficiently accurate for many practical applications. For simple beams, plastic hinges can be introduced easily into a mathematical model. For 3D beam‐columns, however, the concept of a “generalized” hinge is needed, accounting for interaction among axial, torsional and biaxial bending effects. A theory and computational procedure based on plasticity concepts are presented. Numerical examples indicate how the element might be used, and show that results in agreement with more elaborate models can be obtained. Because the lumped plasticity assumption is not necessarily accurate, caution is advised in use of the element.

In the thin plate bending problem a formula is derived for the stress concentration at the end of a rounded notch in a clamped edge. Two different stress states in the vicinity of the notch are considered, i.e., the stress states symmetric and antisymmetric to the bisector of the notch angle. Three kinds of stress concentration at the end of the notch are investigated. It is shown that the stress concentration can be given by an infinite series expressed in terms of the radius of curvature and Williams order of stress singularity. A rational mapping function and complex stress functions are used for the analysis of the displacement boundary value problem. Examples of the stress distribution are also presented.

In typical reservoir a sediment layer of considerable depth may be deposited on top of exposed bedrock foundation. The effect of sediment on the dissipation and damping of earthquake induced hydrodynamic waves is by and large ignored in earlier studies of dam‐reservoir‐foundation system. The present work models the sediment as a poroelastic material. For vertical excitations, analytical solutions are sought with the aid of computer algebra (MACSYMA). As a result, the bottom damping coefficients are explicitly expressed as functions of material properties and earthquake frequency. For a modest amount of sediment and slight desaturation of pore water, significant changes in the hydrodynamic response curves are observed.

The elastic analysis of floor slabs using the finite element method encounters special difficulties at certain types of reentrant corners where classical plate theory predicts singular moments and shear forces. Examples are the corners of floor openings and the corner points of rectangular columns or shear cores. The nature of the stress singularities at these corners is discussed, and a family of special purpose hybrid stress plate bending elements is derived for use at these locations. These elements, which may be rectangular or L‐shaped, contain the appropriate singular moments as part of their assumed moment fields. The elements are tested on three example problems and the results are compared with those obtained using regular hybrid stress elements. Improved convergence and a better representation of the moment field are obtained with these special purpose elements. It is concluded that the more rapid convergence and additional accuracy justify the increase in computational effort.

A new method for the free‐vibration analysis using the boundary element technique is presented. The method utilizes a fictitious vector function to approximate the inertia forces and then uses the well‐known concept of complementary functions and particular integrals to solve the resulting governing differential equations. The necessary particular integrals are defined for the two and three‐dimensional analyses, and the present formulation is applied to a number of two‐dimensional problems to show its accuracy and efficiency in the solution of realistic engineering problems.

An explicit finite element model for unidirectional nonlinear dispersive waves is developed and applied to the problems of propagation and interaction of solitary waves. The proposed method uses linear chapeau functions for interpolation and is very simple to formulate and inexpensive to execute compared to most existing models. The model is sufficiently accurate so that the cumulative effect of numerical errors does not affect the results even at very long computation times. A stability and accuracy analysis of the method is presented and the limits of applicability of the method are established both analytically and by means of computational tests. The method is found to be as accurate as the best available methods and even superior in eliminating spurious oscillatory tails often found near computed solitary waves.

A comparison of Kirchoff and Reissner theories is presented for a particular case of a circular plate loaded by edge moments. The applied edge moments are taken as constant. Any number of evenly-spaced load intervals can be included. The Reissner theory is shown to be superior to the Kirchoff formulation when predicting twisting moments and shear forces.