Journal of Engineering Mechanics

A general solution to the frictional punch problem is obtained for any shape, but the part of the punch is a straight boundary. As an example, a crack initiating from an end of the punch in an elastic half‐plane is analyzed. A rational mapping function and complex stress functions are used for the analysis. The stress distributions, the stress intensity factors and the resultant moment to keep the punch horizontal are evaluated for some Poisson's ratio and frictional coefficient. For a short crack, the effect of the frictional coefficient to the stress intensity factor is investigated.

This paper is concerned with the three‐dimensional elasticity solution of flexure and torsion in adhesive‐bonded multilayered beams of uniform cross section having one end fixed and the other end loaded by transverse forces. In the course of this analysis, stresses and deflections are obtained. Results produced in this paper are also applicable to problems of simply supported or clamped beams with a concentrated load applied at its middle span. The results of the present analysis of flexure of multilayered beams may also be used to calculate Euler's buckling load. Numerical results are presented to illustrate the distribution of shearing stresses due to transverse force and torque. Since delamination failure often occurs at the interfaces of two adjacent layers of laminated structural elements, the distribution of sharing stress in the interfaces of the layers and its intensity are of primary concern in the design of laminated composite beams.

A finite strip‐element method is presented for the analysis of thick and thin plates under transverse loading. The method combines a number of advantages of both finite strips and finite elements. The formulation results in partial uncoupling of the global equations owing to orthogonality relationships of the trigonometric functions used in the displacement approximations. This enables any number of trigonometric series terms to be taken without increasing computer storage requirements. Simply supported and clamped edge conditions are exacfly satisfied, while the free edge condition is approximately satisfied as a natural boundary condition. A selective reduced integration scheme is used to avoid locking in the fhin plate limit. Three examples are considered demonstrating the accuracy and efficiency of the method.

A comprehensive constitutive model is developed for the triaxial behavior of plain concrete. The formulation covers the full load‐response spectrum in tension as well as in compression. The concrete model is based on the nonassociated flow theory of plasticity with hardening in the prepeak regime and fracture energy‐based softening in the post‐peak regime. The constitutive development is guided by recent experimental observations on laboratory specimens which are loaded under “mixed” control in tension and in triaxial compression at different levels of lateral confinements. The constitutive parameters are calibrated from a series of stroke‐controlled laboratory experiments which include direct tension and triaxial compression tests at different confinements. The predictive quality of the fracture energy‐based plasticity model is ascertained with a number of separate load‐history experiments for which triaxial test data are available in the concrete literature. Pertinent remarks on the numerical implementation of the elastic‐plastic constitutive relations with comments on relevant issues related to the uniqueness and stability of nonassociated strain‐softening computations, are also presented.

A numerical method of elastic analysis of thin circular plates under various axisymmetric loading and support conditions is presented. The method of analysis is based on the finite‐difference procedure in the variational formulation (energy approach) and can be regarded as being equivalent to the finite‐element method. A simple computer program was developed and tested on a number of illustrative examples. In most cases the obtained results exhibited a much higher level of accuracy as compared to those obtained from the finite‐element analysis. And, most importantly, in each of the cases considered the number of unknowns involved is only half of that employed in the particular finite‐element procedure (using the simplest finite element).

A predictor‐corrector approach is presented for calculating the composite shear correction factors and analyzing multilayered composite cylinders. In the predictor phase a two‐dimensional first‐order shear deformation theory is used to predict the gross response characteristics of the cylinder (vibration frequencies, average through‐the‐thickness displacements, rotations, and transverse shear strain energy per unit area) as well as the in‐plane strains and stresses in the thickness direction. The three‐dimensional equilibrium equations and constitutive relations are then used to compute the transverse stresses and strains as well as the transverse shear factors, and they are also used to correct the predicted response quantities of the cylinder. For simply supported multilayered cylinders the response quantities obtained by using the proposed approach are shown to be in close agreement with three‐dimensional elasticity solutions for a wide range of lamination and geometric parameters. Also, the potential of the proposed approach for use in conjunction with large‐scale finite element models of composite cylinders is outlined.

The formulation of a predictive control law and its implementation in a computer control system for the seismic response of an experimental model structure is presented. Two main characteristics of the control system are emphasized: (1) The discrete‐time nature imposed by the presence of a computer in the closed loop; and (2) the existence of a time delay between the measurement and the control action. The most common way to take into account both characteristics has been to formulate a continuous‐time control law with a compensation for the time delay. In that case a discrete approximation has to be made a posteriori for computer programming. Alternatively, the predictive control proposed herein is a digital control strategy which directly yields a simple discrete‐time control algorithm for computer control of systems with time delay. Experimental results are presented to illustrate the capability of this predictive control. Its robustness in the presence of errors in the true time delay is discussed based on a comparison between experimental and numerical simulation results.

Kinetic stress for a rapidly deforming granular material is first derived. The derivation uses a simple velocity distribution model together with a mean free path concept. Complete stresses including the collisional stresses are obtained using this method. The results compare favorably with those obtained from other theories and experimental data. This model provides an alternative to the more elaborate perturbation techniques used in determining the velocity distribution function. The close agreement between the results obtained from the present model and theories which use more elaborate velocity distributions suggests that details of the velocity distribution are not as important as the correct averaging method for the computation of stresses in a rapidly deforming granular material.

Boundary conditions are formulated for planar, smooth, rapidly sheared granular flows. The formulation allows the slip at the wall to be large compared to the local mean particle fluctuation speed. In previous work by Jenkins and Richman, slip was assumed small. In order to allow for large slip and obtain tractable results, a simple approximation to the particle velocity distribution is employed in the formulation for the traction forces and energy dissipation rate at the wall. The theory is applied to the Couette flow of granular material and shown to compare well to numerical simulations, and to Jenkins and Richman in the limit of small slip.

This paper is concerned with the solution of some inverse elasticity problems of practical significance to experimental mechanics. More specifically, the boundary tractions and displacements in an elastically deformed two‐dimensional body are calculated using experimentally determined or specified displacements or strains at a finite number of internal points in the body. A brief description of what inverse problems are and why they are important is given. The finite element method is used with regularization techniques to solve the inverse deformation problems of concern here. Some illustrated numerical examples are presented to demonstrate the method. Through these examples, the effect of the error in the internal data and of the number of measurement points and their location is examined and reported. In addition, potential applications for the method are discussed.

A finite element capab?lity is described for the geometrically nonlinear analysis of arbitrarily curved sandwich panels with thick dissimilar faces. Each layer may have orthotropic properties of its own and may deform locally. Examples of bending and buckling problems are solved which illustrate the effectiveness of the proposed technique.

In 1970, Hartlen and Currie published a theory which described the transverse oscillations of a circular cylinder in a normal steady wind. This theory is used here to successfully describe the longitudinal oscillations of a rectangular cylinder with a side length ratio of 10 and standing at an angle of attack of 30% to the oncoming flow of water. This configuration is similar to that sometimes found in trashracks. The model is based on the notion that the fluctuating longitudinal force associated with vortex shedding and exciting the oscillations may be considered to arise from the action of something analogous to an oscillator in the separated flow. The model fndicates a dynamic interaction between the vortex shedding and the cylinder motion. Good agreement between measured amplitude and frequency response curves was obtained. This agreement suggests that a fundamental similarity exists in the physics of the transverse oscillations of Hartlen's and Currie's circular cylinder and the longitudinal oscillations of the rectangular cylinder investigated in the present study.

The reliability with respect to plastic collapse of rigid frame and truss structures is estimated by directional simulation. This conditional expectation simulation method is especiahy attractive for this problem because the mechanical computation for each sample is the same as the computation required in a standard Monte Carlo simulation. For each simulation a mathematical programming problem must be solved. Under suitable conditions this programming problem simplifies to a linear one. How results from methods of identifying likely plastic mechanisms can be used to establish an importance sampling whereby the sample size can be reduced without loss of accuracy is shown. Finally, it is shown how parametric sensitivity can be estimated by directional simulation.

This note summarizes several formulas for lower bounds to fundamental eigenvalues with suitable examples to illustrate their relative merits.